%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRA135-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 06:33:47 PM UTC 2026
% Result : Unsatisfiable 1.34s 1.51s
% Output : Proof 2.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRA135-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.14/0.32 % Computer : n022.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 23:00:22 EDT 2026
% 0.14/0.32 % CPUTime :
% 1.34/1.51 % SZS status Unsatisfiable
% 1.34/1.51 % SZS output start Proof
% 1.34/1.51 tff(b_type, type, (
% 1.34/1.51 b: ( $i * $i ) > $o)).
% 1.34/1.51 tff(s_type, type, (
% 1.34/1.51 s: $i > $i)).
% 1.34/1.51 tff(z_type, type, (
% 1.34/1.51 z: $i)).
% 1.34/1.51 tff(r_type, type, (
% 1.34/1.51 r: ( $i * $i ) > $o)).
% 1.34/1.51 tff(elem_1_type, type, (
% 1.34/1.51 elem_1: $i)).
% 1.34/1.51 tff(inj_0_type, type, (
% 1.34/1.51 inj_0: $i > $i)).
% 1.34/1.51 tff(1,assumption,(~b(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.34/1.51 tff(2,assumption,(~b(s(s(s(z))), s(z))), introduced(assumption)).
% 1.34/1.51 tff(3,assumption,(~(elem!1 = s(z))), introduced(assumption)).
% 1.34/1.51 tff(4,plain,
% 1.34/1.51 ((elem!1 = s(z)) <=> (s(z) = elem!1)),
% 1.34/1.51 inference(commutativity,[status(thm)],[])).
% 1.34/1.51 tff(5,plain,
% 1.34/1.51 ((s(z) = elem!1) <=> (elem!1 = s(z))),
% 1.34/1.51 inference(symmetry,[status(thm)],[4])).
% 1.34/1.51 tff(6,assumption,(s(z) = elem!1), introduced(assumption)).
% 1.34/1.51 tff(7,plain,
% 1.34/1.51 (elem!1 = s(z)),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[6, 5])).
% 1.34/1.51 tff(8,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[3, 7])).
% 1.34/1.51 tff(9,plain,((~(s(z) = elem!1)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(10,plain,
% 1.34/1.51 (~(s(z) = elem!1)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[9, 3])).
% 1.34/1.51 tff(11,plain,
% 1.34/1.51 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(12,plain,
% 1.34/1.51 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(13,plain,
% 1.34/1.51 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(14,axiom,(![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','sinj')).
% 1.34/1.51 tff(15,plain,
% 1.34/1.51 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[14, 13])).
% 1.34/1.51 tff(16,plain,(
% 1.34/1.51 ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.34/1.51 inference(skolemize,[status(sab)],[15])).
% 1.34/1.51 tff(17,plain,
% 1.34/1.51 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[16, 12])).
% 1.34/1.51 tff(18,plain,
% 1.34/1.51 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[17, 11])).
% 1.34/1.51 tff(19,plain,
% 1.34/1.51 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(z)) = z)),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(20,plain,
% 1.34/1.51 (inj_0(s(z)) = z),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[19, 18])).
% 1.34/1.51 tff(21,assumption,(s(s(s(z))) = s(z)), introduced(assumption)).
% 1.34/1.51 tff(22,plain,
% 1.34/1.51 (inj_0(s(s(s(z)))) = inj_0(s(z))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[21])).
% 1.34/1.51 tff(23,plain,
% 1.34/1.51 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(z)))) = s(s(z)))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(24,plain,
% 1.34/1.51 (inj_0(s(s(s(z)))) = s(s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[23, 18])).
% 1.34/1.51 tff(25,plain,
% 1.34/1.51 (s(s(z)) = inj_0(s(s(s(z))))),
% 1.34/1.51 inference(symmetry,[status(thm)],[24])).
% 1.34/1.51 tff(26,plain,
% 1.34/1.51 (s(s(z)) = z),
% 1.34/1.51 inference(transitivity,[status(thm)],[25, 22, 20])).
% 1.34/1.51 tff(27,plain,
% 1.34/1.51 (^[X: $i] : refl((~(s(X) = z)) <=> (~(s(X) = z)))),
% 1.34/1.51 inference(bind,[status(th)],[])).
% 1.34/1.51 tff(28,plain,
% 1.34/1.51 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 1.34/1.51 inference(quant_intro,[status(thm)],[27])).
% 1.34/1.51 tff(29,plain,
% 1.34/1.51 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(30,axiom,(![X: $i] : (~(s(X) = z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','snz')).
% 1.34/1.51 tff(31,plain,
% 1.34/1.51 (![X: $i] : (~(s(X) = z))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[30, 29])).
% 1.34/1.51 tff(32,plain,(
% 1.34/1.51 ![X: $i] : (~(s(X) = z))),
% 1.34/1.51 inference(skolemize,[status(sab)],[31])).
% 1.34/1.51 tff(33,plain,
% 1.34/1.51 (![X: $i] : (~(s(X) = z))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[32, 28])).
% 1.34/1.51 tff(34,plain,
% 1.34/1.51 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(z)) = z))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(35,plain,
% 1.34/1.51 (~(s(s(z)) = z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[34, 33])).
% 1.34/1.51 tff(36,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[35, 26])).
% 1.34/1.51 tff(37,plain,(~(s(s(s(z))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(38,plain,
% 1.34/1.51 (^[Y: $i, X: $i] : refl(((X = Y) | b(X, Y) | r(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 1.34/1.51 inference(bind,[status(th)],[])).
% 1.34/1.51 tff(39,plain,
% 1.34/1.51 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.34/1.51 inference(quant_intro,[status(thm)],[38])).
% 1.34/1.51 tff(40,plain,
% 1.34/1.51 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(41,plain,
% 1.34/1.51 (^[Y: $i, X: $i] : rewrite((((X = Y) | r(X, Y)) | b(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 1.34/1.51 inference(bind,[status(th)],[])).
% 1.34/1.51 tff(42,plain,
% 1.34/1.51 (![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.34/1.51 inference(quant_intro,[status(thm)],[41])).
% 1.34/1.51 tff(43,axiom,(![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rb')).
% 1.34/1.51 tff(44,plain,
% 1.34/1.51 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[43, 42])).
% 1.34/1.51 tff(45,plain,
% 1.34/1.51 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[44, 40])).
% 1.34/1.51 tff(46,plain,(
% 1.34/1.51 ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.34/1.51 inference(skolemize,[status(sab)],[45])).
% 1.34/1.51 tff(47,plain,
% 1.34/1.51 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[46, 39])).
% 1.34/1.51 tff(48,plain,
% 1.34/1.51 (((~![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)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(49,plain,
% 1.34/1.51 ((~![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)))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(50,plain,
% 1.34/1.51 ((~![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))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[49, 48])).
% 1.34/1.51 tff(51,plain,
% 1.34/1.51 ((s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[50, 47])).
% 1.34/1.51 tff(52,plain,
% 1.34/1.51 (b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[51, 37])).
% 1.34/1.51 tff(53,plain,
% 1.34/1.51 (r(s(s(s(z))), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[52, 2])).
% 1.34/1.51 tff(54,assumption,(~b(z, s(z))), introduced(assumption)).
% 1.34/1.51 tff(55,assumption,(~b(z, elem!1)), introduced(assumption)).
% 1.34/1.51 tff(56,assumption,(~r(z, elem!1)), introduced(assumption)).
% 1.34/1.51 tff(57,plain,
% 1.34/1.51 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = elem!1) | b(z, elem!1) | r(z, elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = elem!1) | b(z, elem!1) | r(z, elem!1))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(58,plain,
% 1.34/1.51 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = elem!1) | b(z, elem!1) | r(z, elem!1))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(59,plain,
% 1.34/1.51 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[58, 57])).
% 1.34/1.51 tff(60,plain,
% 1.34/1.51 ((z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[59, 47])).
% 1.34/1.51 tff(61,plain,
% 1.34/1.51 (z = elem!1),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[60, 56, 55])).
% 1.34/1.51 tff(62,plain,
% 1.34/1.51 ((s(s(s(s(s(elem!1))))) = z) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 1.34/1.51 inference(monotonicity,[status(thm)],[61])).
% 1.34/1.51 tff(63,plain,
% 1.34/1.51 ((~(s(s(s(s(s(elem!1))))) = z)) <=> (~(s(s(s(s(s(elem!1))))) = elem!1))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[62])).
% 1.34/1.51 tff(64,plain,
% 1.34/1.51 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(elem!1))))) = z))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(65,plain,
% 1.34/1.51 (~(s(s(s(s(s(elem!1))))) = z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[64, 33])).
% 1.34/1.51 tff(66,plain,
% 1.34/1.51 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[65, 63])).
% 1.34/1.51 tff(67,assumption,(elem!1 = s(s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.34/1.51 tff(68,plain,
% 1.34/1.51 (s(s(s(s(s(elem!1))))) = elem!1),
% 1.34/1.51 inference(symmetry,[status(thm)],[67])).
% 1.34/1.51 tff(69,assumption,(~(s(s(s(s(s(elem!1))))) = elem!1)), introduced(assumption)).
% 1.34/1.51 tff(70,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[69, 68])).
% 1.34/1.51 tff(71,plain,((~(elem!1 = s(s(s(s(s(elem!1))))))) | (s(s(s(s(s(elem!1))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(72,plain,
% 1.34/1.51 (~(elem!1 = s(s(s(s(s(elem!1))))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[71, 66])).
% 1.34/1.51 tff(73,plain,
% 1.34/1.51 ((s(s(s(z))) = elem!1) <=> (elem!1 = s(s(s(z))))),
% 1.34/1.51 inference(commutativity,[status(thm)],[])).
% 1.34/1.51 tff(74,plain,
% 1.34/1.51 ((elem!1 = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 1.34/1.51 inference(symmetry,[status(thm)],[73])).
% 1.34/1.51 tff(75,plain,
% 1.34/1.51 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 1.34/1.51 inference(monotonicity,[status(thm)],[61])).
% 1.34/1.51 tff(76,plain,
% 1.34/1.51 ((s(s(s(z))) = z) <=> (elem!1 = s(s(s(z))))),
% 1.34/1.51 inference(transitivity,[status(thm)],[75, 73])).
% 1.34/1.51 tff(77,plain,
% 1.34/1.51 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 1.34/1.51 inference(transitivity,[status(thm)],[76, 74])).
% 1.34/1.51 tff(78,plain,
% 1.34/1.51 ((~(s(s(s(z))) = z)) <=> (~(s(s(s(z))) = elem!1))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[77])).
% 1.34/1.51 tff(79,plain,
% 1.34/1.51 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(z))) = z))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(80,plain,
% 1.34/1.51 (~(s(s(s(z))) = z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[79, 33])).
% 1.34/1.51 tff(81,plain,
% 1.34/1.51 (~(s(s(s(z))) = elem!1)),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[80, 78])).
% 1.34/1.51 tff(82,assumption,(~b(s(s(s(s(s(elem!1))))), elem!1)), introduced(assumption)).
% 1.34/1.51 tff(83,plain,
% 1.34/1.51 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = elem!1) | b(s(s(s(s(s(elem!1))))), elem!1) | r(s(s(s(s(s(elem!1))))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = elem!1) | b(s(s(s(s(s(elem!1))))), elem!1) | r(s(s(s(s(s(elem!1))))), elem!1))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(84,plain,
% 1.34/1.51 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = elem!1) | b(s(s(s(s(s(elem!1))))), elem!1) | r(s(s(s(s(s(elem!1))))), elem!1))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(85,plain,
% 1.34/1.51 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = elem!1) | b(s(s(s(s(s(elem!1))))), elem!1) | r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[84, 83])).
% 1.34/1.51 tff(86,plain,
% 1.34/1.51 ((s(s(s(s(s(elem!1))))) = elem!1) | b(s(s(s(s(s(elem!1))))), elem!1) | r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[85, 47])).
% 1.34/1.51 tff(87,plain,
% 1.34/1.51 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[86, 82, 66])).
% 1.34/1.51 tff(88,assumption,(z = elem!1), introduced(assumption)).
% 1.34/1.51 tff(89,plain,
% 1.34/1.51 (s(z) = s(elem!1)),
% 1.34/1.51 inference(monotonicity,[status(thm)],[88])).
% 1.34/1.51 tff(90,plain,
% 1.34/1.51 (s(elem!1) = s(z)),
% 1.34/1.51 inference(symmetry,[status(thm)],[89])).
% 1.34/1.51 tff(91,plain,
% 1.34/1.51 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(elem!1))) = s(elem!1))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(92,plain,
% 1.34/1.51 (inj_0(s(s(elem!1))) = s(elem!1)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[91, 18])).
% 1.34/1.51 tff(93,plain,
% 1.34/1.51 (s(s(z)) = s(s(elem!1))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[89])).
% 1.34/1.51 tff(94,plain,
% 1.34/1.51 (s(s(elem!1)) = s(s(z))),
% 1.34/1.51 inference(symmetry,[status(thm)],[93])).
% 1.34/1.51 tff(95,plain,
% 1.34/1.51 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[94])).
% 1.34/1.51 tff(96,plain,
% 1.34/1.51 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.34/1.51 inference(symmetry,[status(thm)],[95])).
% 1.34/1.51 tff(97,assumption,(s(s(s(z))) = s(s(elem!1))), introduced(assumption)).
% 1.34/1.51 tff(98,plain,
% 1.34/1.51 (s(s(elem!1)) = s(s(s(z)))),
% 1.34/1.51 inference(symmetry,[status(thm)],[97])).
% 1.34/1.51 tff(99,plain,
% 1.34/1.51 (s(s(elem!1)) = s(s(s(elem!1)))),
% 1.34/1.51 inference(transitivity,[status(thm)],[98, 96])).
% 1.34/1.51 tff(100,plain,
% 1.34/1.51 (inj_0(s(s(elem!1))) = inj_0(s(s(s(elem!1))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[99])).
% 1.34/1.51 tff(101,plain,
% 1.34/1.51 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(elem!1)))),
% 1.34/1.51 inference(symmetry,[status(thm)],[100])).
% 1.34/1.51 tff(102,plain,
% 1.34/1.51 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(103,plain,
% 1.34/1.51 (inj_0(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[102, 18])).
% 1.34/1.51 tff(104,plain,
% 1.34/1.51 (s(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.34/1.51 inference(symmetry,[status(thm)],[103])).
% 1.34/1.51 tff(105,plain,
% 1.34/1.51 (s(s(elem!1)) = s(z)),
% 1.34/1.51 inference(transitivity,[status(thm)],[104, 101, 92, 90])).
% 1.34/1.51 tff(106,assumption,(s(s(elem!1)) = s(z)), introduced(assumption)).
% 1.34/1.51 tff(107,plain,
% 1.34/1.51 (inj_0(s(s(elem!1))) = inj_0(s(z))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[106])).
% 1.34/1.51 tff(108,plain,
% 1.34/1.51 (s(elem!1) = inj_0(s(s(elem!1)))),
% 1.34/1.51 inference(symmetry,[status(thm)],[92])).
% 1.34/1.51 tff(109,plain,
% 1.34/1.51 (s(elem!1) = z),
% 1.34/1.51 inference(transitivity,[status(thm)],[108, 107, 20])).
% 1.34/1.51 tff(110,plain,
% 1.34/1.51 ((~![X: $i] : (~(s(X) = z))) | (~(s(elem!1) = z))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(111,plain,
% 1.34/1.51 (~(s(elem!1) = z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[110, 33])).
% 1.34/1.51 tff(112,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[111, 109])).
% 1.34/1.51 tff(113,plain,(~(s(s(elem!1)) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(114,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[113, 105])).
% 1.34/1.51 tff(115,plain,((~(s(s(s(z))) = s(s(elem!1)))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(116,plain,
% 1.34/1.51 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[115, 61])).
% 1.34/1.51 tff(117,plain,
% 1.34/1.51 (s(s(z)) = s(elem!1)),
% 1.34/1.51 inference(monotonicity,[status(thm)],[6])).
% 1.34/1.51 tff(118,plain,
% 1.34/1.51 (s(s(s(z))) = s(s(elem!1))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[117])).
% 1.34/1.51 tff(119,assumption,(~(s(s(s(z))) = s(s(elem!1)))), introduced(assumption)).
% 1.34/1.51 tff(120,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[119, 118])).
% 1.34/1.51 tff(121,plain,((~(s(z) = elem!1)) | (s(s(s(z))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(122,plain,
% 1.34/1.51 (~(s(z) = elem!1)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[121, 116])).
% 1.34/1.51 tff(123,plain,
% 1.34/1.51 ((elem!1 = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 1.34/1.51 inference(commutativity,[status(thm)],[])).
% 1.34/1.51 tff(124,plain,
% 1.34/1.51 ((s(s(s(s(s(elem!1))))) = elem!1) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 1.34/1.51 inference(symmetry,[status(thm)],[123])).
% 1.34/1.51 tff(125,plain,
% 1.34/1.51 ((~(s(s(s(s(s(elem!1))))) = elem!1)) <=> (~(elem!1 = s(s(s(s(s(elem!1)))))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[124])).
% 1.34/1.51 tff(126,plain,
% 1.34/1.51 (~(elem!1 = s(s(s(s(s(elem!1))))))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[66, 125])).
% 1.34/1.51 tff(127,plain,
% 1.34/1.51 (elem!1 = z),
% 1.34/1.51 inference(symmetry,[status(thm)],[61])).
% 1.34/1.51 tff(128,plain,
% 1.34/1.51 (r(elem!1, s(s(s(s(s(elem!1)))))) <=> r(z, s(s(s(s(s(elem!1))))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[127])).
% 1.34/1.51 tff(129,plain,
% 1.34/1.51 (r(z, s(s(s(s(s(elem!1)))))) <=> r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.34/1.51 inference(symmetry,[status(thm)],[128])).
% 1.34/1.51 tff(130,plain,
% 1.34/1.51 ((~r(z, s(s(s(s(s(elem!1))))))) <=> (~r(elem!1, s(s(s(s(s(elem!1)))))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[129])).
% 1.34/1.51 tff(131,plain,
% 1.34/1.51 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[61])).
% 1.34/1.51 tff(132,plain,
% 1.34/1.51 (r(elem!1, s(s(elem!1))) <=> r(z, s(s(elem!1)))),
% 1.34/1.51 inference(symmetry,[status(thm)],[131])).
% 1.34/1.51 tff(133,plain,
% 1.34/1.51 ((elem!1 = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 1.34/1.51 inference(commutativity,[status(thm)],[])).
% 1.34/1.51 tff(134,plain,
% 1.34/1.51 ((s(s(elem!1)) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 1.34/1.51 inference(symmetry,[status(thm)],[133])).
% 1.34/1.51 tff(135,plain,
% 1.34/1.51 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 1.34/1.51 inference(monotonicity,[status(thm)],[61])).
% 1.34/1.51 tff(136,plain,
% 1.34/1.51 ((s(s(elem!1)) = z) <=> (elem!1 = s(s(elem!1)))),
% 1.34/1.51 inference(transitivity,[status(thm)],[135, 134])).
% 1.34/1.51 tff(137,plain,
% 1.34/1.51 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = s(s(elem!1))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[136])).
% 1.34/1.51 tff(138,plain,
% 1.34/1.51 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(elem!1)) = z))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(139,plain,
% 1.34/1.51 (~(s(s(elem!1)) = z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[138, 33])).
% 1.34/1.52 tff(140,plain,
% 1.34/1.52 (~(elem!1 = s(s(elem!1)))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[139, 137])).
% 1.34/1.52 tff(141,plain,
% 1.34/1.52 (s(z) = s(elem!1)),
% 1.34/1.52 inference(monotonicity,[status(thm)],[61])).
% 1.34/1.52 tff(142,plain,
% 1.34/1.52 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[141])).
% 1.34/1.52 tff(143,plain,
% 1.34/1.52 (b(z, s(z)) <=> b(elem!1, s(z))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[61])).
% 1.34/1.52 tff(144,plain,
% 1.34/1.52 (b(z, s(z)) <=> b(elem!1, s(elem!1))),
% 1.34/1.52 inference(transitivity,[status(thm)],[143, 142])).
% 1.34/1.52 tff(145,assumption,(~b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.34/1.52 tff(146,plain,
% 1.34/1.52 (b(z, s(z)) <=> b(elem!1, s(z))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[88])).
% 1.34/1.52 tff(147,plain,
% 1.34/1.52 (b(elem!1, s(z)) <=> b(z, s(z))),
% 1.34/1.52 inference(symmetry,[status(thm)],[146])).
% 1.34/1.52 tff(148,plain,
% 1.34/1.52 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 1.34/1.52 inference(monotonicity,[status(thm)],[88])).
% 1.34/1.52 tff(149,plain,
% 1.34/1.52 ((~(s(s(elem!1)) = z)) <=> (~(s(s(elem!1)) = elem!1))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[148])).
% 1.34/1.52 tff(150,plain,
% 1.34/1.52 (~(s(s(elem!1)) = elem!1)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[139, 149])).
% 1.34/1.52 tff(151,plain,
% 1.34/1.52 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 1.34/1.52 inference(monotonicity,[status(thm)],[88])).
% 1.34/1.52 tff(152,plain,
% 1.34/1.52 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), z)),
% 1.34/1.52 inference(symmetry,[status(thm)],[151])).
% 1.34/1.52 tff(153,plain,
% 1.34/1.52 (((~![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))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(154,plain,
% 1.34/1.52 ((~![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))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(155,plain,
% 1.34/1.52 ((~![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)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[154, 153])).
% 1.34/1.52 tff(156,plain,
% 1.34/1.52 ((s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[155, 47])).
% 1.34/1.52 tff(157,plain,
% 1.34/1.52 (r(s(s(elem!1)), elem!1)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[156, 145, 150])).
% 1.34/1.52 tff(158,plain,
% 1.34/1.52 (r(s(s(elem!1)), z)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[157, 152])).
% 1.34/1.52 tff(159,plain,
% 1.34/1.52 ((z = s(z)) <=> (s(z) = z)),
% 1.34/1.52 inference(commutativity,[status(thm)],[])).
% 1.34/1.52 tff(160,plain,
% 1.34/1.52 ((s(z) = z) <=> (z = s(z))),
% 1.34/1.52 inference(symmetry,[status(thm)],[159])).
% 1.34/1.52 tff(161,plain,
% 1.34/1.52 ((~(s(z) = z)) <=> (~(z = s(z)))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[160])).
% 1.34/1.52 tff(162,plain,
% 1.34/1.52 ((~![X: $i] : (~(s(X) = z))) | (~(s(z) = z))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(163,plain,
% 1.34/1.52 (~(s(z) = z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[162, 33])).
% 1.34/1.52 tff(164,plain,
% 1.34/1.52 (~(z = s(z))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[163, 161])).
% 1.34/1.52 tff(165,plain,
% 1.34/1.52 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(z)) | b(z, s(z)) | r(z, s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(z)) | b(z, s(z)) | r(z, s(z)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(166,plain,
% 1.34/1.52 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(z)) | b(z, s(z)) | r(z, s(z)))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(167,plain,
% 1.34/1.52 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[166, 165])).
% 1.34/1.52 tff(168,plain,
% 1.34/1.52 ((z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[167, 47])).
% 1.34/1.52 tff(169,plain,
% 1.34/1.52 (b(z, s(z)) | r(z, s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[168, 164])).
% 1.34/1.52 tff(170,plain,
% 1.34/1.52 (r(z, s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[169, 54])).
% 1.34/1.52 tff(171,assumption,(r(z, s(z))), introduced(assumption)).
% 1.34/1.52 tff(172,assumption,(r(s(s(elem!1)), z)), introduced(assumption)).
% 1.34/1.52 tff(173,assumption,(r(s(s(elem!1)), s(z))), introduced(assumption)).
% 1.34/1.52 tff(174,plain,
% 1.34/1.52 (^[X0: $i, X3: $i, X2: $i, X1: $i] : refl(((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1))) <=> ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1))))),
% 1.34/1.52 inference(bind,[status(th)],[])).
% 1.34/1.52 tff(175,plain,
% 1.34/1.52 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 1.34/1.52 inference(quant_intro,[status(thm)],[174])).
% 1.34/1.52 tff(176,plain,
% 1.34/1.52 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(177,plain,
% 1.34/1.52 (^[X0: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~r(X0, X1)) | (~r(X1, X2))) <=> ((~r(X1, X2)) | (~r(X0, X1)))), ((((~r(X0, X1)) | (~r(X1, X2))) | (~r(X0, X3))) <=> (((~r(X1, X2)) | (~r(X0, X1))) | (~r(X0, X3))))), rewrite((((~r(X1, X2)) | (~r(X0, X1))) | (~r(X0, X3))) <=> ((~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))), ((((~r(X0, X1)) | (~r(X1, X2))) | (~r(X0, X3))) <=> ((~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1))))), (((((~r(X0, X1)) | (~r(X1, X2))) | (~r(X0, X3))) | (~r(X1, X3))) <=> (((~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1))) | (~r(X1, X3))))), rewrite((((~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1))) | (~r(X1, X3))) <=> ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))), (((((~r(X0, X1)) | (~r(X1, X2))) | (~r(X0, X3))) | (~r(X1, X3))) <=> ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))))),
% 1.34/1.52 inference(bind,[status(th)],[])).
% 1.34/1.52 tff(178,plain,
% 1.34/1.52 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((((~r(X0, X1)) | (~r(X1, X2))) | (~r(X0, X3))) | (~r(X1, X3))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 1.34/1.52 inference(quant_intro,[status(thm)],[177])).
% 1.34/1.52 tff(179,axiom,(![X0: $i, X3: $i, X2: $i, X1: $i] : ((((~r(X0, X1)) | (~r(X1, X2))) | (~r(X0, X3))) | (~r(X1, X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axr')).
% 1.34/1.52 tff(180,plain,
% 1.34/1.52 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[179, 178])).
% 1.34/1.52 tff(181,plain,
% 1.34/1.52 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[180, 176])).
% 1.34/1.52 tff(182,plain,(
% 1.34/1.52 ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 1.34/1.52 inference(skolemize,[status(sab)],[181])).
% 1.34/1.52 tff(183,plain,
% 1.34/1.52 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[182, 175])).
% 1.34/1.52 tff(184,plain,
% 1.34/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)) | (~r(z, s(z))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(185,plain,
% 1.34/1.52 (((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)) | (~r(z, s(z))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(186,plain,
% 1.34/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)) | (~r(z, s(z)))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[185])).
% 1.34/1.52 tff(187,plain,
% 1.34/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)) | (~r(z, s(z))))),
% 1.34/1.52 inference(transitivity,[status(thm)],[186, 184])).
% 1.34/1.52 tff(188,plain,
% 1.34/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(189,plain,
% 1.34/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)) | (~r(z, s(z)))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[188, 187])).
% 1.34/1.52 tff(190,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[189, 183, 173, 172, 171])).
% 1.34/1.52 tff(191,plain,((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(192,plain,
% 1.34/1.52 (~r(s(s(elem!1)), s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[191, 170, 158])).
% 1.34/1.52 tff(193,plain,
% 1.34/1.52 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(194,plain,
% 1.34/1.52 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z)))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(195,plain,
% 1.34/1.52 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[194, 193])).
% 1.34/1.52 tff(196,plain,
% 1.34/1.52 ((s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[195, 47])).
% 1.34/1.52 tff(197,plain,
% 1.34/1.52 (b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[196, 113])).
% 1.34/1.52 tff(198,plain,
% 1.34/1.52 (b(s(s(elem!1)), s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[197, 192])).
% 1.34/1.52 tff(199,assumption,(~(s(s(elem!1)) = elem!1)), introduced(assumption)).
% 1.34/1.52 tff(200,plain,
% 1.34/1.52 (r(s(s(elem!1)), elem!1)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[156, 199, 145])).
% 1.34/1.52 tff(201,assumption,(b(s(s(elem!1)), s(z))), introduced(assumption)).
% 1.34/1.52 tff(202,assumption,(elem!1 = s(z)), introduced(assumption)).
% 1.34/1.52 tff(203,plain,
% 1.34/1.52 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(z))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[202])).
% 1.34/1.52 tff(204,plain,
% 1.34/1.52 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 1.34/1.52 inference(symmetry,[status(thm)],[203])).
% 1.34/1.52 tff(205,plain,
% 1.34/1.52 (b(s(s(elem!1)), elem!1)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[201, 204])).
% 1.34/1.52 tff(206,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[145, 205])).
% 1.34/1.52 tff(207,plain,((~(elem!1 = s(z))) | b(s(s(elem!1)), elem!1) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(208,plain,
% 1.34/1.52 (~(elem!1 = s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[207, 201, 145])).
% 1.34/1.52 tff(209,plain,
% 1.34/1.52 (~(s(z) = elem!1)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[9, 208])).
% 1.34/1.52 tff(210,assumption,(~b(elem!1, s(z))), introduced(assumption)).
% 1.34/1.52 tff(211,plain,
% 1.34/1.52 (((~![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)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(212,plain,
% 1.34/1.52 ((~![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)))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(213,plain,
% 1.34/1.52 ((~![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))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[212, 211])).
% 1.34/1.52 tff(214,plain,
% 1.34/1.52 ((elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[213, 47])).
% 1.34/1.52 tff(215,plain,
% 1.34/1.52 (r(elem!1, s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[214, 208, 210])).
% 1.34/1.52 tff(216,assumption,(r(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.34/1.52 tff(217,assumption,(r(s(z), elem!1)), introduced(assumption)).
% 1.34/1.52 tff(218,plain,
% 1.34/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(219,plain,
% 1.34/1.52 (((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(220,plain,
% 1.34/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1))))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[219])).
% 1.34/1.52 tff(221,plain,
% 1.34/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 1.34/1.52 inference(transitivity,[status(thm)],[220, 218])).
% 1.34/1.52 tff(222,plain,
% 1.34/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(223,plain,
% 1.34/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[222, 221])).
% 1.34/1.52 tff(224,plain,
% 1.34/1.52 (~r(s(z), s(s(elem!1)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[223, 183, 217, 216])).
% 1.34/1.52 tff(225,plain,
% 1.34/1.52 ((s(z) = s(s(elem!1))) <=> (s(s(elem!1)) = s(z))),
% 1.34/1.52 inference(commutativity,[status(thm)],[])).
% 1.34/1.52 tff(226,plain,
% 1.34/1.52 ((s(s(elem!1)) = s(z)) <=> (s(z) = s(s(elem!1)))),
% 1.34/1.52 inference(symmetry,[status(thm)],[225])).
% 1.34/1.52 tff(227,plain,
% 1.34/1.52 ((~(s(s(elem!1)) = s(z))) <=> (~(s(z) = s(s(elem!1))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[226])).
% 1.34/1.52 tff(228,plain,
% 1.34/1.52 (~(s(z) = s(s(elem!1)))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[113, 227])).
% 1.34/1.52 tff(229,plain,
% 1.34/1.52 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(230,plain,
% 1.34/1.52 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(231,plain,
% 1.34/1.52 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[230, 229])).
% 1.34/1.52 tff(232,plain,
% 1.34/1.52 ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[231, 47])).
% 1.34/1.52 tff(233,plain,
% 1.34/1.52 (b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[232, 228])).
% 1.34/1.52 tff(234,plain,
% 1.34/1.52 (b(s(z), s(s(elem!1)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[233, 224])).
% 1.34/1.52 tff(235,assumption,(b(s(z), s(s(elem!1)))), introduced(assumption)).
% 1.34/1.52 tff(236,assumption,(b(z, s(z))), introduced(assumption)).
% 1.34/1.52 tff(237,plain,
% 1.34/1.52 (^[X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))))),
% 1.34/1.52 inference(bind,[status(th)],[])).
% 1.34/1.52 tff(238,plain,
% 1.34/1.52 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.34/1.52 inference(quant_intro,[status(thm)],[237])).
% 1.34/1.52 tff(239,plain,
% 1.34/1.52 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(240,plain,
% 1.34/1.52 (^[X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) <=> ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) <=> (((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X2, X3))))), rewrite((((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X2, X3))) <=> ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) <=> ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))))), ((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X1, X4))) <=> (((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X1, X4))))), rewrite((((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X1, X4))) <=> ((~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), ((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X1, X4))) <=> ((~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))))), (((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X1, X4))) | (~b(X3, X4))) <=> (((~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X3, X4))))), rewrite((((~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X3, X4))) <=> ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), (((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X1, X4))) | (~b(X3, X4))) <=> ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))))),
% 1.34/1.52 inference(bind,[status(th)],[])).
% 1.34/1.52 tff(241,plain,
% 1.34/1.52 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X1, X4))) | (~b(X3, X4))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.34/1.52 inference(quant_intro,[status(thm)],[240])).
% 1.34/1.52 tff(242,axiom,(![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X1, X4))) | (~b(X3, X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axb')).
% 1.34/1.52 tff(243,plain,
% 1.34/1.52 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[242, 241])).
% 1.34/1.52 tff(244,plain,
% 1.34/1.52 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[243, 239])).
% 1.34/1.52 tff(245,plain,(
% 1.34/1.52 ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.34/1.52 inference(skolemize,[status(sab)],[244])).
% 1.34/1.52 tff(246,plain,
% 1.34/1.52 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[245, 238])).
% 1.34/1.52 tff(247,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(248,plain,
% 1.34/1.52 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(249,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1))))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[248])).
% 1.34/1.52 tff(250,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))))),
% 1.34/1.52 inference(transitivity,[status(thm)],[249, 247])).
% 1.34/1.52 tff(251,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(252,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[251, 250])).
% 1.34/1.52 tff(253,plain,
% 1.34/1.52 (~b(z, s(s(elem!1)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[252, 246, 201, 236, 235])).
% 1.34/1.52 tff(254,assumption,(z = s(s(elem!1))), introduced(assumption)).
% 1.34/1.52 tff(255,plain,
% 1.34/1.52 (s(s(elem!1)) = z),
% 1.34/1.52 inference(symmetry,[status(thm)],[254])).
% 1.34/1.52 tff(256,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[139, 255])).
% 1.34/1.52 tff(257,plain,(~(z = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(258,assumption,(~r(z, s(s(elem!1)))), introduced(assumption)).
% 1.34/1.52 tff(259,assumption,(~b(z, s(s(elem!1)))), introduced(assumption)).
% 1.34/1.52 tff(260,plain,
% 1.34/1.52 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(261,plain,
% 1.34/1.52 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(262,plain,
% 1.34/1.52 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1)))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[261, 260])).
% 1.34/1.52 tff(263,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[262, 47, 259, 258, 257])).
% 1.34/1.52 tff(264,plain,(r(z, s(s(elem!1))) | b(z, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(265,plain,
% 1.34/1.52 (r(z, s(s(elem!1)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[264, 253])).
% 1.34/1.52 tff(266,assumption,(r(z, s(s(elem!1)))), introduced(assumption)).
% 1.34/1.52 tff(267,assumption,(r(z, elem!1)), introduced(assumption)).
% 1.34/1.52 tff(268,plain,
% 1.34/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(269,plain,
% 1.34/1.52 (((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1))))) <=> ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(270,plain,
% 1.34/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1))))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[269])).
% 1.34/1.52 tff(271,plain,
% 1.34/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))),
% 1.34/1.52 inference(transitivity,[status(thm)],[270, 268])).
% 1.34/1.52 tff(272,plain,
% 1.34/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(273,plain,
% 1.34/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[272, 271])).
% 1.34/1.52 tff(274,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[273, 183, 267, 216, 266])).
% 1.34/1.52 tff(275,plain,((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(276,plain,
% 1.34/1.52 (~r(z, elem!1)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[275, 265, 216])).
% 1.34/1.52 tff(277,plain,
% 1.34/1.52 (z = elem!1),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[60, 276, 55])).
% 1.34/1.52 tff(278,plain,
% 1.34/1.52 (b(z, s(z)) <=> b(elem!1, s(z))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[277])).
% 1.34/1.52 tff(279,plain,
% 1.34/1.52 (b(elem!1, s(z)) <=> b(z, s(z))),
% 1.34/1.52 inference(symmetry,[status(thm)],[278])).
% 1.34/1.52 tff(280,plain,
% 1.34/1.52 ((~b(elem!1, s(z))) <=> (~b(z, s(z)))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[279])).
% 1.34/1.52 tff(281,plain,
% 1.34/1.52 (~b(z, s(z))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[210, 280])).
% 1.34/1.52 tff(282,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[236, 281])).
% 1.34/1.52 tff(283,plain,((~b(z, s(z))) | b(elem!1, s(z)) | b(z, elem!1) | (~r(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(284,plain,
% 1.34/1.52 (~b(z, s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[283, 234, 55, 216, 201, 210])).
% 1.34/1.52 tff(285,plain,
% 1.34/1.52 (r(z, s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[169, 284])).
% 1.34/1.52 tff(286,plain,
% 1.34/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(287,plain,
% 1.34/1.53 (((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(288,plain,
% 1.34/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z)))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[287])).
% 1.34/1.53 tff(289,plain,
% 1.34/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[288, 286])).
% 1.34/1.53 tff(290,plain,
% 1.34/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1)))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(291,plain,
% 1.34/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z)))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[290, 289])).
% 1.34/1.53 tff(292,plain,
% 1.34/1.53 ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[291, 183])).
% 1.34/1.53 tff(293,plain,
% 1.34/1.53 (~r(z, elem!1)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[292, 285, 215])).
% 1.34/1.53 tff(294,plain,
% 1.34/1.53 (z = elem!1),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[60, 293, 55])).
% 1.34/1.53 tff(295,plain,
% 1.34/1.53 (s(z) = s(elem!1)),
% 1.34/1.53 inference(monotonicity,[status(thm)],[294])).
% 1.34/1.53 tff(296,plain,
% 1.34/1.53 (s(s(z)) = s(s(elem!1))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[295])).
% 1.34/1.53 tff(297,plain,
% 1.34/1.53 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[296])).
% 1.34/1.53 tff(298,plain,
% 1.34/1.53 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.34/1.53 inference(symmetry,[status(thm)],[297])).
% 1.34/1.53 tff(299,plain,
% 1.34/1.53 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[298])).
% 1.34/1.53 tff(300,plain,
% 1.34/1.53 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.34/1.53 inference(symmetry,[status(thm)],[299])).
% 1.34/1.53 tff(301,plain,
% 1.34/1.53 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[115, 294])).
% 1.34/1.53 tff(302,plain,
% 1.34/1.53 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 1.34/1.53 inference(monotonicity,[status(thm)],[294])).
% 1.34/1.53 tff(303,plain,
% 1.34/1.53 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), z)),
% 1.34/1.53 inference(symmetry,[status(thm)],[302])).
% 1.34/1.53 tff(304,plain,
% 1.34/1.53 (r(s(s(elem!1)), z)),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[216, 303])).
% 1.34/1.53 tff(305,plain,
% 1.34/1.53 (b(s(s(s(z))), z) <=> b(s(s(s(z))), elem!1)),
% 1.34/1.53 inference(monotonicity,[status(thm)],[294])).
% 1.34/1.53 tff(306,plain,
% 1.34/1.53 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), z)),
% 1.34/1.53 inference(symmetry,[status(thm)],[305])).
% 1.34/1.53 tff(307,plain,
% 1.34/1.53 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.34/1.53 inference(monotonicity,[status(thm)],[298])).
% 1.34/1.53 tff(308,plain,
% 1.34/1.53 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), z)),
% 1.34/1.53 inference(transitivity,[status(thm)],[307, 306])).
% 1.34/1.53 tff(309,plain,
% 1.34/1.53 ((~b(s(s(s(elem!1))), elem!1)) <=> (~b(s(s(s(z))), z))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[308])).
% 1.34/1.53 tff(310,plain,
% 1.34/1.53 ((s(s(s(s(s(elem!1))))) = z) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 1.34/1.53 inference(monotonicity,[status(thm)],[294])).
% 1.34/1.53 tff(311,plain,
% 1.34/1.53 ((~(s(s(s(s(s(elem!1))))) = z)) <=> (~(s(s(s(s(s(elem!1))))) = elem!1))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[310])).
% 1.34/1.53 tff(312,plain,
% 1.34/1.53 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[65, 311])).
% 1.34/1.53 tff(313,plain,
% 1.34/1.53 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[295])).
% 1.34/1.53 tff(314,plain,
% 1.34/1.53 (b(s(s(elem!1)), s(elem!1))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[201, 313])).
% 1.34/1.53 tff(315,plain,
% 1.34/1.53 (r(s(z), elem!1) <=> r(s(elem!1), elem!1)),
% 1.34/1.53 inference(monotonicity,[status(thm)],[295])).
% 1.34/1.53 tff(316,plain,
% 1.34/1.53 (r(s(elem!1), elem!1)),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[217, 315])).
% 1.34/1.53 tff(317,plain,
% 1.34/1.53 ((s(z) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(z))),
% 1.34/1.53 inference(commutativity,[status(thm)],[])).
% 1.34/1.53 tff(318,plain,
% 1.34/1.53 ((s(elem!1) = s(s(s(s(s(elem!1)))))) <=> (s(z) = s(s(s(s(s(elem!1))))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[90])).
% 1.34/1.53 tff(319,plain,
% 1.34/1.53 ((s(elem!1) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(z))),
% 1.34/1.53 inference(transitivity,[status(thm)],[318, 317])).
% 1.34/1.53 tff(320,plain,
% 1.34/1.53 ((s(s(s(s(s(elem!1))))) = s(z)) <=> (s(elem!1) = s(s(s(s(s(elem!1))))))),
% 1.34/1.53 inference(symmetry,[status(thm)],[319])).
% 1.34/1.53 tff(321,plain,
% 1.34/1.53 ((~(s(s(s(s(s(elem!1))))) = s(z))) <=> (~(s(elem!1) = s(s(s(s(s(elem!1)))))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[320])).
% 1.34/1.53 tff(322,assumption,(s(s(s(s(s(elem!1))))) = s(z)), introduced(assumption)).
% 1.34/1.53 tff(323,plain,
% 1.34/1.53 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(z))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[322])).
% 1.34/1.53 tff(324,plain,
% 1.34/1.53 ((~![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)))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(325,plain,
% 1.34/1.53 (inj_0(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[324, 18])).
% 1.34/1.53 tff(326,plain,
% 1.34/1.53 (s(s(s(s(elem!1)))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.34/1.53 inference(symmetry,[status(thm)],[325])).
% 1.34/1.53 tff(327,plain,
% 1.34/1.53 (s(s(s(s(elem!1)))) = z),
% 1.34/1.53 inference(transitivity,[status(thm)],[326, 323, 20])).
% 1.34/1.53 tff(328,plain,
% 1.34/1.53 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(elem!1)))) = z))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(329,plain,
% 1.34/1.53 (~(s(s(s(s(elem!1)))) = z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[328, 33])).
% 1.34/1.53 tff(330,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[329, 327])).
% 1.34/1.53 tff(331,plain,(~(s(s(s(s(s(elem!1))))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(332,plain,
% 1.34/1.53 (~(s(elem!1) = s(s(s(s(s(elem!1))))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[331, 321])).
% 1.34/1.53 tff(333,assumption,(r(s(s(s(s(s(elem!1))))), elem!1)), introduced(assumption)).
% 1.34/1.53 tff(334,plain,
% 1.34/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(335,plain,
% 1.34/1.53 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(336,plain,
% 1.34/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[335])).
% 1.34/1.53 tff(337,plain,
% 1.34/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.34/1.53 inference(transitivity,[status(thm)],[336, 334])).
% 1.34/1.53 tff(338,plain,
% 1.34/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(339,plain,
% 1.34/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[338, 337])).
% 1.34/1.53 tff(340,plain,
% 1.34/1.53 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[339, 183, 216, 333])).
% 1.34/1.53 tff(341,plain,
% 1.34/1.53 (elem!1 = z),
% 1.34/1.53 inference(symmetry,[status(thm)],[88])).
% 1.34/1.53 tff(342,plain,
% 1.34/1.53 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(elem!1)) = elem!1)),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(343,plain,
% 1.34/1.53 (inj_0(s(elem!1)) = elem!1),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[342, 18])).
% 1.34/1.53 tff(344,assumption,(s(s(s(s(s(elem!1))))) = s(s(elem!1))), introduced(assumption)).
% 1.34/1.53 tff(345,plain,
% 1.34/1.53 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(elem!1)))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[344])).
% 1.34/1.53 tff(346,plain,
% 1.34/1.53 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.34/1.53 inference(symmetry,[status(thm)],[345])).
% 1.34/1.53 tff(347,plain,
% 1.34/1.53 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[108, 346, 325])).
% 1.34/1.53 tff(348,plain,
% 1.34/1.53 (inj_0(s(elem!1)) = inj_0(s(s(s(s(elem!1)))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[347])).
% 1.34/1.53 tff(349,plain,
% 1.34/1.53 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(elem!1))),
% 1.34/1.53 inference(symmetry,[status(thm)],[348])).
% 1.34/1.53 tff(350,plain,
% 1.34/1.53 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(351,plain,
% 1.34/1.53 (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[350, 18])).
% 1.34/1.53 tff(352,plain,
% 1.34/1.53 (s(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 1.34/1.53 inference(symmetry,[status(thm)],[351])).
% 1.34/1.53 tff(353,plain,
% 1.34/1.53 (s(s(s(elem!1))) = z),
% 1.34/1.53 inference(transitivity,[status(thm)],[352, 349, 343, 341])).
% 1.34/1.53 tff(354,plain,
% 1.34/1.53 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(elem!1))) = z))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(355,plain,
% 1.34/1.53 (~(s(s(s(elem!1))) = z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[354, 33])).
% 1.34/1.53 tff(356,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[355, 353])).
% 1.34/1.53 tff(357,plain,((~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(358,plain,
% 1.34/1.53 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[357, 88])).
% 1.34/1.53 tff(359,plain,
% 1.34/1.53 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(elem!1))) | b(s(s(s(s(s(elem!1))))), s(s(elem!1))) | r(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | b(s(s(s(s(s(elem!1))))), s(s(elem!1))) | r(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(360,plain,
% 1.34/1.53 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(elem!1))) | b(s(s(s(s(s(elem!1))))), s(s(elem!1))) | r(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(361,plain,
% 1.34/1.53 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | b(s(s(s(s(s(elem!1))))), s(s(elem!1))) | r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[360, 359])).
% 1.34/1.53 tff(362,plain,
% 1.34/1.53 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[361, 47, 358, 340])).
% 1.34/1.53 tff(363,assumption,(b(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 1.34/1.53 tff(364,plain,
% 1.34/1.53 (b(s(z), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[89])).
% 1.34/1.53 tff(365,plain,
% 1.34/1.53 (r(s(elem!1), s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[90])).
% 1.34/1.53 tff(366,plain,
% 1.34/1.53 ((~r(s(elem!1), s(s(elem!1)))) <=> (~r(s(z), s(s(elem!1))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[365])).
% 1.34/1.53 tff(367,assumption,(r(s(elem!1), elem!1)), introduced(assumption)).
% 1.34/1.53 tff(368,plain,
% 1.34/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(369,plain,
% 1.34/1.53 (((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(370,plain,
% 1.34/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[369])).
% 1.34/1.53 tff(371,plain,
% 1.34/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)))),
% 1.34/1.53 inference(transitivity,[status(thm)],[370, 368])).
% 1.34/1.53 tff(372,plain,
% 1.34/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(373,plain,
% 1.34/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[372, 371])).
% 1.34/1.53 tff(374,plain,
% 1.34/1.53 ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[373, 183, 216])).
% 1.34/1.53 tff(375,plain,
% 1.34/1.53 (~r(s(elem!1), s(s(elem!1)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[374, 367])).
% 1.34/1.53 tff(376,plain,
% 1.34/1.53 (~r(s(z), s(s(elem!1)))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[375, 366])).
% 1.34/1.53 tff(377,plain,
% 1.34/1.53 (b(s(z), s(s(elem!1)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[233, 376])).
% 1.34/1.53 tff(378,plain,
% 1.34/1.53 (b(s(elem!1), s(s(elem!1)))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[377, 364])).
% 1.34/1.53 tff(379,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(380,plain,
% 1.34/1.53 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(381,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1)))))))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[380])).
% 1.34/1.53 tff(382,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[381, 379])).
% 1.34/1.53 tff(383,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(384,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1)))))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[383, 382])).
% 1.34/1.53 tff(385,plain,
% 1.34/1.53 (~b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[384, 246, 378, 363, 362])).
% 1.34/1.53 tff(386,plain,
% 1.34/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(387,plain,
% 1.34/1.53 (((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(388,plain,
% 1.34/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[387])).
% 1.34/1.53 tff(389,plain,
% 1.34/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.34/1.53 inference(transitivity,[status(thm)],[388, 386])).
% 1.34/1.53 tff(390,plain,
% 1.34/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(391,plain,
% 1.34/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[390, 389])).
% 1.34/1.53 tff(392,plain,
% 1.34/1.53 (~r(s(elem!1), s(s(s(s(s(elem!1))))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[391, 183, 333, 367])).
% 1.34/1.53 tff(393,plain,
% 1.34/1.53 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(s(elem!1)))))) | b(s(elem!1), s(s(s(s(s(elem!1)))))) | r(s(elem!1), s(s(s(s(s(elem!1)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(s(elem!1)))))) | b(s(elem!1), s(s(s(s(s(elem!1)))))) | r(s(elem!1), s(s(s(s(s(elem!1)))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(394,plain,
% 1.34/1.53 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(s(elem!1)))))) | b(s(elem!1), s(s(s(s(s(elem!1)))))) | r(s(elem!1), s(s(s(s(s(elem!1)))))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(395,plain,
% 1.34/1.53 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(s(elem!1)))))) | b(s(elem!1), s(s(s(s(s(elem!1)))))) | r(s(elem!1), s(s(s(s(s(elem!1))))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[394, 393])).
% 1.34/1.53 tff(396,plain,
% 1.34/1.53 ((s(elem!1) = s(s(s(s(s(elem!1)))))) | b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[395, 47, 392])).
% 1.34/1.53 tff(397,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[396, 385, 332])).
% 1.34/1.53 tff(398,plain,((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~(z = elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(399,plain,
% 1.34/1.53 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[398, 316, 294, 216, 314])).
% 1.34/1.53 tff(400,plain,
% 1.34/1.53 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[86, 399, 312])).
% 1.34/1.53 tff(401,plain,
% 1.34/1.53 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(z))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[298])).
% 1.34/1.53 tff(402,plain,
% 1.34/1.53 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.34/1.53 inference(symmetry,[status(thm)],[401])).
% 1.34/1.53 tff(403,plain,
% 1.34/1.53 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 1.34/1.53 inference(monotonicity,[status(thm)],[294])).
% 1.34/1.53 tff(404,plain,
% 1.34/1.53 ((s(s(s(z))) = z) <=> (elem!1 = s(s(s(z))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[403, 73])).
% 1.34/1.53 tff(405,plain,
% 1.34/1.53 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = s(s(s(z)))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[404])).
% 1.34/1.53 tff(406,plain,
% 1.34/1.53 (~(elem!1 = s(s(s(z))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[80, 405])).
% 1.34/1.53 tff(407,plain,
% 1.34/1.53 (b(s(z), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[295])).
% 1.34/1.53 tff(408,plain,
% 1.34/1.53 (b(s(elem!1), s(s(elem!1)))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[234, 407])).
% 1.34/1.53 tff(409,plain,
% 1.34/1.53 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[93])).
% 1.34/1.53 tff(410,plain,
% 1.34/1.53 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.34/1.53 inference(symmetry,[status(thm)],[409])).
% 1.34/1.53 tff(411,plain,
% 1.34/1.53 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(z))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[410])).
% 1.34/1.53 tff(412,plain,
% 1.34/1.53 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.34/1.53 inference(symmetry,[status(thm)],[411])).
% 1.34/1.53 tff(413,assumption,(r(elem!1, s(s(s(z))))), introduced(assumption)).
% 1.34/1.53 tff(414,plain,
% 1.34/1.53 (r(elem!1, s(s(s(elem!1))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[413, 412])).
% 1.34/1.53 tff(415,plain,
% 1.34/1.53 (r(s(s(elem!1)), s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[409])).
% 1.34/1.53 tff(416,plain,
% 1.34/1.53 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[115, 88])).
% 1.34/1.53 tff(417,plain,
% 1.34/1.53 ((s(s(elem!1)) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 1.34/1.53 inference(commutativity,[status(thm)],[])).
% 1.34/1.53 tff(418,assumption,(s(s(elem!1)) = s(s(s(z)))), introduced(assumption)).
% 1.34/1.53 tff(419,plain,
% 1.34/1.53 (s(s(s(z))) = s(s(elem!1))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[418, 417])).
% 1.34/1.53 tff(420,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[119, 419])).
% 1.34/1.53 tff(421,plain,((~(s(s(elem!1)) = s(s(s(z))))) | (s(s(s(z))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(422,plain,
% 1.34/1.53 (~(s(s(elem!1)) = s(s(s(z))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[421, 416])).
% 1.34/1.53 tff(423,plain,
% 1.34/1.53 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[410])).
% 1.34/1.53 tff(424,plain,
% 1.34/1.53 ((~b(s(s(elem!1)), s(s(s(elem!1))))) <=> (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[423])).
% 1.34/1.53 tff(425,plain,
% 1.34/1.53 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[409, 89])).
% 1.34/1.53 tff(426,plain,
% 1.34/1.53 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[88])).
% 1.34/1.53 tff(427,plain,
% 1.34/1.53 (r(elem!1, s(s(s(z)))) <=> r(z, s(s(s(z))))),
% 1.34/1.53 inference(symmetry,[status(thm)],[426])).
% 1.34/1.53 tff(428,plain,
% 1.34/1.53 (r(z, s(s(s(z))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[413, 427])).
% 1.34/1.53 tff(429,assumption,(r(z, s(s(s(z))))), introduced(assumption)).
% 1.34/1.53 tff(430,assumption,(r(s(s(s(z))), s(z))), introduced(assumption)).
% 1.34/1.53 tff(431,plain,
% 1.34/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(432,plain,
% 1.34/1.53 (((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(433,plain,
% 1.34/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[432])).
% 1.34/1.53 tff(434,plain,
% 1.34/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[433, 431])).
% 1.34/1.53 tff(435,plain,
% 1.34/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(436,plain,
% 1.34/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[435, 434])).
% 1.34/1.53 tff(437,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[436, 183, 171, 430, 429])).
% 1.34/1.53 tff(438,plain,((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(439,plain,
% 1.34/1.53 (~r(s(s(s(z))), s(z))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[438, 428, 171])).
% 1.34/1.53 tff(440,plain,
% 1.34/1.53 (b(s(s(s(z))), s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[52, 439])).
% 1.34/1.54 tff(441,plain,
% 1.34/1.54 (b(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[440, 425])).
% 1.34/1.54 tff(442,assumption,(b(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 1.34/1.54 tff(443,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(444,plain,
% 1.34/1.54 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(445,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1)))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[444])).
% 1.34/1.54 tff(446,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[445, 443])).
% 1.34/1.54 tff(447,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(448,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[447, 446])).
% 1.34/1.54 tff(449,plain,
% 1.34/1.54 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[448, 246, 442, 363, 441])).
% 1.34/1.54 tff(450,plain,
% 1.34/1.54 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[449, 424])).
% 1.34/1.54 tff(451,plain,
% 1.34/1.54 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z)))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(452,plain,
% 1.34/1.54 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z)))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(453,plain,
% 1.34/1.54 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[452, 451])).
% 1.34/1.54 tff(454,plain,
% 1.34/1.54 ((s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[453, 47])).
% 1.34/1.54 tff(455,plain,
% 1.34/1.54 (r(s(s(elem!1)), s(s(s(z))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[454, 450, 422])).
% 1.34/1.54 tff(456,plain,
% 1.34/1.54 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[455, 415])).
% 1.34/1.54 tff(457,plain,
% 1.34/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(458,plain,
% 1.34/1.54 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(459,plain,
% 1.34/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[458])).
% 1.34/1.54 tff(460,plain,
% 1.34/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[459, 457])).
% 1.34/1.54 tff(461,plain,
% 1.34/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(462,plain,
% 1.34/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[461, 460])).
% 1.34/1.54 tff(463,plain,
% 1.34/1.54 (~r(elem!1, s(s(s(elem!1))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[462, 183, 216, 456])).
% 1.34/1.54 tff(464,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[463, 414])).
% 1.34/1.54 tff(465,plain,((~r(elem!1, s(s(s(z))))) | (~(z = elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(466,plain,
% 1.34/1.54 (~r(elem!1, s(s(s(z))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[465, 294, 216, 408, 314, 285])).
% 1.34/1.54 tff(467,plain,
% 1.34/1.54 (((~![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)))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(468,plain,
% 1.34/1.54 ((~![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)))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(469,plain,
% 1.34/1.54 ((~![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))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[468, 467])).
% 1.34/1.54 tff(470,plain,
% 1.34/1.54 ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[469, 47])).
% 1.34/1.54 tff(471,plain,
% 1.34/1.54 (b(elem!1, s(s(s(z))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[470, 466, 406])).
% 1.34/1.54 tff(472,plain,
% 1.34/1.54 (b(elem!1, s(s(s(elem!1))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[471, 402])).
% 1.34/1.54 tff(473,plain,
% 1.34/1.54 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[294])).
% 1.34/1.54 tff(474,assumption,(r(elem!1, s(z))), introduced(assumption)).
% 1.34/1.54 tff(475,plain,
% 1.34/1.54 (~r(z, elem!1)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[292, 171, 474])).
% 1.34/1.54 tff(476,plain,
% 1.34/1.54 (z = elem!1),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[60, 475, 55])).
% 1.34/1.54 tff(477,plain,
% 1.34/1.54 (s(z) = s(elem!1)),
% 1.34/1.54 inference(monotonicity,[status(thm)],[476])).
% 1.34/1.54 tff(478,plain,
% 1.34/1.54 (s(s(z)) = s(s(elem!1))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[477])).
% 1.34/1.54 tff(479,plain,
% 1.34/1.54 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[478])).
% 1.34/1.54 tff(480,plain,
% 1.34/1.54 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.34/1.54 inference(symmetry,[status(thm)],[479])).
% 1.34/1.54 tff(481,plain,
% 1.34/1.54 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.34/1.54 inference(monotonicity,[status(thm)],[480])).
% 1.34/1.54 tff(482,plain,
% 1.34/1.54 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.34/1.54 inference(symmetry,[status(thm)],[481])).
% 1.34/1.54 tff(483,plain,
% 1.34/1.54 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 1.34/1.54 inference(monotonicity,[status(thm)],[476])).
% 1.34/1.54 tff(484,plain,
% 1.34/1.54 ((s(s(s(z))) = z) <=> (elem!1 = s(s(s(z))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[483, 73])).
% 1.34/1.54 tff(485,plain,
% 1.34/1.54 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 1.34/1.54 inference(transitivity,[status(thm)],[484, 74])).
% 1.34/1.54 tff(486,plain,
% 1.34/1.54 ((~(s(s(s(z))) = z)) <=> (~(s(s(s(z))) = elem!1))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[485])).
% 1.34/1.54 tff(487,plain,
% 1.34/1.54 (~(s(s(s(z))) = elem!1)),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[80, 486])).
% 1.34/1.54 tff(488,plain,
% 1.34/1.54 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 1.34/1.54 inference(monotonicity,[status(thm)],[476])).
% 1.34/1.54 tff(489,plain,
% 1.34/1.54 ((~(s(s(elem!1)) = z)) <=> (~(s(s(elem!1)) = elem!1))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[488])).
% 1.34/1.54 tff(490,plain,
% 1.34/1.54 (~(s(s(elem!1)) = elem!1)),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[139, 489])).
% 1.34/1.54 tff(491,plain,
% 1.34/1.54 (r(s(s(elem!1)), elem!1)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[156, 490, 145])).
% 1.34/1.54 tff(492,plain,
% 1.34/1.54 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[480])).
% 1.34/1.54 tff(493,plain,
% 1.34/1.54 ((~b(s(s(s(elem!1))), s(s(elem!1)))) <=> (~b(s(s(s(z))), s(s(elem!1))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[492])).
% 1.34/1.54 tff(494,plain,
% 1.34/1.54 (s(elem!1) = s(z)),
% 1.34/1.54 inference(symmetry,[status(thm)],[477])).
% 1.34/1.54 tff(495,plain,
% 1.34/1.54 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(z))), s(z))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[480, 494])).
% 1.34/1.54 tff(496,plain,
% 1.34/1.54 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.54 inference(symmetry,[status(thm)],[495])).
% 1.34/1.54 tff(497,plain,
% 1.34/1.54 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(z))), s(z))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[480, 494])).
% 1.34/1.54 tff(498,plain,
% 1.34/1.54 ((~r(s(s(s(elem!1))), s(elem!1))) <=> (~r(s(s(s(z))), s(z)))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[497])).
% 1.34/1.54 tff(499,plain,
% 1.34/1.54 (r(elem!1, s(elem!1)) <=> r(elem!1, s(z))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[494])).
% 1.34/1.54 tff(500,plain,
% 1.34/1.54 (r(elem!1, s(z)) <=> r(elem!1, s(elem!1))),
% 1.34/1.54 inference(symmetry,[status(thm)],[499])).
% 1.34/1.54 tff(501,plain,
% 1.34/1.54 (r(elem!1, s(elem!1))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[474, 500])).
% 1.34/1.54 tff(502,assumption,(s(s(s(s(s(s(s(elem!1))))))) = s(elem!1)), introduced(assumption)).
% 1.34/1.54 tff(503,plain,
% 1.34/1.54 (inj_0(s(s(s(s(s(s(s(elem!1)))))))) = inj_0(s(elem!1))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[502])).
% 1.34/1.54 tff(504,plain,
% 1.34/1.54 ((~![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)))))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(505,plain,
% 1.34/1.54 (inj_0(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(s(s(s(elem!1))))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[504, 18])).
% 1.34/1.54 tff(506,plain,
% 1.34/1.54 (s(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(s(s(s(s(elem!1))))))))),
% 1.34/1.54 inference(symmetry,[status(thm)],[505])).
% 1.34/1.54 tff(507,plain,
% 1.34/1.54 (s(s(s(s(s(s(elem!1)))))) = z),
% 1.34/1.54 inference(transitivity,[status(thm)],[506, 503, 343, 341])).
% 1.34/1.54 tff(508,plain,
% 1.34/1.54 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(elem!1)))))) = z))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(509,plain,
% 1.34/1.54 (~(s(s(s(s(s(s(elem!1)))))) = z)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[508, 33])).
% 1.34/1.54 tff(510,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[509, 507])).
% 1.34/1.54 tff(511,plain,((~(s(s(s(s(s(s(s(elem!1))))))) = s(elem!1))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(512,plain,
% 1.34/1.54 (~(s(s(s(s(s(s(s(elem!1))))))) = s(elem!1))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[511, 476])).
% 1.34/1.54 tff(513,plain,
% 1.34/1.54 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[476])).
% 1.34/1.54 tff(514,plain,
% 1.34/1.54 (r(elem!1, s(s(elem!1)))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[266, 513])).
% 1.34/1.54 tff(515,plain,
% 1.34/1.54 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[477])).
% 1.34/1.54 tff(516,plain,
% 1.34/1.54 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 1.34/1.54 inference(monotonicity,[status(thm)],[476])).
% 1.34/1.54 tff(517,plain,
% 1.34/1.54 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), z)),
% 1.34/1.54 inference(symmetry,[status(thm)],[516])).
% 1.34/1.54 tff(518,plain,
% 1.34/1.54 ((~b(s(s(elem!1)), elem!1)) <=> (~b(s(s(elem!1)), z))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[517])).
% 1.34/1.54 tff(519,plain,
% 1.34/1.54 (~b(s(s(elem!1)), z)),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[145, 518])).
% 1.34/1.54 tff(520,plain,
% 1.34/1.54 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = z) | b(s(s(elem!1)), z) | r(s(s(elem!1)), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = z) | b(s(s(elem!1)), z) | r(s(s(elem!1)), z))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(521,plain,
% 1.34/1.54 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = z) | b(s(s(elem!1)), z) | r(s(s(elem!1)), z))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(522,plain,
% 1.34/1.54 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = z) | b(s(s(elem!1)), z) | r(s(s(elem!1)), z)),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[521, 520])).
% 1.34/1.54 tff(523,plain,
% 1.34/1.54 (b(s(s(elem!1)), z) | r(s(s(elem!1)), z)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[522, 47, 139])).
% 1.34/1.54 tff(524,plain,
% 1.34/1.54 (r(s(s(elem!1)), z)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[523, 519])).
% 1.34/1.54 tff(525,plain,
% 1.34/1.54 (~r(s(s(elem!1)), s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[191, 524, 171])).
% 1.34/1.54 tff(526,plain,
% 1.34/1.54 (b(s(s(elem!1)), s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[197, 525])).
% 1.34/1.54 tff(527,plain,
% 1.34/1.54 (b(s(s(elem!1)), s(elem!1))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[526, 515])).
% 1.34/1.54 tff(528,plain,
% 1.34/1.54 (b(s(z), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[477])).
% 1.34/1.54 tff(529,plain,
% 1.34/1.54 (r(s(elem!1), s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[494])).
% 1.34/1.54 tff(530,plain,
% 1.34/1.54 ((~r(s(elem!1), s(s(elem!1)))) <=> (~r(s(z), s(s(elem!1))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[529])).
% 1.34/1.54 tff(531,plain,
% 1.34/1.54 (elem!1 = z),
% 1.34/1.54 inference(symmetry,[status(thm)],[476])).
% 1.34/1.54 tff(532,plain,
% 1.34/1.54 (r(s(elem!1), elem!1) <=> r(s(elem!1), z)),
% 1.34/1.54 inference(monotonicity,[status(thm)],[531])).
% 1.34/1.54 tff(533,plain,
% 1.34/1.54 (r(s(elem!1), z) <=> r(s(elem!1), elem!1)),
% 1.34/1.54 inference(symmetry,[status(thm)],[532])).
% 1.34/1.54 tff(534,plain,
% 1.34/1.54 (r(s(elem!1), z) <=> r(s(z), elem!1)),
% 1.34/1.54 inference(monotonicity,[status(thm)],[494, 476])).
% 1.34/1.54 tff(535,plain,
% 1.34/1.54 (r(s(z), elem!1) <=> r(s(elem!1), z)),
% 1.34/1.54 inference(symmetry,[status(thm)],[534])).
% 1.34/1.54 tff(536,plain,
% 1.34/1.54 (r(s(elem!1), z)),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[217, 535])).
% 1.34/1.54 tff(537,plain,
% 1.34/1.54 (r(s(elem!1), elem!1)),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[536, 533])).
% 1.34/1.54 tff(538,plain,
% 1.34/1.54 ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[373, 183, 491])).
% 1.34/1.54 tff(539,plain,
% 1.34/1.54 (~r(s(elem!1), s(s(elem!1)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[538, 537])).
% 1.34/1.54 tff(540,plain,
% 1.34/1.54 (~r(s(z), s(s(elem!1)))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[539, 530])).
% 1.34/1.54 tff(541,plain,
% 1.34/1.54 (b(s(z), s(s(elem!1)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[233, 540])).
% 1.34/1.54 tff(542,plain,
% 1.34/1.54 (b(s(elem!1), s(s(elem!1)))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[541, 528])).
% 1.34/1.54 tff(543,plain,
% 1.34/1.54 ((s(s(s(s(s(elem!1))))) = z) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 1.34/1.54 inference(monotonicity,[status(thm)],[476])).
% 1.34/1.54 tff(544,plain,
% 1.34/1.54 ((~(s(s(s(s(s(elem!1))))) = z)) <=> (~(s(s(s(s(s(elem!1))))) = elem!1))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[543])).
% 1.34/1.54 tff(545,plain,
% 1.34/1.54 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[65, 544])).
% 1.34/1.54 tff(546,plain,
% 1.34/1.54 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[398, 527, 476, 491, 537])).
% 1.34/1.54 tff(547,plain,
% 1.34/1.54 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[86, 546, 545])).
% 1.34/1.54 tff(548,plain,
% 1.34/1.54 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.34/1.54 inference(monotonicity,[status(thm)],[410])).
% 1.34/1.54 tff(549,plain,
% 1.34/1.54 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.34/1.54 inference(symmetry,[status(thm)],[548])).
% 1.34/1.54 tff(550,plain,
% 1.34/1.54 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 1.34/1.54 inference(monotonicity,[status(thm)],[88])).
% 1.34/1.54 tff(551,plain,
% 1.34/1.54 ((s(s(s(z))) = z) <=> (elem!1 = s(s(s(z))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[550, 73])).
% 1.34/1.54 tff(552,plain,
% 1.34/1.54 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 1.34/1.54 inference(transitivity,[status(thm)],[551, 74])).
% 1.34/1.54 tff(553,plain,
% 1.34/1.54 ((~(s(s(s(z))) = z)) <=> (~(s(s(s(z))) = elem!1))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[552])).
% 1.34/1.54 tff(554,plain,
% 1.34/1.54 (~(s(s(s(z))) = elem!1)),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[80, 553])).
% 1.34/1.54 tff(555,plain,
% 1.34/1.54 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(z))), elem!1)),
% 1.34/1.54 inference(monotonicity,[status(thm)],[410])).
% 1.34/1.54 tff(556,plain,
% 1.34/1.54 ((~r(s(s(s(elem!1))), elem!1)) <=> (~r(s(s(s(z))), elem!1))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[555])).
% 1.34/1.54 tff(557,plain,
% 1.34/1.54 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(z))), s(z))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[410, 90])).
% 1.34/1.54 tff(558,plain,
% 1.34/1.54 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.54 inference(symmetry,[status(thm)],[557])).
% 1.34/1.54 tff(559,plain,
% 1.34/1.54 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(z))), s(z))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[410, 90])).
% 1.34/1.54 tff(560,plain,
% 1.34/1.54 ((~b(s(s(s(elem!1))), s(elem!1))) <=> (~b(s(s(s(z))), s(z)))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[559])).
% 1.34/1.54 tff(561,plain,
% 1.34/1.54 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[410])).
% 1.34/1.54 tff(562,plain,
% 1.34/1.54 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.34/1.54 inference(symmetry,[status(thm)],[561])).
% 1.34/1.54 tff(563,plain,
% 1.34/1.54 ((s(s(s(s(s(s(s(elem!1))))))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(s(s(s(elem!1))))))))),
% 1.34/1.54 inference(commutativity,[status(thm)],[])).
% 1.34/1.54 tff(564,plain,
% 1.34/1.54 ((s(s(elem!1)) = s(s(s(s(s(s(s(elem!1)))))))) <=> (s(s(s(s(s(s(s(elem!1))))))) = s(s(elem!1)))),
% 1.34/1.54 inference(symmetry,[status(thm)],[563])).
% 1.34/1.54 tff(565,plain,
% 1.34/1.54 ((~(s(s(elem!1)) = s(s(s(s(s(s(s(elem!1))))))))) <=> (~(s(s(s(s(s(s(s(elem!1))))))) = s(s(elem!1))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[564])).
% 1.34/1.54 tff(566,plain,
% 1.34/1.54 ((s(s(s(s(s(elem!1))))) = z) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 1.34/1.54 inference(monotonicity,[status(thm)],[88])).
% 1.34/1.54 tff(567,plain,
% 1.34/1.54 ((~(s(s(s(s(s(elem!1))))) = z)) <=> (~(s(s(s(s(s(elem!1))))) = elem!1))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[566])).
% 1.34/1.54 tff(568,plain,
% 1.34/1.54 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[65, 567])).
% 1.34/1.54 tff(569,assumption,(s(s(elem!1)) = s(s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 1.34/1.54 tff(570,plain,
% 1.34/1.54 (s(s(s(s(s(s(s(elem!1))))))) = s(s(elem!1))),
% 1.34/1.54 inference(symmetry,[status(thm)],[569])).
% 1.34/1.54 tff(571,plain,
% 1.34/1.54 (inj_0(s(s(s(s(s(s(s(elem!1)))))))) = inj_0(s(s(elem!1)))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[570])).
% 1.34/1.54 tff(572,plain,
% 1.34/1.54 (s(s(s(s(s(s(elem!1)))))) = s(elem!1)),
% 1.34/1.54 inference(transitivity,[status(thm)],[506, 571, 92])).
% 1.34/1.54 tff(573,plain,
% 1.34/1.54 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(elem!1))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[572])).
% 1.34/1.54 tff(574,plain,
% 1.34/1.54 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(elem!1))))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(575,plain,
% 1.34/1.54 (inj_0(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(elem!1)))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[574, 18])).
% 1.34/1.54 tff(576,plain,
% 1.34/1.54 (s(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 1.34/1.54 inference(symmetry,[status(thm)],[575])).
% 1.34/1.54 tff(577,plain,
% 1.34/1.54 (s(s(s(s(s(elem!1))))) = elem!1),
% 1.34/1.54 inference(transitivity,[status(thm)],[576, 573, 343])).
% 1.34/1.54 tff(578,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[69, 577])).
% 1.34/1.54 tff(579,plain,((~(s(s(elem!1)) = s(s(s(s(s(s(s(elem!1))))))))) | (s(s(s(s(s(elem!1))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(580,plain,
% 1.34/1.54 (~(s(s(elem!1)) = s(s(s(s(s(s(s(elem!1))))))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[579, 568])).
% 1.34/1.54 tff(581,plain,
% 1.34/1.54 (~(s(s(s(s(s(s(s(elem!1))))))) = s(s(elem!1)))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[580, 565])).
% 1.34/1.54 tff(582,assumption,(b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))), introduced(assumption)).
% 1.34/1.54 tff(583,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(584,plain,
% 1.34/1.54 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(585,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1))))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[584])).
% 1.34/1.54 tff(586,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[585, 583])).
% 1.34/1.54 tff(587,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(588,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[587, 586])).
% 1.34/1.54 tff(589,plain,
% 1.34/1.54 (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[588, 246, 442, 363, 582])).
% 1.34/1.54 tff(590,plain,
% 1.34/1.54 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(elem!1))))))) = s(s(elem!1))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1))) | r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(elem!1))))))) = s(s(elem!1))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1))) | r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(591,plain,
% 1.34/1.54 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(elem!1))))))) = s(s(elem!1))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1))) | r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(592,plain,
% 1.34/1.54 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(elem!1))))))) = s(s(elem!1))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1))) | r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[591, 590])).
% 1.34/1.54 tff(593,plain,
% 1.34/1.54 ((s(s(s(s(s(s(s(elem!1))))))) = s(s(elem!1))) | r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[592, 47, 589])).
% 1.34/1.54 tff(594,plain,
% 1.34/1.54 (r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[593, 581])).
% 1.34/1.54 tff(595,plain,
% 1.34/1.54 ((s(s(s(s(s(s(s(elem!1))))))) = elem!1) <=> (s(s(s(s(s(s(s(elem!1))))))) = z)),
% 1.34/1.54 inference(monotonicity,[status(thm)],[341])).
% 1.34/1.54 tff(596,plain,
% 1.34/1.54 ((s(s(s(s(s(s(s(elem!1))))))) = z) <=> (s(s(s(s(s(s(s(elem!1))))))) = elem!1)),
% 1.34/1.54 inference(symmetry,[status(thm)],[595])).
% 1.34/1.54 tff(597,plain,
% 1.34/1.54 ((~(s(s(s(s(s(s(s(elem!1))))))) = z)) <=> (~(s(s(s(s(s(s(s(elem!1))))))) = elem!1))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[596])).
% 1.34/1.54 tff(598,plain,
% 1.34/1.54 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(s(elem!1))))))) = z))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(599,plain,
% 1.34/1.54 (~(s(s(s(s(s(s(s(elem!1))))))) = z)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[598, 33])).
% 1.34/1.54 tff(600,plain,
% 1.34/1.54 (~(s(s(s(s(s(s(s(elem!1))))))) = elem!1)),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[599, 597])).
% 1.34/1.54 tff(601,assumption,(r(elem!1, s(elem!1))), introduced(assumption)).
% 1.34/1.54 tff(602,assumption,(r(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.34/1.54 tff(603,plain,
% 1.34/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(604,plain,
% 1.34/1.54 (((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(605,plain,
% 1.34/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[604])).
% 1.34/1.55 tff(606,plain,
% 1.34/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)))),
% 1.34/1.55 inference(transitivity,[status(thm)],[605, 603])).
% 1.34/1.55 tff(607,plain,
% 1.34/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(608,plain,
% 1.34/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[607, 606])).
% 1.34/1.55 tff(609,plain,
% 1.34/1.55 (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[608, 183, 602, 601, 594])).
% 1.34/1.55 tff(610,plain,
% 1.34/1.55 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(elem!1))))))) = elem!1) | b(s(s(s(s(s(s(s(elem!1))))))), elem!1) | r(s(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(s(elem!1))))))) = elem!1) | b(s(s(s(s(s(s(s(elem!1))))))), elem!1) | r(s(s(s(s(s(s(s(elem!1))))))), elem!1))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(611,plain,
% 1.34/1.55 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(elem!1))))))) = elem!1) | b(s(s(s(s(s(s(s(elem!1))))))), elem!1) | r(s(s(s(s(s(s(s(elem!1))))))), elem!1))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(612,plain,
% 1.34/1.55 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(elem!1))))))) = elem!1) | b(s(s(s(s(s(s(s(elem!1))))))), elem!1) | r(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[611, 610])).
% 1.34/1.55 tff(613,plain,
% 1.34/1.55 ((s(s(s(s(s(s(s(elem!1))))))) = elem!1) | b(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[612, 47, 609])).
% 1.34/1.55 tff(614,plain,
% 1.34/1.55 (b(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[613, 600])).
% 1.34/1.55 tff(615,plain,
% 1.34/1.55 ((z = s(s(s(s(s(s(s(elem!1)))))))) <=> (s(s(s(s(s(s(s(elem!1))))))) = z)),
% 1.34/1.55 inference(commutativity,[status(thm)],[])).
% 1.34/1.55 tff(616,plain,
% 1.34/1.55 ((elem!1 = s(s(s(s(s(s(s(elem!1)))))))) <=> (z = s(s(s(s(s(s(s(elem!1))))))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[341])).
% 1.34/1.55 tff(617,plain,
% 1.34/1.55 ((elem!1 = s(s(s(s(s(s(s(elem!1)))))))) <=> (s(s(s(s(s(s(s(elem!1))))))) = z)),
% 1.34/1.55 inference(transitivity,[status(thm)],[616, 615])).
% 1.34/1.55 tff(618,plain,
% 1.34/1.55 ((s(s(s(s(s(s(s(elem!1))))))) = z) <=> (elem!1 = s(s(s(s(s(s(s(elem!1))))))))),
% 1.34/1.55 inference(symmetry,[status(thm)],[617])).
% 1.34/1.55 tff(619,plain,
% 1.34/1.55 ((~(s(s(s(s(s(s(s(elem!1))))))) = z)) <=> (~(elem!1 = s(s(s(s(s(s(s(elem!1)))))))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[618])).
% 1.34/1.55 tff(620,plain,
% 1.34/1.55 (~(elem!1 = s(s(s(s(s(s(s(elem!1))))))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[599, 619])).
% 1.34/1.55 tff(621,plain,
% 1.34/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(622,plain,
% 1.34/1.55 (((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(elem!1)))))))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(623,plain,
% 1.34/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1))))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[622])).
% 1.34/1.55 tff(624,plain,
% 1.34/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[623, 621])).
% 1.34/1.55 tff(625,plain,
% 1.34/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(elem!1))))))))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(626,plain,
% 1.34/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[625, 624])).
% 1.34/1.55 tff(627,plain,
% 1.34/1.55 (~r(elem!1, s(s(s(s(s(s(s(elem!1))))))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[626, 183, 602, 594])).
% 1.34/1.55 tff(628,plain,
% 1.34/1.55 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(s(s(elem!1)))))))) | b(elem!1, s(s(s(s(s(s(s(elem!1)))))))) | r(elem!1, s(s(s(s(s(s(s(elem!1)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(s(s(s(elem!1)))))))) | b(elem!1, s(s(s(s(s(s(s(elem!1)))))))) | r(elem!1, s(s(s(s(s(s(s(elem!1)))))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(629,plain,
% 1.34/1.55 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(s(s(elem!1)))))))) | b(elem!1, s(s(s(s(s(s(s(elem!1)))))))) | r(elem!1, s(s(s(s(s(s(s(elem!1)))))))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(630,plain,
% 1.34/1.55 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(s(s(s(elem!1)))))))) | b(elem!1, s(s(s(s(s(s(s(elem!1)))))))) | r(elem!1, s(s(s(s(s(s(s(elem!1))))))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[629, 628])).
% 1.34/1.55 tff(631,plain,
% 1.34/1.55 ((elem!1 = s(s(s(s(s(s(s(elem!1)))))))) | b(elem!1, s(s(s(s(s(s(s(elem!1))))))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[630, 47, 627])).
% 1.34/1.55 tff(632,plain,
% 1.34/1.55 (b(elem!1, s(s(s(s(s(s(s(elem!1))))))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[631, 620])).
% 1.34/1.55 tff(633,assumption,(r(s(s(s(z))), s(s(elem!1)))), introduced(assumption)).
% 1.34/1.55 tff(634,assumption,(r(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.34/1.55 tff(635,plain,
% 1.34/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(636,plain,
% 1.34/1.55 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(637,plain,
% 1.34/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[636])).
% 1.34/1.55 tff(638,plain,
% 1.34/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)))),
% 1.34/1.55 inference(transitivity,[status(thm)],[637, 635])).
% 1.34/1.55 tff(639,plain,
% 1.34/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(640,plain,
% 1.34/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[639, 638])).
% 1.34/1.55 tff(641,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[640, 183, 216, 634, 633])).
% 1.34/1.55 tff(642,plain,((~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(643,plain,
% 1.34/1.55 (~r(s(s(s(z))), elem!1)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[642, 633, 216])).
% 1.34/1.55 tff(644,plain,
% 1.34/1.55 (((~![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))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(645,plain,
% 1.34/1.55 ((~![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))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(646,plain,
% 1.34/1.55 ((~![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)),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[645, 644])).
% 1.34/1.55 tff(647,plain,
% 1.34/1.55 ((s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[646, 47])).
% 1.34/1.55 tff(648,plain,
% 1.34/1.55 (b(s(s(s(z))), elem!1)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[647, 643, 554])).
% 1.34/1.55 tff(649,plain,
% 1.34/1.55 (b(s(s(s(elem!1))), elem!1)),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[648, 549])).
% 1.34/1.55 tff(650,assumption,(r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))), introduced(assumption)).
% 1.34/1.55 tff(651,plain,
% 1.34/1.55 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[410])).
% 1.34/1.55 tff(652,plain,
% 1.34/1.55 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.34/1.55 inference(symmetry,[status(thm)],[651])).
% 1.34/1.55 tff(653,plain,
% 1.34/1.55 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[633, 652])).
% 1.34/1.55 tff(654,plain,
% 1.34/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(655,plain,
% 1.34/1.55 (((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1)))))))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(656,plain,
% 1.34/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1)))))))))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[655])).
% 1.34/1.55 tff(657,plain,
% 1.34/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[656, 654])).
% 1.34/1.55 tff(658,plain,
% 1.34/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(659,plain,
% 1.34/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1)))))))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[658, 657])).
% 1.34/1.55 tff(660,plain,
% 1.34/1.55 (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[659, 183, 653, 650])).
% 1.34/1.55 tff(661,assumption,(s(s(s(elem!1))) = s(s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 1.34/1.55 tff(662,plain,
% 1.34/1.55 (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(elem!1)))),
% 1.34/1.55 inference(symmetry,[status(thm)],[661])).
% 1.34/1.55 tff(663,plain,
% 1.34/1.55 (inj_0(s(s(s(s(s(s(s(elem!1)))))))) = inj_0(s(s(s(elem!1))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[662])).
% 1.34/1.55 tff(664,plain,
% 1.34/1.55 (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))),
% 1.34/1.55 inference(transitivity,[status(thm)],[506, 663, 103])).
% 1.34/1.55 tff(665,plain,
% 1.34/1.55 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(elem!1)))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[664])).
% 1.34/1.55 tff(666,plain,
% 1.34/1.55 (s(s(s(s(s(elem!1))))) = s(z)),
% 1.34/1.55 inference(transitivity,[status(thm)],[576, 665, 92, 90])).
% 1.34/1.55 tff(667,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[331, 666])).
% 1.34/1.55 tff(668,plain,((~(s(s(s(elem!1))) = s(s(s(s(s(s(s(elem!1))))))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(669,plain,
% 1.34/1.55 (~(s(s(s(elem!1))) = s(s(s(s(s(s(s(elem!1))))))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[668, 88])).
% 1.34/1.55 tff(670,plain,
% 1.34/1.55 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1)))))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(671,plain,
% 1.34/1.55 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1)))))))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(672,plain,
% 1.34/1.55 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[671, 670])).
% 1.34/1.55 tff(673,plain,
% 1.34/1.55 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[672, 47, 669, 660])).
% 1.34/1.55 tff(674,assumption,(b(s(s(s(s(s(s(s(elem!1))))))), elem!1)), introduced(assumption)).
% 1.34/1.55 tff(675,assumption,(b(elem!1, s(s(s(s(s(s(s(elem!1))))))))), introduced(assumption)).
% 1.34/1.55 tff(676,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(677,plain,
% 1.34/1.55 (((~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(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(s(s(elem!1)))))))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(678,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(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(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[677])).
% 1.34/1.55 tff(679,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(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(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[678, 676])).
% 1.34/1.55 tff(680,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(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(s(s(elem!1))))))))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(681,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[680, 679])).
% 1.34/1.55 tff(682,plain,
% 1.34/1.55 ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1)))))))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[681, 246, 582, 675, 674])).
% 1.34/1.55 tff(683,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[682, 673, 649])).
% 1.34/1.55 tff(684,plain,((~r(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~(z = elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(685,plain,
% 1.34/1.55 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[684, 582, 632, 614, 88, 594, 216])).
% 1.34/1.55 tff(686,plain,
% 1.34/1.55 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(687,plain,
% 1.34/1.55 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(688,plain,
% 1.34/1.55 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1)))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[687, 686])).
% 1.34/1.55 tff(689,plain,
% 1.34/1.55 ((s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1)))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[688, 47])).
% 1.34/1.55 tff(690,plain,
% 1.34/1.55 (b(s(s(s(z))), s(s(elem!1)))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[689, 685, 119])).
% 1.34/1.55 tff(691,plain,
% 1.34/1.55 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[690, 562])).
% 1.34/1.55 tff(692,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(693,plain,
% 1.34/1.55 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(694,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1)))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[693])).
% 1.34/1.56 tff(695,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[694, 692])).
% 1.34/1.56 tff(696,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(697,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[696, 695])).
% 1.34/1.56 tff(698,plain,
% 1.34/1.56 ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[697, 246, 442, 363])).
% 1.34/1.56 tff(699,plain,
% 1.34/1.56 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[698, 691])).
% 1.34/1.56 tff(700,plain,
% 1.34/1.56 (~b(s(s(s(z))), s(z))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[699, 560])).
% 1.34/1.56 tff(701,plain,
% 1.34/1.56 (r(s(s(s(z))), s(z))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[52, 700])).
% 1.34/1.56 tff(702,plain,
% 1.34/1.56 (r(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[701, 558])).
% 1.34/1.56 tff(703,plain,
% 1.34/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(704,plain,
% 1.34/1.56 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(705,plain,
% 1.34/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[704])).
% 1.34/1.56 tff(706,plain,
% 1.34/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.34/1.56 inference(transitivity,[status(thm)],[705, 703])).
% 1.34/1.56 tff(707,plain,
% 1.34/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(708,plain,
% 1.34/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[707, 706])).
% 1.34/1.56 tff(709,plain,
% 1.34/1.56 ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[708, 183, 601])).
% 1.34/1.56 tff(710,plain,
% 1.34/1.56 (~r(s(s(s(elem!1))), elem!1)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[709, 702])).
% 1.34/1.56 tff(711,plain,
% 1.34/1.56 (~r(s(s(s(z))), elem!1)),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[710, 556])).
% 1.34/1.56 tff(712,plain,
% 1.34/1.56 (b(s(s(s(z))), elem!1)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[647, 711, 554])).
% 1.34/1.56 tff(713,plain,
% 1.34/1.56 (b(s(s(s(elem!1))), elem!1)),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[712, 549])).
% 1.34/1.56 tff(714,assumption,(b(s(s(s(s(s(elem!1))))), elem!1)), introduced(assumption)).
% 1.34/1.56 tff(715,plain,
% 1.34/1.56 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(z))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[410])).
% 1.34/1.56 tff(716,plain,
% 1.34/1.56 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.34/1.56 inference(symmetry,[status(thm)],[715])).
% 1.34/1.56 tff(717,plain,
% 1.34/1.56 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = s(s(s(z)))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[551])).
% 1.34/1.56 tff(718,plain,
% 1.34/1.56 (~(elem!1 = s(s(s(z))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[80, 717])).
% 1.34/1.56 tff(719,plain,
% 1.34/1.56 ((~r(elem!1, s(s(s(elem!1))))) <=> (~r(elem!1, s(s(s(z)))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[411])).
% 1.34/1.56 tff(720,plain,
% 1.34/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(721,plain,
% 1.34/1.56 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(722,plain,
% 1.34/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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)))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[721])).
% 1.34/1.56 tff(723,plain,
% 1.34/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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))))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[722, 720])).
% 1.34/1.56 tff(724,plain,
% 1.34/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(725,plain,
% 1.34/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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)))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[724, 723])).
% 1.34/1.56 tff(726,plain,
% 1.34/1.56 ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1)))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[725, 183, 601])).
% 1.34/1.56 tff(727,plain,
% 1.34/1.56 (~r(elem!1, s(s(s(elem!1))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[726, 702])).
% 1.34/1.56 tff(728,plain,
% 1.34/1.56 (~r(elem!1, s(s(s(z))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[727, 719])).
% 1.34/1.56 tff(729,plain,
% 1.34/1.56 (b(elem!1, s(s(s(z))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[470, 728, 718])).
% 1.34/1.56 tff(730,plain,
% 1.34/1.56 (b(elem!1, s(s(s(elem!1))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[729, 716])).
% 1.34/1.56 tff(731,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(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))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(732,plain,
% 1.34/1.56 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(733,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(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)))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[732])).
% 1.34/1.56 tff(734,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(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))))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[733, 731])).
% 1.34/1.56 tff(735,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(736,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(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)))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[735, 734])).
% 1.34/1.56 tff(737,plain,
% 1.34/1.56 ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[736, 246, 730, 714])).
% 1.34/1.56 tff(738,plain,
% 1.34/1.56 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[737, 713])).
% 1.34/1.56 tff(739,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(740,plain,
% 1.34/1.56 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(741,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(elem!1, s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[740])).
% 1.34/1.56 tff(742,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(elem!1, s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[741, 739])).
% 1.34/1.56 tff(743,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(744,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[743, 742])).
% 1.34/1.56 tff(745,plain,
% 1.34/1.56 ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1)))))))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[744, 246, 442, 582, 632])).
% 1.34/1.56 tff(746,plain,
% 1.34/1.56 (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[745, 730, 691])).
% 1.34/1.56 tff(747,plain,
% 1.34/1.56 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[672, 47, 669, 746])).
% 1.34/1.56 tff(748,plain,
% 1.34/1.56 ((s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(s(elem!1)))))))) <=> (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(elem!1))))))),
% 1.34/1.56 inference(commutativity,[status(thm)],[])).
% 1.34/1.56 tff(749,plain,
% 1.34/1.56 ((s(s(s(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(s(elem!1))))))))),
% 1.34/1.56 inference(symmetry,[status(thm)],[748])).
% 1.34/1.56 tff(750,plain,
% 1.34/1.56 ((~(s(s(s(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(s(elem!1)))))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[749])).
% 1.34/1.56 tff(751,assumption,(s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))), introduced(assumption)).
% 1.34/1.56 tff(752,plain,
% 1.34/1.56 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(elem!1))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[751])).
% 1.34/1.56 tff(753,plain,
% 1.34/1.56 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.34/1.56 inference(symmetry,[status(thm)],[752])).
% 1.34/1.56 tff(754,plain,
% 1.34/1.56 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[104, 753, 325])).
% 1.34/1.56 tff(755,plain,
% 1.34/1.56 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[754])).
% 1.34/1.56 tff(756,plain,
% 1.34/1.56 (s(elem!1) = s(s(s(z)))),
% 1.34/1.56 inference(transitivity,[status(thm)],[108, 755, 351, 410])).
% 1.34/1.56 tff(757,plain,
% 1.34/1.56 ((s(elem!1) = s(s(s(z)))) <=> (s(z) = s(s(s(z))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[90])).
% 1.34/1.56 tff(758,plain,
% 1.34/1.56 ((s(z) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 1.34/1.56 inference(symmetry,[status(thm)],[757])).
% 1.34/1.56 tff(759,plain,
% 1.34/1.56 ((~(s(z) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[758])).
% 1.34/1.56 tff(760,plain,
% 1.34/1.56 ((s(s(s(z))) = s(z)) <=> (s(z) = s(s(s(z))))),
% 1.34/1.56 inference(commutativity,[status(thm)],[])).
% 1.34/1.56 tff(761,plain,
% 1.34/1.56 ((s(z) = s(s(s(z)))) <=> (s(s(s(z))) = s(z))),
% 1.34/1.56 inference(symmetry,[status(thm)],[760])).
% 1.34/1.56 tff(762,assumption,(s(z) = s(s(s(z)))), introduced(assumption)).
% 1.34/1.56 tff(763,plain,
% 1.34/1.56 (s(s(s(z))) = s(z)),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[762, 761])).
% 1.34/1.56 tff(764,assumption,(~(s(s(s(z))) = s(z))), introduced(assumption)).
% 1.34/1.56 tff(765,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[764, 763])).
% 1.34/1.56 tff(766,plain,((~(s(z) = s(s(s(z))))) | (s(s(s(z))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(767,plain,
% 1.34/1.56 (~(s(z) = s(s(s(z))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[766, 37])).
% 1.34/1.56 tff(768,plain,
% 1.34/1.56 (~(s(elem!1) = s(s(s(z))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[767, 759])).
% 1.34/1.56 tff(769,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[768, 756])).
% 1.34/1.56 tff(770,plain,((~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(771,plain,
% 1.34/1.56 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[770, 88])).
% 1.34/1.56 tff(772,plain,
% 1.34/1.56 ((s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.34/1.56 inference(commutativity,[status(thm)],[])).
% 1.34/1.56 tff(773,assumption,(s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.34/1.56 tff(774,plain,
% 1.34/1.56 (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[773, 772])).
% 1.34/1.56 tff(775,assumption,(~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))), introduced(assumption)).
% 1.34/1.56 tff(776,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[775, 774])).
% 1.34/1.56 tff(777,plain,((~(s(s(s(elem!1))) = s(s(s(s(s(elem!1))))))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(778,plain,
% 1.34/1.56 (~(s(s(s(elem!1))) = s(s(s(s(s(elem!1))))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[777, 771])).
% 1.34/1.56 tff(779,assumption,(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.34/1.56 tff(780,plain,
% 1.34/1.56 (inj_0(s(s(s(s(s(s(s(elem!1)))))))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[779])).
% 1.34/1.56 tff(781,plain,
% 1.34/1.56 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[506, 780, 325])).
% 1.34/1.56 tff(782,plain,
% 1.34/1.56 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(s(s(elem!1)))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[781])).
% 1.34/1.56 tff(783,plain,
% 1.34/1.56 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 1.34/1.56 inference(symmetry,[status(thm)],[782])).
% 1.34/1.56 tff(784,plain,
% 1.34/1.56 (s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[352, 783, 575])).
% 1.34/1.56 tff(785,assumption,(~(s(s(s(elem!1))) = s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.34/1.56 tff(786,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[785, 784])).
% 1.34/1.56 tff(787,plain,((~(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(elem!1))))))) | (s(s(s(elem!1))) = s(s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(788,plain,
% 1.34/1.56 (~(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(elem!1))))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[787, 778])).
% 1.34/1.56 tff(789,plain,
% 1.34/1.56 (~(s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(s(elem!1))))))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[788, 750])).
% 1.34/1.56 tff(790,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(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(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(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(elem!1))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(791,plain,
% 1.34/1.56 (((~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(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(elem!1))))), s(s(s(s(s(s(s(elem!1)))))))))) <=> ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(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(elem!1))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(792,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(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(elem!1)))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[791])).
% 1.34/1.57 tff(793,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(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(elem!1))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[792, 790])).
% 1.34/1.57 tff(794,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(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(elem!1))))), s(s(s(s(s(s(s(elem!1))))))))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(795,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(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(elem!1)))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[794, 793])).
% 1.34/1.57 tff(796,plain,
% 1.34/1.57 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[795, 246, 714, 582, 632, 614])).
% 1.34/1.57 tff(797,plain,
% 1.34/1.57 (((~![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(s(elem!1)))))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(s(s(elem!1))))), 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(elem!1))))) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(s(elem!1)))))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(798,plain,
% 1.34/1.57 ((~![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(s(elem!1)))))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(s(elem!1)))))))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(799,plain,
% 1.34/1.57 ((~![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(s(elem!1)))))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[798, 797])).
% 1.34/1.57 tff(800,plain,
% 1.34/1.57 ((s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[799, 47, 796])).
% 1.34/1.57 tff(801,plain,
% 1.34/1.57 (r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[800, 789])).
% 1.34/1.57 tff(802,plain,
% 1.34/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(s(elem!1))))))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(803,plain,
% 1.34/1.57 (((~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(s(elem!1))))))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(804,plain,
% 1.34/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(s(elem!1)))))))))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[803])).
% 1.34/1.57 tff(805,plain,
% 1.34/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(s(elem!1))))))))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[804, 802])).
% 1.34/1.57 tff(806,plain,
% 1.34/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(807,plain,
% 1.34/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(s(elem!1)))))))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[806, 805])).
% 1.34/1.57 tff(808,plain,
% 1.34/1.57 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[807, 183, 801, 747])).
% 1.34/1.57 tff(809,plain,
% 1.34/1.57 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) | r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) | r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(810,plain,
% 1.34/1.57 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) | r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(811,plain,
% 1.34/1.57 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) | r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[810, 809])).
% 1.34/1.57 tff(812,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[811, 47, 771, 808, 738])).
% 1.34/1.57 tff(813,plain,((~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~(z = elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(814,plain,
% 1.34/1.57 (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[813, 547, 476, 542, 501, 527, 119, 491, 514])).
% 1.34/1.57 tff(815,plain,
% 1.34/1.57 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(elem!1))))))) = s(elem!1)) | b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)) | r(s(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(s(elem!1))))))) = s(elem!1)) | b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)) | r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(816,plain,
% 1.34/1.57 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(elem!1))))))) = s(elem!1)) | b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)) | r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(817,plain,
% 1.34/1.57 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(elem!1))))))) = s(elem!1)) | b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)) | r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[816, 815])).
% 1.34/1.57 tff(818,plain,
% 1.34/1.57 ((s(s(s(s(s(s(s(elem!1))))))) = s(elem!1)) | b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)) | r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[817, 47])).
% 1.34/1.57 tff(819,plain,
% 1.34/1.57 (r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[818, 814, 512])).
% 1.34/1.57 tff(820,assumption,(r(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 1.34/1.57 tff(821,assumption,(r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))), introduced(assumption)).
% 1.34/1.57 tff(822,plain,
% 1.34/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(823,plain,
% 1.34/1.57 (((~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1)))))))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(824,plain,
% 1.34/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1)))))))))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[823])).
% 1.34/1.57 tff(825,plain,
% 1.34/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[824, 822])).
% 1.34/1.57 tff(826,plain,
% 1.34/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(827,plain,
% 1.34/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1)))))))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[826, 825])).
% 1.34/1.57 tff(828,plain,
% 1.34/1.57 ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1)))))))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[827, 183, 821])).
% 1.34/1.57 tff(829,plain,
% 1.34/1.57 (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[828, 820])).
% 1.34/1.57 tff(830,plain,
% 1.34/1.57 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[672, 47, 669, 829])).
% 1.34/1.57 tff(831,plain,
% 1.34/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(832,plain,
% 1.34/1.57 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(833,plain,
% 1.34/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[832])).
% 1.34/1.57 tff(834,plain,
% 1.34/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)))),
% 1.34/1.57 inference(transitivity,[status(thm)],[833, 831])).
% 1.34/1.57 tff(835,plain,
% 1.34/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(836,plain,
% 1.34/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[835, 834])).
% 1.34/1.57 tff(837,plain,
% 1.34/1.57 (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[836, 183, 821, 601])).
% 1.34/1.57 tff(838,plain,
% 1.34/1.57 ((s(s(s(s(s(s(s(elem!1))))))) = elem!1) | b(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[612, 47, 837])).
% 1.34/1.57 tff(839,plain,
% 1.34/1.57 (b(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[838, 600])).
% 1.34/1.57 tff(840,plain,
% 1.34/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(841,plain,
% 1.34/1.57 (((~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(elem!1)))))))))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(842,plain,
% 1.34/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[841])).
% 1.34/1.57 tff(843,plain,
% 1.34/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[842, 840])).
% 1.34/1.57 tff(844,plain,
% 1.34/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(elem!1))))))))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(845,plain,
% 1.34/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[844, 843])).
% 1.34/1.57 tff(846,plain,
% 1.34/1.57 (~r(elem!1, s(s(s(s(s(s(s(elem!1))))))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[845, 183, 821, 601])).
% 1.34/1.57 tff(847,plain,
% 1.34/1.57 ((elem!1 = s(s(s(s(s(s(s(elem!1)))))))) | b(elem!1, s(s(s(s(s(s(s(elem!1))))))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[630, 47, 846])).
% 1.34/1.57 tff(848,plain,
% 1.34/1.57 (b(elem!1, s(s(s(s(s(s(s(elem!1))))))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[847, 620])).
% 1.34/1.57 tff(849,plain,
% 1.34/1.57 (~r(elem!1, s(s(s(elem!1))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[726, 820])).
% 1.34/1.57 tff(850,plain,
% 1.34/1.57 (~r(elem!1, s(s(s(z))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[849, 719])).
% 1.34/1.57 tff(851,plain,
% 1.34/1.57 (b(elem!1, s(s(s(z))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[470, 850, 718])).
% 1.34/1.57 tff(852,plain,
% 1.34/1.57 (b(elem!1, s(s(s(elem!1))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[851, 716])).
% 1.34/1.57 tff(853,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(854,plain,
% 1.34/1.57 (((~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(elem!1, s(s(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(s(s(elem!1))))))))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(855,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(elem!1, s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[854])).
% 1.34/1.57 tff(856,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(elem!1, s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)))),
% 1.34/1.57 inference(transitivity,[status(thm)],[855, 853])).
% 1.34/1.57 tff(857,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(858,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[857, 856])).
% 1.34/1.57 tff(859,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[858, 246, 852, 848, 839, 830])).
% 1.34/1.57 tff(860,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~(z = elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(861,plain,
% 1.34/1.57 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[860, 476, 819, 501])).
% 1.34/1.57 tff(862,plain,
% 1.34/1.57 (~r(s(s(s(z))), s(z))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[861, 498])).
% 1.34/1.57 tff(863,plain,
% 1.34/1.57 (b(s(s(s(z))), s(z))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[52, 862])).
% 1.34/1.57 tff(864,plain,
% 1.34/1.57 (b(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[863, 496])).
% 1.34/1.57 tff(865,plain,
% 1.34/1.57 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(866,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1)))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[865])).
% 1.34/1.57 tff(867,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[866, 692])).
% 1.34/1.57 tff(868,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(869,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[868, 867])).
% 1.34/1.57 tff(870,plain,
% 1.34/1.57 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[869, 246, 542, 527, 864])).
% 1.34/1.57 tff(871,plain,
% 1.34/1.57 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[870, 493])).
% 1.34/1.57 tff(872,plain,
% 1.34/1.57 (r(s(s(s(z))), s(s(elem!1)))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[689, 871, 119])).
% 1.34/1.57 tff(873,plain,
% 1.34/1.57 (~r(s(s(s(z))), elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[642, 872, 491])).
% 1.34/1.57 tff(874,plain,
% 1.34/1.57 (b(s(s(s(z))), elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[647, 873, 487])).
% 1.34/1.58 tff(875,plain,
% 1.34/1.58 (b(s(s(s(elem!1))), elem!1)),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[874, 482])).
% 1.34/1.58 tff(876,plain,
% 1.34/1.58 ((s(s(s(s(s(s(s(elem!1))))))) = elem!1) <=> (s(s(s(s(s(s(s(elem!1))))))) = z)),
% 1.34/1.58 inference(monotonicity,[status(thm)],[531])).
% 1.34/1.58 tff(877,plain,
% 1.34/1.58 ((s(s(s(s(s(s(s(elem!1))))))) = z) <=> (s(s(s(s(s(s(s(elem!1))))))) = elem!1)),
% 1.34/1.58 inference(symmetry,[status(thm)],[876])).
% 1.34/1.58 tff(878,plain,
% 1.34/1.58 ((~(s(s(s(s(s(s(s(elem!1))))))) = z)) <=> (~(s(s(s(s(s(s(s(elem!1))))))) = elem!1))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[877])).
% 1.34/1.58 tff(879,plain,
% 1.34/1.58 (~(s(s(s(s(s(s(s(elem!1))))))) = elem!1)),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[599, 878])).
% 1.34/1.58 tff(880,plain,
% 1.34/1.58 (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[836, 183, 819, 501])).
% 1.34/1.58 tff(881,plain,
% 1.34/1.58 ((s(s(s(s(s(s(s(elem!1))))))) = elem!1) | b(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[612, 47, 880])).
% 1.34/1.58 tff(882,plain,
% 1.34/1.58 (b(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[881, 879])).
% 1.34/1.58 tff(883,plain,
% 1.34/1.58 ((elem!1 = s(s(s(s(s(s(s(elem!1)))))))) <=> (z = s(s(s(s(s(s(s(elem!1))))))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[531])).
% 1.34/1.58 tff(884,plain,
% 1.34/1.58 ((elem!1 = s(s(s(s(s(s(s(elem!1)))))))) <=> (s(s(s(s(s(s(s(elem!1))))))) = z)),
% 1.34/1.58 inference(transitivity,[status(thm)],[883, 615])).
% 1.34/1.58 tff(885,plain,
% 1.34/1.58 ((s(s(s(s(s(s(s(elem!1))))))) = z) <=> (elem!1 = s(s(s(s(s(s(s(elem!1))))))))),
% 1.34/1.58 inference(symmetry,[status(thm)],[884])).
% 1.34/1.58 tff(886,plain,
% 1.34/1.58 ((~(s(s(s(s(s(s(s(elem!1))))))) = z)) <=> (~(elem!1 = s(s(s(s(s(s(s(elem!1)))))))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[885])).
% 1.34/1.58 tff(887,plain,
% 1.34/1.58 (~(elem!1 = s(s(s(s(s(s(s(elem!1))))))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[599, 886])).
% 1.34/1.58 tff(888,plain,
% 1.34/1.58 (~r(elem!1, s(s(s(s(s(s(s(elem!1))))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[845, 183, 819, 501])).
% 1.34/1.58 tff(889,plain,
% 1.34/1.58 ((elem!1 = s(s(s(s(s(s(s(elem!1)))))))) | b(elem!1, s(s(s(s(s(s(s(elem!1))))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[630, 47, 888])).
% 1.34/1.58 tff(890,plain,
% 1.34/1.58 (b(elem!1, s(s(s(s(s(s(s(elem!1))))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[889, 887])).
% 1.34/1.58 tff(891,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(892,plain,
% 1.34/1.58 (((~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(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(s(s(elem!1)))))))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(893,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(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(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[892])).
% 1.34/1.58 tff(894,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(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(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)))),
% 1.34/1.58 inference(transitivity,[status(thm)],[893, 891])).
% 1.34/1.58 tff(895,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(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(s(s(elem!1))))))))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(896,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[895, 894])).
% 1.34/1.58 tff(897,plain,
% 1.34/1.58 ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1)))))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[896, 246, 890, 882])).
% 1.34/1.58 tff(898,plain,
% 1.34/1.58 (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[897, 875])).
% 1.34/1.58 tff(899,plain,
% 1.34/1.58 (~(s(s(s(elem!1))) = s(s(s(s(s(s(s(elem!1))))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[668, 476])).
% 1.34/1.58 tff(900,plain,
% 1.34/1.58 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[672, 47, 899, 898])).
% 1.34/1.58 tff(901,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(902,plain,
% 1.34/1.58 (((~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(903,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[902])).
% 1.34/1.58 tff(904,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)))),
% 1.34/1.58 inference(transitivity,[status(thm)],[903, 901])).
% 1.34/1.58 tff(905,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(906,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[905, 904])).
% 1.34/1.58 tff(907,plain,
% 1.34/1.58 ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[906, 246, 547, 890, 882])).
% 1.34/1.58 tff(908,plain,
% 1.34/1.58 (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[907, 875])).
% 1.34/1.58 tff(909,plain,
% 1.34/1.58 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[770, 476])).
% 1.34/1.58 tff(910,plain,
% 1.34/1.58 (~(s(s(s(elem!1))) = s(s(s(s(s(elem!1))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[777, 909])).
% 1.34/1.58 tff(911,plain,
% 1.34/1.58 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))) | r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))) | r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(912,plain,
% 1.34/1.58 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))) | r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(913,plain,
% 1.34/1.58 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))) | r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[912, 911])).
% 1.34/1.58 tff(914,plain,
% 1.34/1.58 (r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[913, 47, 910, 908])).
% 1.34/1.58 tff(915,plain,
% 1.34/1.58 (~(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(elem!1))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[787, 910])).
% 1.34/1.58 tff(916,plain,
% 1.34/1.58 (~(s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(s(elem!1))))))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[915, 750])).
% 1.34/1.58 tff(917,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(s(elem!1))))))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(918,plain,
% 1.34/1.58 (((~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(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(elem!1))))), s(s(s(s(s(s(s(elem!1)))))))))) <=> ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(s(elem!1))))))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(919,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(s(elem!1)))))))))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[918])).
% 1.34/1.58 tff(920,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(s(elem!1))))))))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[919, 917])).
% 1.34/1.58 tff(921,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(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(elem!1))))), s(s(s(s(s(s(s(elem!1))))))))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(922,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(s(elem!1)))))))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[921, 920])).
% 1.34/1.58 tff(923,plain,
% 1.34/1.58 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[922, 246, 547, 890, 882])).
% 1.34/1.58 tff(924,plain,
% 1.34/1.58 ((s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[799, 47, 923])).
% 1.34/1.58 tff(925,plain,
% 1.34/1.58 (r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[924, 916])).
% 1.34/1.58 tff(926,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(927,plain,
% 1.34/1.58 (((~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(928,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[927])).
% 1.34/1.58 tff(929,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)))),
% 1.34/1.58 inference(transitivity,[status(thm)],[928, 926])).
% 1.34/1.58 tff(930,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(931,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[930, 929])).
% 1.34/1.58 tff(932,plain,
% 1.34/1.58 ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[931, 246, 547, 890, 882])).
% 1.34/1.58 tff(933,plain,
% 1.34/1.58 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[932, 875])).
% 1.34/1.58 tff(934,plain,
% 1.34/1.58 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[811, 47, 909, 933])).
% 1.34/1.58 tff(935,plain,
% 1.34/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(936,plain,
% 1.34/1.58 (((~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(937,plain,
% 1.34/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[936])).
% 1.34/1.58 tff(938,plain,
% 1.34/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[937, 935])).
% 1.34/1.58 tff(939,plain,
% 1.34/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(940,plain,
% 1.34/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[939, 938])).
% 1.34/1.58 tff(941,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[940, 183, 934, 925, 914, 900])).
% 1.34/1.58 tff(942,plain,((~r(z, s(z))) | (s(s(s(z))) = s(s(elem!1))) | (~r(elem!1, s(z))) | b(s(s(elem!1)), elem!1) | (~r(s(z), elem!1)) | (~r(z, s(s(elem!1)))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(943,plain,
% 1.34/1.58 (~r(z, s(s(elem!1)))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[942, 301, 145, 215, 217, 285, 55])).
% 1.34/1.58 tff(944,plain,
% 1.34/1.58 (b(z, s(s(elem!1)))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[264, 943])).
% 1.34/1.58 tff(945,plain,
% 1.34/1.58 (b(elem!1, s(s(elem!1)))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[944, 473])).
% 1.34/1.58 tff(946,assumption,(b(s(s(s(s(s(elem!1))))), s(s(elem!1)))), introduced(assumption)).
% 1.34/1.58 tff(947,assumption,(b(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.34/1.58 tff(948,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(949,plain,
% 1.34/1.58 (((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(950,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[949])).
% 1.34/1.59 tff(951,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.34/1.59 inference(transitivity,[status(thm)],[950, 948])).
% 1.34/1.59 tff(952,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(953,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[952, 951])).
% 1.34/1.59 tff(954,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[953, 246, 947, 442, 363, 714, 946])).
% 1.34/1.59 tff(955,plain,((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(956,plain,
% 1.34/1.59 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[955, 945, 408, 314, 400])).
% 1.34/1.59 tff(957,plain,
% 1.34/1.59 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[357, 294])).
% 1.34/1.59 tff(958,plain,
% 1.34/1.59 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[361, 47, 957, 956])).
% 1.34/1.59 tff(959,assumption,(r(s(s(s(s(s(elem!1))))), s(s(elem!1)))), introduced(assumption)).
% 1.34/1.59 tff(960,assumption,(b(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.34/1.59 tff(961,assumption,(b(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.34/1.59 tff(962,plain,
% 1.34/1.59 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.34/1.59 inference(symmetry,[status(thm)],[423])).
% 1.34/1.59 tff(963,assumption,(b(s(s(elem!1)), s(s(s(z))))), introduced(assumption)).
% 1.34/1.59 tff(964,plain,
% 1.34/1.59 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[963, 962])).
% 1.34/1.59 tff(965,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(966,plain,
% 1.34/1.59 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(967,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[966])).
% 1.34/1.59 tff(968,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[967, 965])).
% 1.34/1.59 tff(969,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(970,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[969, 968])).
% 1.34/1.59 tff(971,plain,
% 1.34/1.59 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[970, 246, 947, 960, 961])).
% 1.34/1.59 tff(972,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[971, 964])).
% 1.34/1.59 tff(973,plain,((~b(s(s(elem!1)), s(s(s(z))))) | (~(z = elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(974,plain,
% 1.34/1.59 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[973, 961, 947, 960, 88])).
% 1.34/1.59 tff(975,plain,
% 1.34/1.59 (r(s(s(elem!1)), s(s(s(z))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[454, 974, 422])).
% 1.34/1.59 tff(976,plain,
% 1.34/1.59 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[975, 415])).
% 1.34/1.59 tff(977,plain,
% 1.34/1.59 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[736, 246, 960, 714, 961])).
% 1.34/1.59 tff(978,plain,
% 1.34/1.59 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[811, 47, 771, 977])).
% 1.34/1.59 tff(979,plain,
% 1.34/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(980,plain,
% 1.34/1.59 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(981,plain,
% 1.34/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[980])).
% 1.34/1.59 tff(982,plain,
% 1.34/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[981, 979])).
% 1.34/1.59 tff(983,plain,
% 1.34/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(984,plain,
% 1.34/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[983, 982])).
% 1.34/1.59 tff(985,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[984, 183, 216, 978, 976, 959])).
% 1.34/1.59 tff(986,plain,((~b(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~(z = elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(987,plain,
% 1.34/1.59 (~b(s(s(s(elem!1))), elem!1)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[986, 958, 216, 294, 945, 472, 400])).
% 1.34/1.59 tff(988,plain,
% 1.34/1.59 (~b(s(s(s(z))), z)),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[987, 309])).
% 1.34/1.59 tff(989,assumption,(~b(s(s(s(z))), z)), introduced(assumption)).
% 1.34/1.59 tff(990,assumption,(~r(s(s(s(z))), z)), introduced(assumption)).
% 1.34/1.59 tff(991,plain,
% 1.34/1.59 (((~![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))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(992,plain,
% 1.34/1.59 ((~![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))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(993,plain,
% 1.34/1.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z)),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[992, 991])).
% 1.34/1.59 tff(994,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[993, 47, 80, 990, 989])).
% 1.34/1.59 tff(995,plain,(r(s(s(s(z))), z) | b(s(s(s(z))), z)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(996,plain,
% 1.34/1.59 (r(s(s(s(z))), z)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[995, 988])).
% 1.34/1.59 tff(997,assumption,(r(s(s(s(z))), z)), introduced(assumption)).
% 1.34/1.59 tff(998,plain,
% 1.34/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(999,plain,
% 1.34/1.59 (((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1000,plain,
% 1.34/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[999])).
% 1.34/1.59 tff(1001,plain,
% 1.34/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 1.34/1.59 inference(transitivity,[status(thm)],[1000, 998])).
% 1.34/1.59 tff(1002,plain,
% 1.34/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(1003,plain,
% 1.34/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1002, 1001])).
% 1.34/1.59 tff(1004,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1003, 183, 216, 172, 633, 997])).
% 1.34/1.59 tff(1005,plain,((~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(1006,plain,
% 1.34/1.59 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1005, 996, 304, 216])).
% 1.34/1.59 tff(1007,plain,
% 1.34/1.59 (b(s(s(s(z))), s(s(elem!1)))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[689, 1006, 301])).
% 1.34/1.59 tff(1008,plain,
% 1.34/1.59 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1007, 300])).
% 1.34/1.59 tff(1009,plain,
% 1.34/1.59 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[297, 295])).
% 1.34/1.59 tff(1010,plain,
% 1.34/1.59 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 1.34/1.59 inference(transitivity,[status(thm)],[404, 74])).
% 1.34/1.59 tff(1011,plain,
% 1.34/1.59 ((~(s(s(s(z))) = z)) <=> (~(s(s(s(z))) = elem!1))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[1010])).
% 1.34/1.59 tff(1012,plain,
% 1.34/1.59 (~(s(s(s(z))) = elem!1)),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[80, 1011])).
% 1.34/1.59 tff(1013,plain,
% 1.34/1.59 ((~b(s(s(s(elem!1))), elem!1)) <=> (~b(s(s(s(z))), elem!1))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[307])).
% 1.34/1.59 tff(1014,plain,
% 1.34/1.59 (~b(s(s(s(z))), elem!1)),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[987, 1013])).
% 1.34/1.59 tff(1015,plain,
% 1.34/1.59 (r(s(s(s(z))), elem!1)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[647, 1014, 1012])).
% 1.34/1.59 tff(1016,plain,
% 1.34/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1017,plain,
% 1.34/1.59 (((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1018,plain,
% 1.34/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[1017])).
% 1.34/1.59 tff(1019,plain,
% 1.34/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[1018, 1016])).
% 1.34/1.59 tff(1020,plain,
% 1.34/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(1021,plain,
% 1.34/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1020, 1019])).
% 1.34/1.59 tff(1022,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1021, 183, 474, 634, 430])).
% 1.34/1.59 tff(1023,plain,((~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(1024,plain,
% 1.34/1.59 (~r(s(s(s(z))), s(z))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1023, 1015, 215])).
% 1.34/1.59 tff(1025,plain,
% 1.34/1.59 (b(s(s(s(z))), s(z))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[52, 1024])).
% 1.34/1.59 tff(1026,plain,
% 1.34/1.59 (b(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1025, 1009])).
% 1.34/1.59 tff(1027,plain,
% 1.34/1.59 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[697, 246, 408, 314, 1026])).
% 1.34/1.59 tff(1028,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1027, 1008])).
% 1.34/1.59 tff(1029,plain,((~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | b(s(s(elem!1)), elem!1) | b(z, elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(1030,plain,
% 1.34/1.59 (~r(s(z), elem!1)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1029, 201, 200, 145, 55, 210])).
% 1.34/1.59 tff(1031,plain,
% 1.34/1.59 (((~![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))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1032,plain,
% 1.34/1.59 ((~![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))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(1033,plain,
% 1.34/1.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1)),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1032, 1031])).
% 1.34/1.59 tff(1034,plain,
% 1.34/1.59 ((s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1033, 47])).
% 1.34/1.59 tff(1035,plain,
% 1.34/1.59 (b(s(z), elem!1)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1034, 1030, 209])).
% 1.34/1.59 tff(1036,assumption,(~(z = elem!1)), introduced(assumption)).
% 1.34/1.59 tff(1037,plain,
% 1.34/1.59 ((elem!1 = z) <=> (z = elem!1)),
% 1.34/1.59 inference(commutativity,[status(thm)],[])).
% 1.34/1.59 tff(1038,assumption,(elem!1 = z), introduced(assumption)).
% 1.34/1.59 tff(1039,plain,
% 1.34/1.59 (z = elem!1),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1038, 1037])).
% 1.34/1.59 tff(1040,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1036, 1039])).
% 1.34/1.59 tff(1041,plain,((~(elem!1 = z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(1042,plain,
% 1.34/1.59 (~(elem!1 = z)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1041, 1036])).
% 1.34/1.59 tff(1043,plain,
% 1.34/1.59 (r(z, elem!1)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[60, 1036, 55])).
% 1.34/1.59 tff(1044,assumption,(b(s(z), elem!1)), introduced(assumption)).
% 1.34/1.59 tff(1045,plain,
% 1.34/1.59 (~r(z, s(z))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[292, 1043, 474])).
% 1.34/1.59 tff(1046,plain,
% 1.34/1.59 (b(z, s(z))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[169, 1045])).
% 1.34/1.59 tff(1047,plain,
% 1.34/1.59 ((z = s(s(elem!1))) <=> (s(s(elem!1)) = z)),
% 1.34/1.59 inference(commutativity,[status(thm)],[])).
% 1.34/1.59 tff(1048,plain,
% 1.34/1.59 ((s(s(elem!1)) = z) <=> (z = s(s(elem!1)))),
% 1.34/1.59 inference(symmetry,[status(thm)],[1047])).
% 1.34/1.59 tff(1049,plain,
% 1.34/1.59 ((~(s(s(elem!1)) = z)) <=> (~(z = s(s(elem!1))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[1048])).
% 1.34/1.59 tff(1050,plain,
% 1.34/1.59 (~(z = s(s(elem!1)))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[139, 1049])).
% 1.34/1.59 tff(1051,assumption,(b(elem!1, z)), introduced(assumption)).
% 1.34/1.59 tff(1052,assumption,(~(s(s(elem!1)) = s(z))), introduced(assumption)).
% 1.34/1.59 tff(1053,plain,
% 1.34/1.59 (~(s(z) = s(s(elem!1)))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1052, 227])).
% 1.34/1.59 tff(1054,assumption,(~b(s(s(elem!1)), z)), introduced(assumption)).
% 1.34/1.59 tff(1055,plain,
% 1.34/1.59 (r(s(s(elem!1)), z)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[523, 1054])).
% 1.34/1.59 tff(1056,assumption,(b(s(z), z)), introduced(assumption)).
% 1.34/1.59 tff(1057,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, s(z))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1058,plain,
% 1.34/1.59 (((~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, s(z))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1059,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, s(z)))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[1058])).
% 1.34/1.59 tff(1060,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, s(z))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[1059, 1057])).
% 1.34/1.59 tff(1061,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(1062,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, s(z)))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1061, 1060])).
% 1.34/1.59 tff(1063,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1062, 246, 1051, 1056, 1044, 236])).
% 1.34/1.59 tff(1064,plain,((~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(1065,plain,
% 1.34/1.59 (~b(s(z), z)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1064, 1044, 1051, 236])).
% 1.34/1.59 tff(1066,plain,
% 1.34/1.59 (((~![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))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1067,plain,
% 1.34/1.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = z) | b(s(z), z) | r(s(z), z))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(1068,plain,
% 1.34/1.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = z) | b(s(z), z) | r(s(z), z)),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1067, 1066])).
% 1.34/1.59 tff(1069,plain,
% 1.34/1.59 (b(s(z), z) | r(s(z), z)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1068, 47, 163])).
% 1.34/1.59 tff(1070,plain,
% 1.44/1.60 (r(s(z), z)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1069, 1065])).
% 1.44/1.60 tff(1071,plain,
% 1.44/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(1072,plain,
% 1.44/1.60 (((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(1073,plain,
% 1.44/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1))))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[1072])).
% 1.44/1.60 tff(1074,plain,
% 1.44/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))),
% 1.44/1.60 inference(transitivity,[status(thm)],[1073, 1071])).
% 1.44/1.60 tff(1075,plain,
% 1.44/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(1076,plain,
% 1.44/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[1075, 1074])).
% 1.44/1.60 tff(1077,plain,
% 1.44/1.60 (~r(s(z), s(s(elem!1)))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1076, 183, 1070, 1055])).
% 1.44/1.60 tff(1078,plain,
% 1.44/1.60 ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1)))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[231, 47, 1077])).
% 1.44/1.60 tff(1079,plain,
% 1.44/1.60 (b(s(z), s(s(elem!1)))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1078, 1053])).
% 1.44/1.60 tff(1080,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(1081,plain,
% 1.44/1.60 (((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(1082,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1))))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[1081])).
% 1.44/1.60 tff(1083,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))))),
% 1.44/1.60 inference(transitivity,[status(thm)],[1082, 1080])).
% 1.44/1.60 tff(1084,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(1085,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[1084, 1083])).
% 1.44/1.60 tff(1086,plain,
% 1.44/1.60 ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1085, 246, 1051, 201, 1044, 236])).
% 1.44/1.60 tff(1087,plain,
% 1.44/1.60 (~b(s(s(elem!1)), elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1086, 1079])).
% 1.44/1.60 tff(1088,plain,
% 1.44/1.60 (~b(z, s(s(elem!1)))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[252, 246, 201, 236, 1079])).
% 1.44/1.60 tff(1089,plain,
% 1.44/1.60 ((z = s(s(elem!1))) | r(z, s(s(elem!1)))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[262, 47, 1088])).
% 1.44/1.60 tff(1090,plain,
% 1.44/1.60 (r(z, s(s(elem!1)))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1089, 1050])).
% 1.44/1.60 tff(1091,plain,
% 1.44/1.60 (~r(s(s(elem!1)), elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[275, 1090, 267])).
% 1.44/1.60 tff(1092,plain,
% 1.44/1.60 (s(s(elem!1)) = elem!1),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[156, 1091, 1087])).
% 1.44/1.60 tff(1093,plain,
% 1.44/1.60 (b(s(s(elem!1)), z) <=> b(elem!1, z)),
% 1.44/1.60 inference(monotonicity,[status(thm)],[1092])).
% 1.44/1.60 tff(1094,plain,
% 1.44/1.60 (b(elem!1, z) <=> b(s(s(elem!1)), z)),
% 1.44/1.60 inference(symmetry,[status(thm)],[1093])).
% 1.44/1.60 tff(1095,plain,
% 1.44/1.60 (b(s(s(elem!1)), z)),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[1051, 1094])).
% 1.44/1.60 tff(1096,plain,
% 1.44/1.60 ($false),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1054, 1095])).
% 1.44/1.60 tff(1097,plain,(b(s(s(elem!1)), z) | (~b(elem!1, z)) | (~r(z, elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (s(s(elem!1)) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.60 tff(1098,plain,
% 1.44/1.60 (b(s(s(elem!1)), z)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1097, 1044, 267, 201, 236, 1051, 1052])).
% 1.44/1.60 tff(1099,assumption,(b(z, s(s(elem!1)))), introduced(assumption)).
% 1.44/1.60 tff(1100,assumption,(b(s(s(elem!1)), z)), introduced(assumption)).
% 1.44/1.60 tff(1101,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(1102,plain,
% 1.44/1.60 (((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1))))) <=> ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(1103,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1))))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[1102])).
% 1.44/1.60 tff(1104,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))))),
% 1.44/1.60 inference(transitivity,[status(thm)],[1103, 1101])).
% 1.44/1.60 tff(1105,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(1106,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[1105, 1104])).
% 1.44/1.60 tff(1107,plain,
% 1.44/1.60 ($false),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1106, 246, 1051, 201, 1044, 1100, 236, 1099])).
% 1.44/1.60 tff(1108,plain,((~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.60 tff(1109,plain,
% 1.44/1.60 (~b(z, s(s(elem!1)))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1108, 1098, 201, 1044, 236, 1051])).
% 1.44/1.60 tff(1110,plain,
% 1.44/1.60 ((z = s(s(elem!1))) | r(z, s(s(elem!1)))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[262, 47, 1109])).
% 1.44/1.60 tff(1111,plain,
% 1.44/1.60 (r(z, s(s(elem!1)))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1110, 1050])).
% 1.44/1.60 tff(1112,plain,
% 1.44/1.60 (~r(s(s(elem!1)), elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[275, 1111, 267])).
% 1.44/1.60 tff(1113,assumption,(r(s(z), s(s(elem!1)))), introduced(assumption)).
% 1.44/1.60 tff(1114,assumption,(r(s(z), z)), introduced(assumption)).
% 1.44/1.60 tff(1115,plain,
% 1.44/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(1116,plain,
% 1.44/1.60 (((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(z), z))) <=> ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(1117,plain,
% 1.44/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1))))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[1116])).
% 1.44/1.60 tff(1118,plain,
% 1.44/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))))),
% 1.44/1.60 inference(transitivity,[status(thm)],[1117, 1115])).
% 1.44/1.60 tff(1119,plain,
% 1.44/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(z), z)))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(1120,plain,
% 1.44/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[1119, 1118])).
% 1.44/1.60 tff(1121,plain,
% 1.44/1.60 ($false),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1120, 183, 267, 1114, 266, 1113])).
% 1.44/1.60 tff(1122,plain,((~r(s(z), s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.60 tff(1123,plain,
% 1.44/1.60 (~r(s(z), s(s(elem!1)))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1122, 1070, 267, 1111])).
% 1.44/1.60 tff(1124,plain,
% 1.44/1.60 ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1)))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[231, 47, 1123])).
% 1.44/1.60 tff(1125,plain,
% 1.44/1.60 (b(s(z), s(s(elem!1)))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1124, 1053])).
% 1.44/1.60 tff(1126,plain,
% 1.44/1.60 (~b(s(s(elem!1)), elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1086, 1125])).
% 1.44/1.60 tff(1127,plain,
% 1.44/1.60 (s(s(elem!1)) = elem!1),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[156, 1126, 1112])).
% 1.44/1.60 tff(1128,plain,
% 1.44/1.60 (b(s(s(elem!1)), s(z)) <=> b(elem!1, s(z))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[1127])).
% 1.44/1.60 tff(1129,plain,
% 1.44/1.60 (b(elem!1, s(z))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[201, 1128])).
% 1.44/1.60 tff(1130,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(1131,plain,
% 1.44/1.60 (((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(1132,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z)))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[1131])).
% 1.44/1.60 tff(1133,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))))),
% 1.44/1.60 inference(transitivity,[status(thm)],[1132, 1130])).
% 1.44/1.60 tff(1134,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(1135,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z)))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[1134, 1133])).
% 1.44/1.60 tff(1136,plain,
% 1.44/1.60 ($false),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1135, 246, 1051, 1044, 1129, 236])).
% 1.44/1.60 tff(1137,plain,((~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (s(s(elem!1)) = s(z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.60 tff(1138,plain,
% 1.44/1.60 ((~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~r(z, elem!1))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1137, 113])).
% 1.44/1.60 tff(1139,plain,
% 1.44/1.60 (~b(elem!1, z)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1138, 1046, 201, 1044, 1043])).
% 1.44/1.60 tff(1140,plain,
% 1.44/1.60 (((~![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))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(1141,plain,
% 1.44/1.60 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = z) | b(elem!1, z) | r(elem!1, z))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(1142,plain,
% 1.44/1.60 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[1141, 1140])).
% 1.44/1.60 tff(1143,plain,
% 1.44/1.60 ((elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1142, 47])).
% 1.44/1.60 tff(1144,plain,
% 1.44/1.60 (r(elem!1, z)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1143, 1139, 1042])).
% 1.44/1.60 tff(1145,plain,
% 1.44/1.60 (~r(z, s(s(elem!1)))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[275, 1043, 216])).
% 1.44/1.60 tff(1146,plain,
% 1.44/1.60 (b(z, s(s(elem!1)))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[264, 1145])).
% 1.44/1.60 tff(1147,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(1148,plain,
% 1.44/1.60 (((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(1149,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1))))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[1148])).
% 1.44/1.60 tff(1150,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))))),
% 1.44/1.60 inference(transitivity,[status(thm)],[1149, 1147])).
% 1.44/1.60 tff(1151,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(1152,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[1151, 1150])).
% 1.44/1.61 tff(1153,plain,
% 1.44/1.61 ($false),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1152, 246, 201, 1056, 236, 1099])).
% 1.44/1.61 tff(1154,plain,((~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.61 tff(1155,plain,
% 1.44/1.61 (~b(s(z), z)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1154, 1046, 1146, 201])).
% 1.44/1.61 tff(1156,plain,
% 1.44/1.61 (r(s(z), z)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1069, 1155])).
% 1.44/1.61 tff(1157,plain,
% 1.44/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(1158,plain,
% 1.44/1.61 (((~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z)))) <=> ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(1159,plain,
% 1.44/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z)))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1158])).
% 1.44/1.61 tff(1160,plain,
% 1.44/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[1159, 1157])).
% 1.44/1.61 tff(1161,plain,
% 1.44/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(1162,plain,
% 1.44/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z)))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[1161, 1160])).
% 1.44/1.61 tff(1163,plain,
% 1.44/1.61 ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z)))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1162, 183])).
% 1.44/1.61 tff(1164,plain,
% 1.44/1.61 ($false),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1163, 1156, 1144, 474])).
% 1.44/1.61 tff(1165,plain,((z = elem!1) | (~r(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.61 tff(1166,plain,
% 1.44/1.61 (z = elem!1),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1165, 215, 201, 1035, 200, 55])).
% 1.44/1.61 tff(1167,plain,
% 1.44/1.61 (s(z) = s(elem!1)),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1166])).
% 1.44/1.61 tff(1168,plain,
% 1.44/1.61 (s(s(z)) = s(s(elem!1))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1167])).
% 1.44/1.61 tff(1169,plain,
% 1.44/1.61 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1168])).
% 1.44/1.61 tff(1170,plain,
% 1.44/1.61 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.44/1.61 inference(symmetry,[status(thm)],[1169])).
% 1.44/1.61 tff(1171,plain,
% 1.44/1.61 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1170])).
% 1.44/1.61 tff(1172,plain,
% 1.44/1.61 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.44/1.61 inference(symmetry,[status(thm)],[1171])).
% 1.44/1.61 tff(1173,plain,
% 1.44/1.61 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[115, 1166])).
% 1.44/1.61 tff(1174,plain,
% 1.44/1.61 (~(s(s(elem!1)) = s(s(s(z))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[421, 1173])).
% 1.44/1.61 tff(1175,plain,
% 1.44/1.61 (r(s(s(elem!1)), s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1169])).
% 1.44/1.61 tff(1176,plain,
% 1.44/1.61 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 1.44/1.61 inference(symmetry,[status(thm)],[1175])).
% 1.44/1.61 tff(1177,plain,
% 1.44/1.61 ((~r(s(s(elem!1)), s(s(s(elem!1))))) <=> (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1176])).
% 1.44/1.61 tff(1178,plain,
% 1.44/1.61 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(z))), elem!1)),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1170])).
% 1.44/1.61 tff(1179,plain,
% 1.44/1.61 (r(s(s(s(z))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 1.44/1.61 inference(symmetry,[status(thm)],[1178])).
% 1.44/1.61 tff(1180,plain,
% 1.44/1.61 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1166])).
% 1.44/1.61 tff(1181,plain,
% 1.44/1.61 ((s(s(s(z))) = z) <=> (elem!1 = s(s(s(z))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[1180, 73])).
% 1.44/1.61 tff(1182,plain,
% 1.44/1.61 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 1.44/1.61 inference(transitivity,[status(thm)],[1181, 74])).
% 1.44/1.61 tff(1183,plain,
% 1.44/1.61 ((~(s(s(s(z))) = z)) <=> (~(s(s(s(z))) = elem!1))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1182])).
% 1.44/1.61 tff(1184,plain,
% 1.44/1.61 (~(s(s(s(z))) = elem!1)),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[80, 1183])).
% 1.44/1.61 tff(1185,plain,
% 1.44/1.61 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1170])).
% 1.44/1.61 tff(1186,plain,
% 1.44/1.61 ((~b(s(s(s(elem!1))), elem!1)) <=> (~b(s(s(s(z))), elem!1))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1185])).
% 1.44/1.61 tff(1187,plain,
% 1.44/1.61 (r(z, s(z)) <=> r(elem!1, s(z))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1166])).
% 1.44/1.61 tff(1188,plain,
% 1.44/1.61 (r(elem!1, s(z)) <=> r(z, s(z))),
% 1.44/1.61 inference(symmetry,[status(thm)],[1187])).
% 1.44/1.61 tff(1189,plain,
% 1.44/1.61 (r(z, s(z))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[215, 1188])).
% 1.44/1.61 tff(1190,plain,
% 1.44/1.61 ((~(s(s(elem!1)) = elem!1)) <=> (~(elem!1 = s(s(elem!1))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[134])).
% 1.44/1.61 tff(1191,plain,
% 1.44/1.61 (~(elem!1 = s(s(elem!1)))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[199, 1190])).
% 1.44/1.61 tff(1192,plain,
% 1.44/1.61 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1167])).
% 1.44/1.61 tff(1193,plain,
% 1.44/1.61 (b(s(s(elem!1)), s(elem!1))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[201, 1192])).
% 1.44/1.61 tff(1194,plain,
% 1.44/1.61 (s(elem!1) = s(z)),
% 1.44/1.61 inference(symmetry,[status(thm)],[1167])).
% 1.44/1.61 tff(1195,plain,
% 1.44/1.61 (r(elem!1, s(elem!1)) <=> r(elem!1, s(z))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1194])).
% 1.44/1.61 tff(1196,plain,
% 1.44/1.61 (r(elem!1, s(z)) <=> r(elem!1, s(elem!1))),
% 1.44/1.61 inference(symmetry,[status(thm)],[1195])).
% 1.44/1.61 tff(1197,plain,
% 1.44/1.61 (r(elem!1, s(elem!1))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[215, 1196])).
% 1.44/1.61 tff(1198,plain,
% 1.44/1.61 (b(s(z), elem!1) <=> b(s(elem!1), elem!1)),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1167])).
% 1.44/1.61 tff(1199,plain,
% 1.44/1.61 (b(s(elem!1), elem!1)),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[1035, 1198])).
% 1.44/1.61 tff(1200,assumption,(b(s(elem!1), elem!1)), introduced(assumption)).
% 1.44/1.61 tff(1201,plain,
% 1.44/1.61 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[409, 89])).
% 1.44/1.61 tff(1202,plain,
% 1.44/1.61 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(z))), s(z))),
% 1.44/1.61 inference(symmetry,[status(thm)],[1201])).
% 1.44/1.61 tff(1203,plain,
% 1.44/1.61 ((~r(s(s(s(elem!1))), s(elem!1))) <=> (~r(s(s(s(z))), s(z)))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1202])).
% 1.44/1.61 tff(1204,assumption,(~(elem!1 = s(s(elem!1)))), introduced(assumption)).
% 1.44/1.61 tff(1205,plain,
% 1.44/1.61 ((s(s(s(s(s(elem!1))))) = s(elem!1)) <=> (s(s(s(s(s(elem!1))))) = s(z))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[90])).
% 1.44/1.61 tff(1206,plain,
% 1.44/1.61 ((s(s(s(s(s(elem!1))))) = s(z)) <=> (s(s(s(s(s(elem!1))))) = s(elem!1))),
% 1.44/1.61 inference(symmetry,[status(thm)],[1205])).
% 1.44/1.61 tff(1207,plain,
% 1.44/1.61 ((~(s(s(s(s(s(elem!1))))) = s(z))) <=> (~(s(s(s(s(s(elem!1))))) = s(elem!1)))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1206])).
% 1.44/1.61 tff(1208,plain,
% 1.44/1.61 (~(s(s(s(s(s(elem!1))))) = s(elem!1))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[331, 1207])).
% 1.44/1.61 tff(1209,assumption,(r(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 1.44/1.61 tff(1210,plain,
% 1.44/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(1211,plain,
% 1.44/1.61 (((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(1212,plain,
% 1.44/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1211])).
% 1.44/1.61 tff(1213,plain,
% 1.44/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[1212, 1210])).
% 1.44/1.61 tff(1214,plain,
% 1.44/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(1215,plain,
% 1.44/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[1214, 1213])).
% 1.44/1.61 tff(1216,plain,
% 1.44/1.61 ($false),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1215, 183, 602, 601, 1209])).
% 1.44/1.61 tff(1217,plain,((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.61 tff(1218,plain,
% 1.44/1.61 (~r(s(elem!1), s(s(elem!1)))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1217, 602, 601])).
% 1.44/1.61 tff(1219,plain,
% 1.44/1.61 (~r(s(z), s(s(elem!1)))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[1218, 366])).
% 1.44/1.61 tff(1220,plain,
% 1.44/1.61 (b(s(z), s(s(elem!1)))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[233, 1219])).
% 1.44/1.61 tff(1221,plain,
% 1.44/1.61 (b(s(elem!1), s(s(elem!1)))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[1220, 364])).
% 1.44/1.61 tff(1222,plain,
% 1.44/1.61 (~(s(s(s(s(s(s(s(elem!1))))))) = s(elem!1))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[511, 88])).
% 1.44/1.61 tff(1223,plain,
% 1.44/1.61 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(z))), s(z))),
% 1.44/1.61 inference(symmetry,[status(thm)],[425])).
% 1.44/1.61 tff(1224,plain,
% 1.44/1.61 ((~b(s(s(s(elem!1))), s(elem!1))) <=> (~b(s(s(s(z))), s(z)))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1223])).
% 1.44/1.61 tff(1225,plain,
% 1.44/1.61 (~r(elem!1, s(s(s(z))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[465, 1221, 216, 88, 363, 171])).
% 1.44/1.61 tff(1226,plain,
% 1.44/1.61 (b(elem!1, s(s(s(z))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[470, 1225, 718])).
% 1.44/1.61 tff(1227,plain,
% 1.44/1.61 (b(elem!1, s(s(s(elem!1))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[1226, 716])).
% 1.44/1.61 tff(1228,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(1229,plain,
% 1.44/1.61 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(1230,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1229])).
% 1.44/1.61 tff(1231,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.61 inference(transitivity,[status(thm)],[1230, 1228])).
% 1.44/1.61 tff(1232,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(1233,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[1232, 1231])).
% 1.44/1.61 tff(1234,plain,
% 1.44/1.61 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1233, 246, 1227, 1200, 961])).
% 1.44/1.61 tff(1235,plain,
% 1.44/1.61 (~b(s(s(s(z))), s(z))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[1234, 1224])).
% 1.44/1.61 tff(1236,plain,
% 1.44/1.61 (r(s(s(s(z))), s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[52, 1235])).
% 1.44/1.61 tff(1237,plain,
% 1.44/1.61 (r(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[1236, 1201])).
% 1.44/1.61 tff(1238,plain,
% 1.44/1.61 (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[860, 1237, 601, 88])).
% 1.44/1.61 tff(1239,plain,
% 1.44/1.61 (b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[818, 1238, 1222])).
% 1.44/1.61 tff(1240,plain,
% 1.44/1.61 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[813, 1239, 88, 602, 601, 363, 416, 216, 1221])).
% 1.44/1.61 tff(1241,plain,
% 1.44/1.61 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[86, 1240, 568])).
% 1.44/1.61 tff(1242,plain,
% 1.44/1.61 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[339, 183, 216, 1241])).
% 1.44/1.61 tff(1243,plain,
% 1.44/1.61 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[361, 47, 358, 1242])).
% 1.44/1.61 tff(1244,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(1245,plain,
% 1.44/1.61 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(1246,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1245])).
% 1.44/1.61 tff(1247,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[1246, 1244])).
% 1.44/1.61 tff(1248,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(1249,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[1248, 1247])).
% 1.44/1.61 tff(1250,plain,
% 1.44/1.61 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1249, 246, 1221, 363, 1243])).
% 1.44/1.61 tff(1251,plain,
% 1.44/1.61 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(elem!1)) | b(s(s(s(s(s(elem!1))))), s(elem!1)) | r(s(s(s(s(s(elem!1))))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(elem!1)) | b(s(s(s(s(s(elem!1))))), s(elem!1)) | r(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(1252,plain,
% 1.44/1.61 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(elem!1)) | b(s(s(s(s(s(elem!1))))), s(elem!1)) | r(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(1253,plain,
% 1.44/1.61 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(elem!1)) | b(s(s(s(s(s(elem!1))))), s(elem!1)) | r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[1252, 1251])).
% 1.44/1.61 tff(1254,plain,
% 1.44/1.61 ((s(s(s(s(s(elem!1))))) = s(elem!1)) | r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1253, 47, 1250])).
% 1.44/1.61 tff(1255,plain,
% 1.44/1.61 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1254, 1208])).
% 1.44/1.61 tff(1256,plain,
% 1.44/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(1257,plain,
% 1.44/1.61 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(1258,plain,
% 1.44/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1257])).
% 1.44/1.61 tff(1259,plain,
% 1.44/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.44/1.61 inference(transitivity,[status(thm)],[1258, 1256])).
% 1.44/1.61 tff(1260,plain,
% 1.44/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(1261,plain,
% 1.44/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[1260, 1259])).
% 1.44/1.61 tff(1262,plain,
% 1.44/1.61 ($false),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1261, 183, 602, 1241, 1255, 601])).
% 1.44/1.61 tff(1263,plain,((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~(z = elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.61 tff(1264,plain,
% 1.44/1.61 (~r(elem!1, s(s(elem!1)))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1263, 961, 88, 363, 216, 1200, 601, 171])).
% 1.44/1.61 tff(1265,plain,
% 1.44/1.61 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(1266,plain,
% 1.44/1.61 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1))))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(1267,plain,
% 1.44/1.61 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1)))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[1266, 1265])).
% 1.44/1.61 tff(1268,plain,
% 1.44/1.61 ((elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1)))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1267, 47])).
% 1.44/1.61 tff(1269,plain,
% 1.44/1.61 (b(elem!1, s(s(elem!1)))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1268, 1264, 1204])).
% 1.44/1.61 tff(1270,plain,
% 1.44/1.61 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(z), s(s(s(z))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[90, 410])).
% 1.44/1.61 tff(1271,plain,
% 1.44/1.61 (r(s(z), s(s(s(z)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.61 inference(symmetry,[status(thm)],[1270])).
% 1.44/1.61 tff(1272,plain,
% 1.44/1.61 (b(s(z), s(s(s(z)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[89, 409])).
% 1.44/1.61 tff(1273,plain,
% 1.44/1.61 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(z), s(s(s(z))))),
% 1.44/1.61 inference(symmetry,[status(thm)],[1272])).
% 1.44/1.61 tff(1274,plain,
% 1.44/1.61 ((~b(s(elem!1), s(s(s(elem!1))))) <=> (~b(s(z), s(s(s(z)))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1273])).
% 1.44/1.61 tff(1275,plain,
% 1.44/1.61 (~r(elem!1, s(s(s(elem!1))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[725, 183, 601, 820])).
% 1.44/1.61 tff(1276,plain,
% 1.44/1.61 (~r(elem!1, s(s(s(z))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[1275, 719])).
% 1.44/1.61 tff(1277,plain,
% 1.44/1.61 (b(elem!1, s(s(s(z))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[470, 1276, 718])).
% 1.44/1.61 tff(1278,plain,
% 1.44/1.61 (b(elem!1, s(s(s(elem!1))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[1277, 716])).
% 1.44/1.61 tff(1279,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(1280,plain,
% 1.44/1.61 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(1281,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1280])).
% 1.44/1.61 tff(1282,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.61 inference(transitivity,[status(thm)],[1281, 1279])).
% 1.44/1.61 tff(1283,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(1284,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[1283, 1282])).
% 1.44/1.62 tff(1285,plain,
% 1.44/1.62 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1284, 246, 1278, 1200, 961])).
% 1.44/1.62 tff(1286,plain,
% 1.44/1.62 (~b(s(z), s(s(s(z))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[1285, 1274])).
% 1.44/1.62 tff(1287,plain,
% 1.44/1.62 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(1288,plain,
% 1.44/1.62 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(1289,plain,
% 1.44/1.62 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[1288, 1287])).
% 1.44/1.62 tff(1290,plain,
% 1.44/1.62 ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1289, 47])).
% 1.44/1.62 tff(1291,plain,
% 1.44/1.62 (b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1290, 767])).
% 1.44/1.62 tff(1292,plain,
% 1.44/1.62 (r(s(z), s(s(s(z))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1291, 1286])).
% 1.44/1.62 tff(1293,plain,
% 1.44/1.62 (r(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[1292, 1271])).
% 1.44/1.62 tff(1294,plain,
% 1.44/1.62 (r(s(z), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.44/1.62 inference(symmetry,[status(thm)],[365])).
% 1.44/1.62 tff(1295,plain,
% 1.44/1.62 (b(s(elem!1), s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 1.44/1.62 inference(symmetry,[status(thm)],[364])).
% 1.44/1.62 tff(1296,plain,
% 1.44/1.62 ((~b(s(elem!1), s(s(elem!1)))) <=> (~b(s(z), s(s(elem!1))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[1295])).
% 1.44/1.62 tff(1297,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(1298,plain,
% 1.44/1.62 (((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(1299,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[1298])).
% 1.44/1.62 tff(1300,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.62 inference(transitivity,[status(thm)],[1299, 1297])).
% 1.44/1.62 tff(1301,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(1302,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[1301, 1300])).
% 1.44/1.62 tff(1303,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1302, 246, 947, 442, 363, 1200])).
% 1.44/1.62 tff(1304,plain,((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(1305,plain,
% 1.44/1.62 (~b(s(elem!1), s(s(elem!1)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1304, 947, 363, 1200])).
% 1.44/1.62 tff(1306,plain,
% 1.44/1.62 (~b(s(z), s(s(elem!1)))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[1305, 1296])).
% 1.44/1.62 tff(1307,plain,
% 1.44/1.62 (r(s(z), s(s(elem!1)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[233, 1306])).
% 1.44/1.62 tff(1308,plain,
% 1.44/1.62 (r(s(elem!1), s(s(elem!1)))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[1307, 1294])).
% 1.44/1.62 tff(1309,plain,
% 1.44/1.62 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[409])).
% 1.44/1.62 tff(1310,plain,
% 1.44/1.62 ((~b(s(s(s(elem!1))), s(s(elem!1)))) <=> (~b(s(s(s(z))), s(s(elem!1))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[561])).
% 1.44/1.62 tff(1311,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(1312,plain,
% 1.44/1.62 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(1313,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[1312])).
% 1.44/1.62 tff(1314,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.62 inference(transitivity,[status(thm)],[1313, 1311])).
% 1.44/1.62 tff(1315,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(1316,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[1315, 1314])).
% 1.44/1.62 tff(1317,plain,
% 1.44/1.62 ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1316, 246, 947, 363, 1200, 961])).
% 1.44/1.62 tff(1318,plain,
% 1.44/1.62 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1317, 1278])).
% 1.44/1.62 tff(1319,plain,
% 1.44/1.62 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[1318, 1310])).
% 1.44/1.62 tff(1320,plain,
% 1.44/1.62 (r(s(s(s(z))), s(s(elem!1)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[689, 1319, 416])).
% 1.44/1.62 tff(1321,plain,
% 1.44/1.62 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[1320, 1309])).
% 1.44/1.62 tff(1322,plain,
% 1.44/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(1323,plain,
% 1.44/1.62 (((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), 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(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(1324,plain,
% 1.44/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1)))))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[1323])).
% 1.44/1.62 tff(1325,plain,
% 1.44/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.44/1.62 inference(transitivity,[status(thm)],[1324, 1322])).
% 1.44/1.62 tff(1326,plain,
% 1.44/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(1327,plain,
% 1.44/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[1326, 1325])).
% 1.44/1.62 tff(1328,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1327, 183, 1321, 820, 1308, 1293])).
% 1.44/1.62 tff(1329,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~(z = elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(1330,plain,
% 1.44/1.62 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1329, 1269, 88, 363, 1200, 961, 601])).
% 1.44/1.62 tff(1331,plain,
% 1.44/1.62 (~r(s(s(s(z))), s(z))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[1330, 1203])).
% 1.44/1.62 tff(1332,plain,
% 1.44/1.62 (b(s(s(s(z))), s(z))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[52, 1331])).
% 1.44/1.62 tff(1333,plain,
% 1.44/1.62 (b(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[1332, 425])).
% 1.44/1.62 tff(1334,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(1335,plain,
% 1.44/1.62 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(1336,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[1335])).
% 1.44/1.62 tff(1337,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.62 inference(transitivity,[status(thm)],[1336, 1334])).
% 1.44/1.62 tff(1338,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(1339,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[1338, 1337])).
% 1.44/1.62 tff(1340,plain,
% 1.44/1.62 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1339, 246, 1269, 363, 1333, 1200, 961])).
% 1.44/1.62 tff(1341,plain,
% 1.44/1.62 (~b(s(z), s(s(s(z))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[1340, 1274])).
% 1.44/1.62 tff(1342,plain,
% 1.44/1.62 (r(s(z), s(s(s(z))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1291, 1341])).
% 1.44/1.62 tff(1343,plain,
% 1.44/1.62 (r(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[1342, 1271])).
% 1.44/1.62 tff(1344,plain,
% 1.44/1.62 (~b(s(elem!1), s(s(elem!1)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1304, 1269, 363, 1200])).
% 1.44/1.62 tff(1345,plain,
% 1.44/1.62 (~b(s(z), s(s(elem!1)))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[1344, 1296])).
% 1.44/1.62 tff(1346,plain,
% 1.44/1.62 (r(s(z), s(s(elem!1)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[233, 1345])).
% 1.44/1.62 tff(1347,plain,
% 1.44/1.62 (r(s(elem!1), s(s(elem!1)))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[1346, 1294])).
% 1.44/1.62 tff(1348,assumption,(r(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 1.44/1.62 tff(1349,plain,
% 1.44/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(1350,plain,
% 1.44/1.62 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(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(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(1351,plain,
% 1.44/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1)))))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[1350])).
% 1.44/1.62 tff(1352,plain,
% 1.44/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.44/1.62 inference(transitivity,[status(thm)],[1351, 1349])).
% 1.44/1.62 tff(1353,plain,
% 1.44/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(1354,plain,
% 1.44/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[1353, 1352])).
% 1.44/1.62 tff(1355,plain,
% 1.44/1.62 (~r(elem!1, s(s(s(elem!1))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1354, 183, 601, 1209, 1348])).
% 1.44/1.62 tff(1356,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1355, 414])).
% 1.44/1.62 tff(1357,plain,((~r(elem!1, s(s(s(z))))) | (~(z = elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(1358,plain,
% 1.44/1.62 (~r(elem!1, s(s(s(z))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1357, 1347, 601, 88, 1343])).
% 1.44/1.62 tff(1359,plain,
% 1.44/1.62 (b(elem!1, s(s(s(z))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[470, 1358, 718])).
% 1.44/1.62 tff(1360,plain,
% 1.44/1.62 (b(elem!1, s(s(s(elem!1))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[1359, 716])).
% 1.44/1.62 tff(1361,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1233, 246, 1360, 1333, 1200, 961])).
% 1.44/1.62 tff(1362,plain,((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~(z = elem!1)) | (~r(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (elem!1 = s(s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(1363,plain,
% 1.44/1.62 (~b(s(s(s(elem!1))), elem!1)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1362, 1199, 1166, 1197, 1193, 1191, 200, 1189])).
% 1.44/1.62 tff(1364,plain,
% 1.44/1.62 (~b(s(s(s(z))), elem!1)),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[1363, 1186])).
% 1.44/1.62 tff(1365,plain,
% 1.44/1.62 (r(s(s(s(z))), elem!1)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[647, 1364, 1184])).
% 1.44/1.62 tff(1366,plain,
% 1.44/1.62 (r(s(s(s(elem!1))), elem!1)),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[1365, 1179])).
% 1.44/1.62 tff(1367,plain,
% 1.44/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(1368,plain,
% 1.44/1.62 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), 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)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(1369,plain,
% 1.44/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[1368])).
% 1.44/1.62 tff(1370,plain,
% 1.44/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.44/1.62 inference(transitivity,[status(thm)],[1369, 1367])).
% 1.44/1.62 tff(1371,plain,
% 1.44/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(1372,plain,
% 1.44/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[1371, 1370])).
% 1.44/1.62 tff(1373,plain,
% 1.44/1.62 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1372, 183, 200, 1366])).
% 1.44/1.62 tff(1374,plain,
% 1.44/1.62 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[1373, 1177])).
% 1.44/1.63 tff(1375,plain,
% 1.44/1.63 (b(s(s(elem!1)), s(s(s(z))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[454, 1374, 1174])).
% 1.44/1.63 tff(1376,plain,
% 1.44/1.63 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[1375, 1172])).
% 1.44/1.63 tff(1377,plain,
% 1.44/1.63 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1170])).
% 1.44/1.63 tff(1378,plain,
% 1.44/1.63 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.63 inference(symmetry,[status(thm)],[1377])).
% 1.44/1.63 tff(1379,plain,
% 1.44/1.63 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1166])).
% 1.44/1.63 tff(1380,plain,
% 1.44/1.63 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), z)),
% 1.44/1.63 inference(symmetry,[status(thm)],[1379])).
% 1.44/1.63 tff(1381,plain,
% 1.44/1.63 (r(s(s(elem!1)), z)),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[200, 1380])).
% 1.44/1.63 tff(1382,plain,
% 1.44/1.63 (b(s(s(s(z))), z) <=> b(s(s(s(z))), elem!1)),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1166])).
% 1.44/1.63 tff(1383,plain,
% 1.44/1.63 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), z)),
% 1.44/1.63 inference(symmetry,[status(thm)],[1382])).
% 1.44/1.63 tff(1384,plain,
% 1.44/1.63 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), z)),
% 1.44/1.63 inference(transitivity,[status(thm)],[1185, 1383])).
% 1.44/1.63 tff(1385,plain,
% 1.44/1.63 ((~b(s(s(s(elem!1))), elem!1)) <=> (~b(s(s(s(z))), z))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1384])).
% 1.44/1.63 tff(1386,plain,
% 1.44/1.63 (~b(s(s(s(z))), z)),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[1363, 1385])).
% 1.44/1.63 tff(1387,plain,
% 1.44/1.63 (r(s(s(s(z))), z)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[995, 1386])).
% 1.44/1.63 tff(1388,plain,
% 1.44/1.63 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1005, 1387, 1381, 200])).
% 1.44/1.63 tff(1389,plain,
% 1.44/1.63 (b(s(s(s(z))), s(s(elem!1)))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[689, 1388, 1173])).
% 1.44/1.63 tff(1390,plain,
% 1.44/1.63 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[1389, 1378])).
% 1.44/1.63 tff(1391,plain,
% 1.44/1.63 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1169, 1167])).
% 1.44/1.63 tff(1392,plain,
% 1.44/1.63 (~r(s(s(s(z))), s(z))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1023, 1365, 215])).
% 1.44/1.63 tff(1393,plain,
% 1.44/1.63 (b(s(s(s(z))), s(z))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[52, 1392])).
% 1.44/1.63 tff(1394,plain,
% 1.44/1.63 (b(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[1393, 1391])).
% 1.44/1.63 tff(1395,plain,
% 1.44/1.63 (r(s(elem!1), s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1194])).
% 1.44/1.63 tff(1396,plain,
% 1.44/1.63 (r(s(z), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.44/1.63 inference(symmetry,[status(thm)],[1395])).
% 1.44/1.63 tff(1397,plain,
% 1.44/1.63 (b(s(z), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1167])).
% 1.44/1.63 tff(1398,plain,
% 1.44/1.63 (b(s(elem!1), s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 1.44/1.63 inference(symmetry,[status(thm)],[1397])).
% 1.44/1.63 tff(1399,plain,
% 1.44/1.63 ((~b(s(elem!1), s(s(elem!1)))) <=> (~b(s(z), s(s(elem!1))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1398])).
% 1.44/1.63 tff(1400,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(1401,plain,
% 1.44/1.63 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(1402,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1401])).
% 1.44/1.63 tff(1403,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.63 inference(transitivity,[status(thm)],[1402, 1400])).
% 1.44/1.63 tff(1404,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(1405,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[1404, 1403])).
% 1.44/1.63 tff(1406,plain,
% 1.44/1.63 ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1405, 246, 1193, 1394, 1199])).
% 1.44/1.63 tff(1407,plain,
% 1.44/1.63 (~b(s(elem!1), s(s(elem!1)))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1406, 1390])).
% 1.44/1.63 tff(1408,plain,
% 1.44/1.63 (~b(s(z), s(s(elem!1)))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[1407, 1399])).
% 1.44/1.63 tff(1409,plain,
% 1.44/1.63 (r(s(z), s(s(elem!1)))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[233, 1408])).
% 1.44/1.63 tff(1410,plain,
% 1.44/1.63 (r(s(elem!1), s(s(elem!1)))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[1409, 1396])).
% 1.44/1.63 tff(1411,plain,
% 1.44/1.63 (~r(elem!1, s(s(elem!1)))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1217, 1410, 1197])).
% 1.44/1.63 tff(1412,plain,
% 1.44/1.63 (b(elem!1, s(s(elem!1)))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1268, 1411, 1191])).
% 1.44/1.63 tff(1413,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(1414,plain,
% 1.44/1.63 (((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(1415,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1414])).
% 1.44/1.63 tff(1416,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.63 inference(transitivity,[status(thm)],[1415, 1413])).
% 1.44/1.63 tff(1417,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(1418,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[1417, 1416])).
% 1.44/1.63 tff(1419,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1418, 246, 1412, 1193, 1394, 1199, 1390, 1376])).
% 1.44/1.63 tff(1420,plain,((~b(s(s(elem!1)), s(z))) | (s(s(elem!1)) = elem!1) | b(z, elem!1) | b(s(s(elem!1)), elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(1421,plain,
% 1.44/1.63 (b(elem!1, s(z))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1420, 198, 55, 145, 150])).
% 1.44/1.63 tff(1422,plain,
% 1.44/1.63 (b(z, s(z))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[1421, 147])).
% 1.44/1.63 tff(1423,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[54, 1422])).
% 1.44/1.63 tff(1424,plain,(b(z, s(z)) | (~(z = elem!1)) | b(z, elem!1) | b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(1425,plain,
% 1.44/1.63 (b(z, s(z))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1424, 145, 55, 61])).
% 1.44/1.63 tff(1426,plain,
% 1.44/1.63 (b(elem!1, s(elem!1))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[1425, 144])).
% 1.44/1.63 tff(1427,plain,
% 1.44/1.63 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[141])).
% 1.44/1.63 tff(1428,plain,
% 1.44/1.63 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(z))), s(elem!1))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[410])).
% 1.44/1.63 tff(1429,plain,
% 1.44/1.63 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.63 inference(symmetry,[status(thm)],[1428])).
% 1.44/1.63 tff(1430,plain,
% 1.44/1.63 (r(s(s(s(z))), s(z)) <=> r(s(s(s(z))), s(elem!1))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[89])).
% 1.44/1.63 tff(1431,plain,
% 1.44/1.63 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.63 inference(transitivity,[status(thm)],[1430, 1429])).
% 1.44/1.63 tff(1432,plain,
% 1.44/1.63 (b(z, s(z))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1424, 145, 55, 88])).
% 1.44/1.63 tff(1433,plain,
% 1.44/1.63 (b(s(s(s(z))), z) <=> b(s(s(s(z))), elem!1)),
% 1.44/1.63 inference(monotonicity,[status(thm)],[88])).
% 1.44/1.63 tff(1434,plain,
% 1.44/1.63 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), z)),
% 1.44/1.63 inference(symmetry,[status(thm)],[1433])).
% 1.44/1.63 tff(1435,plain,
% 1.44/1.63 (b(elem!1, s(z))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[1432, 146])).
% 1.44/1.63 tff(1436,plain,
% 1.44/1.63 ((z = elem!1) <=> (elem!1 = z)),
% 1.44/1.63 inference(symmetry,[status(thm)],[1037])).
% 1.44/1.63 tff(1437,plain,
% 1.44/1.63 (elem!1 = z),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[88, 1436])).
% 1.44/1.63 tff(1438,assumption,(~(elem!1 = z)), introduced(assumption)).
% 1.44/1.63 tff(1439,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1438, 1437])).
% 1.44/1.63 tff(1440,plain,((~(z = elem!1)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(1441,plain,
% 1.44/1.63 (elem!1 = z),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1440, 88])).
% 1.44/1.63 tff(1442,plain,
% 1.44/1.63 (b(s(z), elem!1) <=> b(s(z), z)),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1038])).
% 1.44/1.63 tff(1443,plain,
% 1.44/1.63 (b(s(z), z) <=> b(s(z), elem!1)),
% 1.44/1.63 inference(symmetry,[status(thm)],[1442])).
% 1.44/1.63 tff(1444,plain,
% 1.44/1.63 (b(s(z), elem!1)),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[1056, 1443])).
% 1.44/1.63 tff(1445,assumption,(~b(s(z), elem!1)), introduced(assumption)).
% 1.44/1.63 tff(1446,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1445, 1444])).
% 1.44/1.63 tff(1447,plain,((~(elem!1 = z)) | b(s(z), elem!1) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(1448,plain,
% 1.44/1.63 (b(s(z), elem!1)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1447, 1056, 1441])).
% 1.44/1.63 tff(1449,plain,
% 1.44/1.63 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[89])).
% 1.44/1.63 tff(1450,plain,
% 1.44/1.63 (b(z, s(z)) <=> b(elem!1, s(elem!1))),
% 1.44/1.63 inference(transitivity,[status(thm)],[146, 1449])).
% 1.44/1.63 tff(1451,plain,
% 1.44/1.63 (b(elem!1, s(elem!1))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[1432, 1450])).
% 1.44/1.63 tff(1452,plain,
% 1.44/1.63 (b(s(z), elem!1) <=> b(s(elem!1), elem!1)),
% 1.44/1.63 inference(monotonicity,[status(thm)],[89])).
% 1.44/1.63 tff(1453,plain,
% 1.44/1.63 (b(s(z), z) <=> b(s(z), elem!1)),
% 1.44/1.63 inference(monotonicity,[status(thm)],[88])).
% 1.44/1.63 tff(1454,plain,
% 1.44/1.63 (b(s(z), z) <=> b(s(elem!1), elem!1)),
% 1.44/1.63 inference(transitivity,[status(thm)],[1453, 1452])).
% 1.44/1.63 tff(1455,plain,
% 1.44/1.63 (b(s(elem!1), elem!1)),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[1056, 1454])).
% 1.44/1.63 tff(1456,plain,
% 1.44/1.63 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[409])).
% 1.44/1.63 tff(1457,plain,
% 1.44/1.63 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.44/1.63 inference(symmetry,[status(thm)],[1456])).
% 1.44/1.63 tff(1458,plain,
% 1.44/1.63 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1457, 410])).
% 1.44/1.63 tff(1459,plain,
% 1.44/1.63 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.44/1.63 inference(symmetry,[status(thm)],[1458])).
% 1.44/1.63 tff(1460,plain,
% 1.44/1.63 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[409])).
% 1.44/1.63 tff(1461,plain,
% 1.44/1.63 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.63 inference(symmetry,[status(thm)],[1460])).
% 1.44/1.63 tff(1462,plain,
% 1.44/1.63 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1457])).
% 1.44/1.63 tff(1463,plain,
% 1.44/1.63 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.63 inference(transitivity,[status(thm)],[1462, 1461])).
% 1.44/1.63 tff(1464,plain,
% 1.44/1.63 ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1463])).
% 1.44/1.63 tff(1465,plain,
% 1.44/1.63 ((s(s(s(s(elem!1)))) = elem!1) <=> (s(s(s(s(elem!1)))) = z)),
% 1.44/1.63 inference(monotonicity,[status(thm)],[341])).
% 1.44/1.63 tff(1466,plain,
% 1.44/1.63 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.44/1.63 inference(symmetry,[status(thm)],[1465])).
% 1.44/1.63 tff(1467,plain,
% 1.44/1.63 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1466])).
% 1.44/1.63 tff(1468,plain,
% 1.44/1.63 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[329, 1467])).
% 1.44/1.63 tff(1469,plain,
% 1.44/1.63 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[86, 82, 568])).
% 1.44/1.63 tff(1470,plain,
% 1.44/1.63 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1457])).
% 1.44/1.63 tff(1471,plain,
% 1.44/1.63 (b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.44/1.63 inference(symmetry,[status(thm)],[1470])).
% 1.44/1.63 tff(1472,plain,
% 1.44/1.63 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) <=> r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1457])).
% 1.44/1.63 tff(1473,plain,
% 1.44/1.63 ((~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) <=> (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1472])).
% 1.44/1.63 tff(1474,assumption,(r(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 1.44/1.63 tff(1475,plain,
% 1.44/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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))))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(1476,plain,
% 1.44/1.63 (((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(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))))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(1477,plain,
% 1.44/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(s(elem!1))))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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)))))))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1476])).
% 1.44/1.63 tff(1478,plain,
% 1.44/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(s(elem!1))))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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))))))))),
% 1.44/1.63 inference(transitivity,[status(thm)],[1477, 1475])).
% 1.44/1.63 tff(1479,plain,
% 1.44/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(s(elem!1))))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(1480,plain,
% 1.44/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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)))))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[1479, 1478])).
% 1.44/1.63 tff(1481,plain,
% 1.44/1.63 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1480, 183, 333, 1474])).
% 1.44/1.63 tff(1482,plain,
% 1.44/1.63 (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[1481, 1473])).
% 1.44/1.63 tff(1483,plain,
% 1.44/1.63 ((s(s(s(s(s(elem!1))))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))),
% 1.44/1.63 inference(commutativity,[status(thm)],[])).
% 1.44/1.63 tff(1484,plain,
% 1.44/1.63 ((~(s(s(s(s(s(elem!1))))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1483])).
% 1.44/1.63 tff(1485,plain,
% 1.44/1.63 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(z))) = s(z))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(1486,plain,
% 1.44/1.63 (inj_0(s(s(z))) = s(z)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1485, 18])).
% 1.44/1.63 tff(1487,assumption,(s(s(s(s(s(elem!1))))) = s(s(s(s(z))))), introduced(assumption)).
% 1.44/1.63 tff(1488,plain,
% 1.44/1.63 (s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))),
% 1.44/1.63 inference(symmetry,[status(thm)],[1487])).
% 1.44/1.63 tff(1489,plain,
% 1.44/1.63 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1488])).
% 1.44/1.63 tff(1490,plain,
% 1.44/1.63 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(z))))) = s(s(s(z))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(1491,plain,
% 1.44/1.63 (inj_0(s(s(s(s(z))))) = s(s(s(z)))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1490, 18])).
% 1.44/1.63 tff(1492,plain,
% 1.44/1.63 (s(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 1.44/1.63 inference(symmetry,[status(thm)],[1491])).
% 1.44/1.63 tff(1493,plain,
% 1.44/1.63 (s(s(s(z))) = s(s(s(s(elem!1))))),
% 1.44/1.63 inference(transitivity,[status(thm)],[1492, 1489, 325])).
% 1.44/1.63 tff(1494,plain,
% 1.44/1.63 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(elem!1)))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1493])).
% 1.44/1.63 tff(1495,plain,
% 1.44/1.63 (s(s(z)) = s(s(s(elem!1)))),
% 1.44/1.63 inference(transitivity,[status(thm)],[25, 1494, 351])).
% 1.44/1.63 tff(1496,plain,
% 1.44/1.63 (inj_0(s(s(z))) = inj_0(s(s(s(elem!1))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1495])).
% 1.44/1.63 tff(1497,plain,
% 1.44/1.63 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(z)))),
% 1.44/1.63 inference(symmetry,[status(thm)],[1496])).
% 1.44/1.63 tff(1498,plain,
% 1.44/1.63 (s(s(elem!1)) = s(z)),
% 1.44/1.63 inference(transitivity,[status(thm)],[104, 1497, 1486])).
% 1.44/1.63 tff(1499,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[113, 1498])).
% 1.44/1.63 tff(1500,plain,(~(s(s(s(s(s(elem!1))))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(1501,plain,
% 1.44/1.63 (~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[1500, 1484])).
% 1.44/1.63 tff(1502,plain,
% 1.44/1.63 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))) | r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))) | r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(1503,plain,
% 1.44/1.63 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))) | r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(1504,plain,
% 1.44/1.63 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))) | r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[1503, 1502])).
% 1.44/1.63 tff(1505,plain,
% 1.44/1.63 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))) | r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1504, 47])).
% 1.44/1.63 tff(1506,plain,
% 1.44/1.63 (b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))) | r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1505, 1501])).
% 1.44/1.63 tff(1507,plain,
% 1.44/1.63 (b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1506, 1482])).
% 1.44/1.63 tff(1508,plain,
% 1.44/1.63 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[1507, 1471])).
% 1.44/1.63 tff(1509,plain,
% 1.44/1.63 (b(s(s(elem!1)), s(s(s(s(elem!1))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[94, 1457])).
% 1.44/1.63 tff(1510,plain,
% 1.44/1.63 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.44/1.63 inference(symmetry,[status(thm)],[1509])).
% 1.44/1.63 tff(1511,plain,
% 1.44/1.63 (r(s(s(elem!1)), s(s(s(s(elem!1))))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[94, 1457])).
% 1.44/1.63 tff(1512,plain,
% 1.44/1.63 ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) <=> (~r(s(s(z)), s(s(s(s(z))))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1511])).
% 1.44/1.63 tff(1513,plain,
% 1.44/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(1514,plain,
% 1.44/1.64 (((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(1515,plain,
% 1.44/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[1514])).
% 1.44/1.64 tff(1516,plain,
% 1.44/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.44/1.64 inference(transitivity,[status(thm)],[1515, 1513])).
% 1.44/1.64 tff(1517,plain,
% 1.44/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(1518,plain,
% 1.44/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[1517, 1516])).
% 1.44/1.64 tff(1519,plain,
% 1.44/1.64 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1518, 183, 216, 1474])).
% 1.44/1.64 tff(1520,plain,
% 1.44/1.64 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[1519, 1512])).
% 1.44/1.64 tff(1521,assumption,(s(s(z)) = s(s(s(s(z))))), introduced(assumption)).
% 1.44/1.64 tff(1522,plain,
% 1.44/1.64 (inj_0(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[1521])).
% 1.44/1.64 tff(1523,plain,
% 1.44/1.64 (s(z) = inj_0(s(s(z)))),
% 1.44/1.64 inference(symmetry,[status(thm)],[1486])).
% 1.44/1.64 tff(1524,plain,
% 1.44/1.64 (s(z) = s(s(s(z)))),
% 1.44/1.64 inference(transitivity,[status(thm)],[1523, 1522, 1491])).
% 1.44/1.64 tff(1525,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[767, 1524])).
% 1.44/1.64 tff(1526,plain,(~(s(s(z)) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(1527,plain,
% 1.44/1.64 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(1528,plain,
% 1.44/1.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z))))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(1529,plain,
% 1.44/1.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[1528, 1527])).
% 1.44/1.64 tff(1530,plain,
% 1.44/1.64 ((s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1529, 47])).
% 1.44/1.64 tff(1531,plain,
% 1.44/1.64 (b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1530, 1526])).
% 1.44/1.64 tff(1532,plain,
% 1.44/1.64 (b(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1531, 1520])).
% 1.44/1.64 tff(1533,plain,
% 1.44/1.64 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[1532, 1510])).
% 1.44/1.64 tff(1534,plain,
% 1.44/1.64 ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 1.44/1.64 inference(commutativity,[status(thm)],[])).
% 1.44/1.64 tff(1535,plain,
% 1.44/1.64 ((s(s(s(s(s(elem!1))))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 1.44/1.64 inference(symmetry,[status(thm)],[1534])).
% 1.44/1.64 tff(1536,plain,
% 1.44/1.64 ((~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(s(s(s(s(elem!1)))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[1535])).
% 1.44/1.64 tff(1537,plain,
% 1.44/1.64 (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[358, 1536])).
% 1.44/1.64 tff(1538,plain,
% 1.44/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(1539,plain,
% 1.44/1.64 (((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(1540,plain,
% 1.44/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[1539])).
% 1.44/1.64 tff(1541,plain,
% 1.44/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.44/1.64 inference(transitivity,[status(thm)],[1540, 1538])).
% 1.44/1.64 tff(1542,plain,
% 1.44/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(1543,plain,
% 1.44/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[1542, 1541])).
% 1.44/1.64 tff(1544,plain,
% 1.44/1.64 (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1543, 183, 216, 333])).
% 1.44/1.64 tff(1545,plain,
% 1.44/1.64 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | b(s(s(elem!1)), s(s(s(s(s(elem!1)))))) | r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | b(s(s(elem!1)), s(s(s(s(s(elem!1)))))) | r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(1546,plain,
% 1.44/1.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | b(s(s(elem!1)), s(s(s(s(s(elem!1)))))) | r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(1547,plain,
% 1.44/1.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | b(s(s(elem!1)), s(s(s(s(s(elem!1)))))) | r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[1546, 1545])).
% 1.44/1.64 tff(1548,plain,
% 1.44/1.64 ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1547, 47, 1544])).
% 1.44/1.64 tff(1549,plain,
% 1.44/1.64 (b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1548, 1537])).
% 1.44/1.64 tff(1550,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[339, 183, 216, 333, 959])).
% 1.44/1.64 tff(1551,plain,((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(1552,plain,
% 1.44/1.64 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1551, 333, 216])).
% 1.44/1.64 tff(1553,assumption,(~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))), introduced(assumption)).
% 1.44/1.64 tff(1554,assumption,(~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))), introduced(assumption)).
% 1.44/1.64 tff(1555,assumption,(~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))), introduced(assumption)).
% 1.44/1.64 tff(1556,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[361, 47, 1555, 1554, 1553])).
% 1.44/1.64 tff(1557,plain,(r(s(s(s(s(s(elem!1))))), s(s(elem!1))) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | b(s(s(s(s(s(elem!1))))), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(1558,plain,
% 1.44/1.64 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1557, 1552, 358])).
% 1.44/1.64 tff(1559,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(1560,plain,
% 1.44/1.64 (((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(1561,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[1560])).
% 1.44/1.64 tff(1562,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.44/1.64 inference(transitivity,[status(thm)],[1561, 1559])).
% 1.44/1.64 tff(1563,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(1564,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[1563, 1562])).
% 1.44/1.64 tff(1565,plain,
% 1.44/1.64 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1564, 246, 1558, 1549, 1533])).
% 1.44/1.64 tff(1566,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1565, 1508])).
% 1.44/1.64 tff(1567,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (~(z = elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(1568,plain,
% 1.44/1.64 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1567, 1469, 88, 216])).
% 1.44/1.64 tff(1569,plain,
% 1.44/1.64 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(1570,plain,
% 1.44/1.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(1571,plain,
% 1.44/1.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1)),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[1570, 1569])).
% 1.44/1.64 tff(1572,plain,
% 1.44/1.64 ((s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1571, 47, 1568])).
% 1.44/1.64 tff(1573,plain,
% 1.44/1.64 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1572, 1468])).
% 1.44/1.64 tff(1574,assumption,(b(elem!1, s(elem!1))), introduced(assumption)).
% 1.44/1.64 tff(1575,plain,
% 1.44/1.64 (r(s(s(elem!1)), z)),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[216, 152])).
% 1.44/1.64 tff(1576,plain,
% 1.44/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(1577,plain,
% 1.44/1.64 (((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z))) <=> ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(1578,plain,
% 1.44/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[1577])).
% 1.44/1.64 tff(1579,plain,
% 1.44/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))),
% 1.44/1.64 inference(transitivity,[status(thm)],[1578, 1576])).
% 1.44/1.64 tff(1580,plain,
% 1.44/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(1581,plain,
% 1.44/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[1580, 1579])).
% 1.44/1.64 tff(1582,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1581, 183, 267, 216, 172])).
% 1.44/1.64 tff(1583,plain,((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(1584,plain,
% 1.44/1.64 (~r(z, elem!1)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1583, 216, 172])).
% 1.44/1.64 tff(1585,plain,
% 1.44/1.64 (z = elem!1),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[60, 1584, 55])).
% 1.44/1.64 tff(1586,plain,
% 1.44/1.64 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 1.44/1.64 inference(monotonicity,[status(thm)],[1585])).
% 1.44/1.64 tff(1587,plain,
% 1.44/1.64 ((s(s(s(z))) = z) <=> (elem!1 = s(s(s(z))))),
% 1.44/1.64 inference(transitivity,[status(thm)],[1586, 73])).
% 1.44/1.64 tff(1588,plain,
% 1.44/1.64 ((elem!1 = s(s(s(z)))) <=> (s(s(s(z))) = z)),
% 1.44/1.64 inference(symmetry,[status(thm)],[1587])).
% 1.44/1.64 tff(1589,plain,
% 1.44/1.64 (elem!1 = z),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1440, 1585])).
% 1.44/1.64 tff(1590,plain,
% 1.44/1.64 (s(elem!1) = s(z)),
% 1.44/1.64 inference(monotonicity,[status(thm)],[1038])).
% 1.44/1.64 tff(1591,plain,
% 1.44/1.64 (s(s(elem!1)) = s(s(z))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[1590])).
% 1.44/1.64 tff(1592,plain,
% 1.44/1.64 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[1591])).
% 1.44/1.64 tff(1593,plain,
% 1.44/1.64 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[1592])).
% 1.44/1.64 tff(1594,plain,
% 1.44/1.64 (b(s(s(s(s(s(elem!1))))), s(s(s(z)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.44/1.64 inference(symmetry,[status(thm)],[1593])).
% 1.44/1.64 tff(1595,plain,
% 1.44/1.64 (b(s(s(s(s(s(elem!1))))), elem!1) <=> b(s(s(s(s(s(elem!1))))), z)),
% 1.44/1.64 inference(monotonicity,[status(thm)],[1038])).
% 1.44/1.64 tff(1596,plain,
% 1.44/1.64 ((~b(s(s(s(s(s(elem!1))))), elem!1)) <=> (~b(s(s(s(s(s(elem!1))))), z))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[1595])).
% 1.44/1.64 tff(1597,plain,
% 1.44/1.64 (~b(s(s(s(s(s(elem!1))))), z)),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[82, 1596])).
% 1.44/1.64 tff(1598,plain,
% 1.44/1.64 (((~![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))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(1599,plain,
% 1.44/1.64 ((~![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))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(1600,plain,
% 1.44/1.64 ((~![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)),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[1599, 1598])).
% 1.44/1.64 tff(1601,plain,
% 1.44/1.64 (b(s(s(s(s(s(elem!1))))), z) | r(s(s(s(s(s(elem!1))))), z)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1600, 47, 65])).
% 1.44/1.64 tff(1602,plain,
% 1.44/1.64 (r(s(s(s(s(s(elem!1))))), z)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1601, 1597])).
% 1.44/1.64 tff(1603,plain,
% 1.44/1.64 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), z)),
% 1.44/1.64 inference(monotonicity,[status(thm)],[1038])).
% 1.44/1.64 tff(1604,plain,
% 1.44/1.64 (r(s(s(s(z))), z)),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[634, 1603])).
% 1.44/1.64 tff(1605,plain,
% 1.44/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(1606,plain,
% 1.44/1.64 (((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(1607,plain,
% 1.44/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), z))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[1606])).
% 1.44/1.64 tff(1608,plain,
% 1.44/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 1.44/1.64 inference(transitivity,[status(thm)],[1607, 1605])).
% 1.44/1.64 tff(1609,plain,
% 1.44/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(1610,plain,
% 1.44/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), z))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[1609, 1608])).
% 1.44/1.64 tff(1611,plain,
% 1.44/1.64 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1610, 183, 1604, 1602])).
% 1.44/1.64 tff(1612,assumption,(s(s(s(s(s(elem!1))))) = s(s(s(z)))), introduced(assumption)).
% 1.44/1.64 tff(1613,plain,
% 1.44/1.64 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(z))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[1612])).
% 1.44/1.64 tff(1614,plain,
% 1.44/1.64 (s(s(s(s(elem!1)))) = s(s(z))),
% 1.44/1.64 inference(transitivity,[status(thm)],[326, 1613, 24])).
% 1.44/1.64 tff(1615,plain,
% 1.44/1.64 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(z)))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[1614])).
% 1.44/1.64 tff(1616,plain,
% 1.44/1.64 (inj_0(s(s(z))) = inj_0(s(s(s(s(elem!1)))))),
% 1.44/1.64 inference(symmetry,[status(thm)],[1615])).
% 1.44/1.64 tff(1617,plain,
% 1.44/1.64 (s(z) = s(s(s(elem!1)))),
% 1.44/1.64 inference(transitivity,[status(thm)],[1523, 1616, 351])).
% 1.44/1.64 tff(1618,plain,
% 1.44/1.64 (inj_0(s(z)) = inj_0(s(s(s(elem!1))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[1617])).
% 1.44/1.64 tff(1619,plain,
% 1.44/1.64 (inj_0(s(s(s(elem!1)))) = inj_0(s(z))),
% 1.44/1.64 inference(symmetry,[status(thm)],[1618])).
% 1.44/1.64 tff(1620,plain,
% 1.44/1.64 (s(s(elem!1)) = z),
% 1.44/1.64 inference(transitivity,[status(thm)],[104, 1619, 20])).
% 1.44/1.64 tff(1621,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[139, 1620])).
% 1.44/1.64 tff(1622,plain,(~(s(s(s(s(s(elem!1))))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(1623,plain,
% 1.44/1.64 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(s(z)))) | b(s(s(s(s(s(elem!1))))), s(s(s(z)))) | r(s(s(s(s(s(elem!1))))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(s(z)))) | b(s(s(s(s(s(elem!1))))), s(s(s(z)))) | r(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(1624,plain,
% 1.44/1.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(s(z)))) | b(s(s(s(s(s(elem!1))))), s(s(s(z)))) | r(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(1625,plain,
% 1.44/1.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(s(z)))) | b(s(s(s(s(s(elem!1))))), s(s(s(z)))) | r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[1624, 1623])).
% 1.44/1.64 tff(1626,plain,
% 1.44/1.64 (b(s(s(s(s(s(elem!1))))), s(s(s(z)))) | r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1625, 47, 1622])).
% 1.44/1.64 tff(1627,plain,
% 1.44/1.64 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1626, 1611])).
% 1.44/1.64 tff(1628,plain,
% 1.44/1.64 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[1627, 1594])).
% 1.44/1.64 tff(1629,plain,
% 1.44/1.64 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(z))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[1591, 1592])).
% 1.44/1.64 tff(1630,plain,
% 1.44/1.64 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.44/1.64 inference(symmetry,[status(thm)],[1629])).
% 1.44/1.64 tff(1631,plain,
% 1.44/1.64 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(z)), s(s(s(z))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[1591])).
% 1.44/1.64 tff(1632,plain,
% 1.44/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(1633,plain,
% 1.44/1.64 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z)))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(1634,plain,
% 1.44/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[1633])).
% 1.44/1.64 tff(1635,plain,
% 1.44/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.44/1.64 inference(transitivity,[status(thm)],[1634, 1632])).
% 1.44/1.64 tff(1636,plain,
% 1.44/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(1637,plain,
% 1.44/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[1636, 1635])).
% 1.44/1.64 tff(1638,plain,
% 1.44/1.64 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1637, 183, 216, 634])).
% 1.44/1.64 tff(1639,plain,
% 1.44/1.64 (z = elem!1),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1041, 1038])).
% 1.44/1.64 tff(1640,plain,
% 1.44/1.64 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[115, 1639])).
% 1.44/1.64 tff(1641,plain,
% 1.44/1.64 (~(s(s(elem!1)) = s(s(s(z))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[421, 1640])).
% 1.44/1.64 tff(1642,plain,
% 1.44/1.64 (b(s(s(elem!1)), s(s(s(z))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[454, 1641, 1638])).
% 1.44/1.65 tff(1643,plain,
% 1.44/1.65 (b(s(s(z)), s(s(s(z))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[1642, 1631])).
% 1.44/1.65 tff(1644,plain,
% 1.44/1.65 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[1643, 1630])).
% 1.44/1.65 tff(1645,plain,
% 1.44/1.65 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[1592])).
% 1.44/1.65 tff(1646,plain,
% 1.44/1.65 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.65 inference(symmetry,[status(thm)],[1645])).
% 1.44/1.65 tff(1647,plain,
% 1.44/1.65 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[642, 634, 216])).
% 1.44/1.65 tff(1648,plain,
% 1.44/1.65 (b(s(s(s(z))), s(s(elem!1)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[689, 1640, 1647])).
% 1.44/1.65 tff(1649,plain,
% 1.44/1.65 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[1648, 1646])).
% 1.44/1.65 tff(1650,plain,
% 1.44/1.65 ((s(s(s(s(s(elem!1))))) = elem!1) <=> (s(s(s(s(s(elem!1))))) = z)),
% 1.44/1.65 inference(monotonicity,[status(thm)],[1038])).
% 1.44/1.65 tff(1651,plain,
% 1.44/1.65 ((s(s(s(s(s(elem!1))))) = z) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 1.44/1.65 inference(symmetry,[status(thm)],[1650])).
% 1.44/1.65 tff(1652,plain,
% 1.44/1.65 ((~(s(s(s(s(s(elem!1))))) = z)) <=> (~(s(s(s(s(s(elem!1))))) = elem!1))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[1651])).
% 1.44/1.65 tff(1653,plain,
% 1.44/1.65 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[65, 1652])).
% 1.44/1.65 tff(1654,plain,
% 1.44/1.65 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[86, 1653, 82])).
% 1.44/1.65 tff(1655,plain,
% 1.44/1.65 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1551, 1654, 216])).
% 1.44/1.65 tff(1656,plain,
% 1.44/1.65 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1557, 1655, 1555])).
% 1.44/1.65 tff(1657,assumption,(b(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 1.44/1.65 tff(1658,assumption,(b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))), introduced(assumption)).
% 1.44/1.65 tff(1659,assumption,(b(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 1.44/1.65 tff(1660,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(1661,plain,
% 1.44/1.65 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(1662,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[1661])).
% 1.44/1.65 tff(1663,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[1662, 1660])).
% 1.44/1.65 tff(1664,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(1665,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[1664, 1663])).
% 1.44/1.65 tff(1666,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1665, 246, 946, 1659, 1658, 1657])).
% 1.44/1.65 tff(1667,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(1668,plain,
% 1.44/1.65 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1667, 1656, 1649, 1644])).
% 1.44/1.65 tff(1669,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1668, 1628])).
% 1.44/1.65 tff(1670,plain,((~(elem!1 = z)) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | b(s(s(s(s(s(elem!1))))), elem!1) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(1671,plain,
% 1.44/1.65 (~r(s(s(s(z))), elem!1)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1670, 1589, 216, 82, 1555])).
% 1.44/1.65 tff(1672,plain,
% 1.44/1.65 (s(s(s(z))) = elem!1),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[647, 1671, 1])).
% 1.44/1.65 tff(1673,assumption,(s(s(s(z))) = elem!1), introduced(assumption)).
% 1.44/1.65 tff(1674,plain,
% 1.44/1.65 (elem!1 = s(s(s(z)))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[1673, 73])).
% 1.44/1.65 tff(1675,assumption,(~(elem!1 = s(s(s(z))))), introduced(assumption)).
% 1.44/1.65 tff(1676,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1675, 1674])).
% 1.44/1.65 tff(1677,plain,((~(s(s(s(z))) = elem!1)) | (elem!1 = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(1678,plain,
% 1.44/1.65 (elem!1 = s(s(s(z)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1677, 1672])).
% 1.44/1.65 tff(1679,plain,
% 1.44/1.65 (s(s(s(z))) = z),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[1678, 1588])).
% 1.44/1.65 tff(1680,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[80, 1679])).
% 1.44/1.65 tff(1681,plain,((~r(s(s(elem!1)), elem!1)) | b(s(s(s(z))), elem!1) | b(s(s(s(s(s(elem!1))))), elem!1) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | b(z, elem!1) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(1682,plain,
% 1.44/1.65 (b(s(s(s(z))), elem!1)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1681, 82, 55, 358, 216, 1575])).
% 1.44/1.65 tff(1683,plain,
% 1.44/1.65 (b(s(s(s(elem!1))), elem!1)),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[1682, 549])).
% 1.44/1.65 tff(1684,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(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)))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(1685,plain,
% 1.44/1.65 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(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)))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(1686,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(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))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[1685])).
% 1.44/1.65 tff(1687,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(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)))),
% 1.44/1.65 inference(transitivity,[status(thm)],[1686, 1684])).
% 1.44/1.65 tff(1688,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(1689,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[1688, 1687])).
% 1.44/1.65 tff(1690,plain,
% 1.44/1.65 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1689, 246, 1200, 1683, 1574, 1573])).
% 1.44/1.65 tff(1691,plain,
% 1.44/1.65 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[1690, 1464])).
% 1.44/1.65 tff(1692,assumption,(s(s(s(s(z)))) = s(s(s(z)))), introduced(assumption)).
% 1.44/1.65 tff(1693,plain,
% 1.44/1.65 (s(s(s(z))) = s(s(s(s(z))))),
% 1.44/1.65 inference(symmetry,[status(thm)],[1692])).
% 1.44/1.65 tff(1694,plain,
% 1.44/1.65 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(z)))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[1693])).
% 1.44/1.65 tff(1695,plain,
% 1.44/1.65 (s(s(z)) = s(s(s(s(z))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[25, 1694, 1491, 1693])).
% 1.44/1.65 tff(1696,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1526, 1695])).
% 1.44/1.65 tff(1697,plain,(~(s(s(s(s(z)))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(1698,plain,
% 1.44/1.65 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(1699,plain,
% 1.44/1.65 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(1700,plain,
% 1.44/1.65 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[1699, 1698])).
% 1.44/1.65 tff(1701,plain,
% 1.44/1.65 ((s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1700, 47])).
% 1.44/1.65 tff(1702,plain,
% 1.44/1.65 (b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1701, 1697])).
% 1.44/1.65 tff(1703,plain,
% 1.44/1.65 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1702, 1691])).
% 1.44/1.65 tff(1704,plain,
% 1.44/1.65 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[1703, 1459])).
% 1.44/1.65 tff(1705,plain,
% 1.44/1.65 (r(s(s(s(s(elem!1)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(elem!1))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[1457])).
% 1.44/1.65 tff(1706,plain,
% 1.44/1.65 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.44/1.65 inference(symmetry,[status(thm)],[1705])).
% 1.44/1.65 tff(1707,plain,
% 1.44/1.65 ((s(s(s(s(z)))) = s(z)) <=> (s(s(s(s(z)))) = s(elem!1))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[89])).
% 1.44/1.65 tff(1708,plain,
% 1.44/1.65 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[1707])).
% 1.44/1.65 tff(1709,assumption,(s(s(s(s(z)))) = s(z)), introduced(assumption)).
% 1.44/1.65 tff(1710,plain,
% 1.44/1.65 (inj_0(s(s(s(s(z))))) = inj_0(s(z))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[1709])).
% 1.44/1.65 tff(1711,plain,
% 1.44/1.65 (s(s(s(z))) = z),
% 1.44/1.65 inference(transitivity,[status(thm)],[1492, 1710, 20])).
% 1.44/1.65 tff(1712,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[80, 1711])).
% 1.44/1.65 tff(1713,plain,(~(s(s(s(s(z)))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(1714,plain,
% 1.44/1.65 (~(s(s(s(s(z)))) = s(elem!1))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[1713, 1708])).
% 1.44/1.65 tff(1715,plain,
% 1.44/1.65 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(elem!1))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[1457])).
% 1.44/1.65 tff(1716,plain,
% 1.44/1.65 ((~b(s(s(s(s(elem!1)))), s(elem!1))) <=> (~b(s(s(s(s(z)))), s(elem!1)))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[1715])).
% 1.44/1.65 tff(1717,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(1718,plain,
% 1.44/1.65 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(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)))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(1719,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[1718])).
% 1.44/1.65 tff(1720,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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)))),
% 1.44/1.65 inference(transitivity,[status(thm)],[1719, 1717])).
% 1.44/1.65 tff(1721,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(1722,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[1721, 1720])).
% 1.44/1.65 tff(1723,plain,
% 1.44/1.65 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1722, 246, 1200, 1574, 1573])).
% 1.44/1.65 tff(1724,plain,
% 1.44/1.65 (~b(s(s(s(s(z)))), s(elem!1))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[1723, 1716])).
% 1.44/1.65 tff(1725,plain,
% 1.44/1.65 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1)))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(1726,plain,
% 1.44/1.65 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1)))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(1727,plain,
% 1.44/1.65 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[1726, 1725])).
% 1.44/1.65 tff(1728,plain,
% 1.44/1.65 ((s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1727, 47])).
% 1.44/1.65 tff(1729,plain,
% 1.44/1.65 (r(s(s(s(s(z)))), s(elem!1))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1728, 1724, 1714])).
% 1.44/1.65 tff(1730,plain,
% 1.44/1.65 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[1729, 1706])).
% 1.44/1.65 tff(1731,plain,
% 1.44/1.65 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(z))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[410])).
% 1.44/1.65 tff(1732,plain,
% 1.44/1.65 (r(s(elem!1), s(s(s(z)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.65 inference(symmetry,[status(thm)],[1731])).
% 1.44/1.65 tff(1733,plain,
% 1.44/1.65 ((s(z) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[89])).
% 1.44/1.65 tff(1734,plain,
% 1.44/1.65 ((~(s(z) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[1733])).
% 1.44/1.65 tff(1735,plain,
% 1.44/1.65 (~(s(elem!1) = s(s(s(z))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[767, 1734])).
% 1.44/1.65 tff(1736,plain,
% 1.44/1.65 (b(s(elem!1), s(s(s(z)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[409])).
% 1.44/1.65 tff(1737,plain,
% 1.44/1.65 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(z))))),
% 1.44/1.65 inference(symmetry,[status(thm)],[1736])).
% 1.44/1.65 tff(1738,plain,
% 1.44/1.65 ((~b(s(elem!1), s(s(s(elem!1))))) <=> (~b(s(elem!1), s(s(s(z)))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[1737])).
% 1.44/1.65 tff(1739,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(1740,plain,
% 1.44/1.65 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(1741,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[1740])).
% 1.44/1.65 tff(1742,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.65 inference(transitivity,[status(thm)],[1741, 1739])).
% 1.44/1.65 tff(1743,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(1744,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[1743, 1742])).
% 1.44/1.65 tff(1745,plain,
% 1.44/1.65 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1744, 246, 1200, 1683, 1574])).
% 1.44/1.65 tff(1746,plain,
% 1.44/1.65 (~b(s(elem!1), s(s(s(z))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[1745, 1738])).
% 1.44/1.65 tff(1747,assumption,(~b(s(elem!1), s(s(s(z))))), introduced(assumption)).
% 1.44/1.65 tff(1748,assumption,(~r(s(elem!1), s(s(s(z))))), introduced(assumption)).
% 1.44/1.65 tff(1749,assumption,(~(s(elem!1) = s(s(s(z))))), introduced(assumption)).
% 1.44/1.65 tff(1750,plain,
% 1.44/1.65 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z)))) | r(s(elem!1), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z)))) | r(s(elem!1), s(s(s(z)))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(1751,plain,
% 1.44/1.65 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z)))) | r(s(elem!1), s(s(s(z)))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(1752,plain,
% 1.44/1.65 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z)))) | r(s(elem!1), s(s(s(z))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[1751, 1750])).
% 1.44/1.65 tff(1753,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1752, 47, 1749, 1748, 1747])).
% 1.44/1.65 tff(1754,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,[]))).
% 1.44/1.66 tff(1755,plain,
% 1.44/1.66 (r(s(elem!1), s(s(s(z))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1754, 1746, 1735])).
% 1.44/1.66 tff(1756,plain,
% 1.44/1.66 (r(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[1755, 1732])).
% 1.44/1.66 tff(1757,plain,
% 1.44/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(1758,plain,
% 1.44/1.66 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(1759,plain,
% 1.44/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[1758])).
% 1.44/1.66 tff(1760,plain,
% 1.44/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[1759, 1757])).
% 1.44/1.66 tff(1761,plain,
% 1.44/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(1762,plain,
% 1.44/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[1761, 1760])).
% 1.44/1.66 tff(1763,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1762, 183, 1756, 1730, 1704])).
% 1.44/1.66 tff(1764,plain,(b(s(s(s(s(s(elem!1))))), elem!1) | (~(z = elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(1765,plain,
% 1.44/1.66 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1764, 1451, 1455, 88, 157, 55])).
% 1.44/1.66 tff(1766,plain,
% 1.44/1.66 (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(s(z)))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[1457])).
% 1.44/1.66 tff(1767,plain,
% 1.44/1.66 (r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.44/1.66 inference(symmetry,[status(thm)],[1766])).
% 1.44/1.66 tff(1768,plain,
% 1.44/1.66 (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(z)))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[1457])).
% 1.44/1.66 tff(1769,plain,
% 1.44/1.66 ((~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(z))))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[1768])).
% 1.44/1.66 tff(1770,plain,
% 1.44/1.66 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[93])).
% 1.44/1.66 tff(1771,plain,
% 1.44/1.66 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(z)), s(s(s(z))))),
% 1.44/1.66 inference(symmetry,[status(thm)],[1770])).
% 1.44/1.66 tff(1772,plain,
% 1.44/1.66 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 1.44/1.66 inference(symmetry,[status(thm)],[415])).
% 1.44/1.66 tff(1773,plain,
% 1.44/1.66 ((~r(s(s(elem!1)), s(s(s(elem!1))))) <=> (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[1772])).
% 1.44/1.66 tff(1774,plain,
% 1.44/1.66 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), z)),
% 1.44/1.66 inference(monotonicity,[status(thm)],[341])).
% 1.44/1.66 tff(1775,plain,
% 1.44/1.66 (r(s(s(s(elem!1))), z) <=> r(s(s(s(elem!1))), elem!1)),
% 1.44/1.66 inference(symmetry,[status(thm)],[1774])).
% 1.44/1.66 tff(1776,plain,
% 1.44/1.66 (r(s(s(s(elem!1))), z) <=> r(s(s(s(z))), elem!1)),
% 1.44/1.66 inference(monotonicity,[status(thm)],[410, 88])).
% 1.44/1.66 tff(1777,plain,
% 1.44/1.66 (r(s(s(s(z))), elem!1) <=> r(s(s(s(elem!1))), z)),
% 1.44/1.66 inference(symmetry,[status(thm)],[1776])).
% 1.44/1.66 tff(1778,plain,
% 1.44/1.66 (r(s(s(s(elem!1))), z)),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[634, 1777])).
% 1.44/1.66 tff(1779,plain,
% 1.44/1.66 (r(s(s(s(elem!1))), elem!1)),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[1778, 1775])).
% 1.44/1.66 tff(1780,plain,
% 1.44/1.66 ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1372, 183, 216])).
% 1.44/1.66 tff(1781,plain,
% 1.44/1.66 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1780, 1779])).
% 1.44/1.66 tff(1782,plain,
% 1.44/1.66 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[1781, 1773])).
% 1.44/1.66 tff(1783,plain,
% 1.44/1.66 (b(s(s(elem!1)), s(s(s(z))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[454, 1782, 422])).
% 1.44/1.66 tff(1784,plain,
% 1.44/1.66 (b(s(s(z)), s(s(s(z))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[1783, 1771])).
% 1.44/1.66 tff(1785,plain,
% 1.44/1.66 ((s(s(s(s(s(elem!1))))) = s(z)) <=> (s(s(s(s(s(elem!1))))) = s(elem!1))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[89])).
% 1.44/1.66 tff(1786,plain,
% 1.44/1.66 ((~(s(s(s(s(s(elem!1))))) = s(z))) <=> (~(s(s(s(s(s(elem!1))))) = s(elem!1)))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[1785])).
% 1.44/1.66 tff(1787,plain,
% 1.44/1.66 (~(s(s(s(s(s(elem!1))))) = s(elem!1))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[331, 1786])).
% 1.44/1.66 tff(1788,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(1789,plain,
% 1.44/1.66 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(1790,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[1789])).
% 1.44/1.66 tff(1791,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[1790, 1788])).
% 1.44/1.66 tff(1792,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(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))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(1793,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(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)))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[1792, 1791])).
% 1.44/1.66 tff(1794,plain,
% 1.44/1.66 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1793, 246, 714, 1200, 1574])).
% 1.44/1.66 tff(1795,plain,
% 1.44/1.66 ((s(s(s(s(s(elem!1))))) = s(elem!1)) | b(s(s(s(s(s(elem!1))))), s(elem!1)) | r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1253, 47])).
% 1.44/1.66 tff(1796,plain,
% 1.44/1.66 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1795, 1794, 1787])).
% 1.44/1.66 tff(1797,plain,
% 1.44/1.66 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[409])).
% 1.44/1.66 tff(1798,plain,
% 1.44/1.66 (b(s(s(s(z))), s(s(elem!1)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[689, 1647, 416])).
% 1.44/1.66 tff(1799,plain,
% 1.44/1.66 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[1798, 1797])).
% 1.44/1.66 tff(1800,plain,
% 1.44/1.66 ((s(elem!1) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(elem!1))),
% 1.44/1.66 inference(commutativity,[status(thm)],[])).
% 1.44/1.66 tff(1801,plain,
% 1.44/1.66 ((s(s(s(s(s(elem!1))))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(elem!1))))))),
% 1.44/1.66 inference(symmetry,[status(thm)],[1800])).
% 1.44/1.66 tff(1802,plain,
% 1.44/1.66 ((~(s(s(s(s(s(elem!1))))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(s(elem!1)))))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[1801])).
% 1.44/1.66 tff(1803,plain,
% 1.44/1.66 (~(s(elem!1) = s(s(s(s(s(elem!1))))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[1787, 1802])).
% 1.44/1.66 tff(1804,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(1805,plain,
% 1.44/1.66 (((~b(s(elem!1), elem!1)) | (~b(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(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(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(elem!1), s(s(s(s(s(elem!1))))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(1806,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1)))))))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[1805])).
% 1.44/1.66 tff(1807,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[1806, 1804])).
% 1.44/1.66 tff(1808,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(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(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(1809,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1)))))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[1808, 1807])).
% 1.44/1.66 tff(1810,plain,
% 1.44/1.66 (~b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1809, 246, 714, 1200, 1574])).
% 1.44/1.66 tff(1811,plain,
% 1.44/1.66 ((s(elem!1) = s(s(s(s(s(elem!1)))))) | r(s(elem!1), s(s(s(s(s(elem!1))))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[395, 47, 1810])).
% 1.44/1.66 tff(1812,plain,
% 1.44/1.66 (r(s(elem!1), s(s(s(s(s(elem!1))))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1811, 1803])).
% 1.44/1.66 tff(1813,plain,
% 1.44/1.66 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[410])).
% 1.44/1.66 tff(1814,plain,
% 1.44/1.66 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 1.44/1.66 inference(transitivity,[status(thm)],[1813, 417])).
% 1.44/1.66 tff(1815,plain,
% 1.44/1.66 ((s(s(s(z))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 1.44/1.66 inference(symmetry,[status(thm)],[1814])).
% 1.44/1.66 tff(1816,plain,
% 1.44/1.66 ((~(s(s(s(z))) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[1815])).
% 1.44/1.66 tff(1817,plain,
% 1.44/1.66 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[416, 1816])).
% 1.44/1.66 tff(1818,plain,
% 1.44/1.66 (((~![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)))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(1819,plain,
% 1.44/1.66 ((~![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)))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(1820,plain,
% 1.44/1.66 ((~![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))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[1819, 1818])).
% 1.44/1.66 tff(1821,plain,
% 1.44/1.66 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1820, 47, 1781, 1817])).
% 1.44/1.66 tff(1822,plain,
% 1.44/1.66 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[1457])).
% 1.44/1.66 tff(1823,plain,
% 1.44/1.66 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.44/1.66 inference(symmetry,[status(thm)],[1822])).
% 1.44/1.66 tff(1824,plain,
% 1.44/1.66 ((~(s(s(s(s(z)))) = s(s(elem!1)))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[1823])).
% 1.44/1.66 tff(1825,plain,
% 1.44/1.66 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 1.44/1.66 inference(commutativity,[status(thm)],[])).
% 1.44/1.66 tff(1826,plain,
% 1.44/1.66 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[93])).
% 1.44/1.66 tff(1827,plain,
% 1.44/1.66 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 1.44/1.66 inference(transitivity,[status(thm)],[1826, 1825])).
% 1.44/1.66 tff(1828,plain,
% 1.44/1.66 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(elem!1))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[1827])).
% 1.44/1.66 tff(1829,plain,
% 1.44/1.66 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[1526, 1828])).
% 1.44/1.66 tff(1830,plain,
% 1.44/1.66 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[1829, 1824])).
% 1.44/1.66 tff(1831,plain,
% 1.44/1.66 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.44/1.66 inference(symmetry,[status(thm)],[1462])).
% 1.44/1.66 tff(1832,plain,
% 1.44/1.66 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[1460, 1831])).
% 1.44/1.66 tff(1833,assumption,(b(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 1.44/1.66 tff(1834,plain,
% 1.44/1.66 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[1833, 1832])).
% 1.44/1.66 tff(1835,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(1836,plain,
% 1.44/1.66 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(1837,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[1836])).
% 1.44/1.66 tff(1838,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[1837, 1835])).
% 1.44/1.66 tff(1839,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(1840,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[1839, 1838])).
% 1.44/1.66 tff(1841,plain,
% 1.44/1.66 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1840, 246, 1657, 1659, 1834])).
% 1.44/1.66 tff(1842,plain,
% 1.44/1.66 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(1843,plain,
% 1.44/1.66 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(1844,plain,
% 1.44/1.66 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[1843, 1842])).
% 1.44/1.66 tff(1845,plain,
% 1.44/1.66 ((s(s(s(s(elem!1)))) = s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1844, 47, 1841])).
% 1.44/1.66 tff(1846,plain,
% 1.44/1.66 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1845, 1830])).
% 1.44/1.66 tff(1847,plain,
% 1.44/1.66 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[409])).
% 1.44/1.66 tff(1848,plain,
% 1.44/1.66 (b(s(s(s(z))), s(z)) <=> b(s(s(s(z))), s(elem!1))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[89])).
% 1.44/1.66 tff(1849,plain,
% 1.44/1.66 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.66 inference(transitivity,[status(thm)],[1848, 1847])).
% 1.44/1.66 tff(1850,plain,
% 1.44/1.66 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(s(z))), s(z))),
% 1.44/1.66 inference(symmetry,[status(thm)],[1430])).
% 1.44/1.66 tff(1851,plain,
% 1.44/1.66 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(z))), s(z))),
% 1.44/1.66 inference(transitivity,[status(thm)],[1428, 1850])).
% 1.44/1.66 tff(1852,plain,
% 1.44/1.66 ((~r(s(s(s(elem!1))), s(elem!1))) <=> (~r(s(s(s(z))), s(z)))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[1851])).
% 1.44/1.66 tff(1853,assumption,(r(s(s(s(s(s(elem!1))))), s(elem!1))), introduced(assumption)).
% 1.44/1.66 tff(1854,assumption,(b(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 1.44/1.66 tff(1855,plain,
% 1.44/1.66 (r(s(s(s(s(s(elem!1))))), s(s(z))) <=> r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[93])).
% 1.44/1.66 tff(1856,plain,
% 1.44/1.66 (r(s(s(s(s(s(elem!1))))), s(s(elem!1))) <=> r(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.44/1.66 inference(symmetry,[status(thm)],[1855])).
% 1.44/1.66 tff(1857,plain,
% 1.44/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(1858,plain,
% 1.44/1.66 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(1859,plain,
% 1.44/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[1858])).
% 1.44/1.67 tff(1860,plain,
% 1.44/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[1859, 1857])).
% 1.44/1.67 tff(1861,plain,
% 1.44/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(1862,plain,
% 1.44/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[1861, 1860])).
% 1.44/1.67 tff(1863,plain,
% 1.44/1.67 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1862, 183, 1853, 820])).
% 1.44/1.67 tff(1864,plain,
% 1.44/1.67 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[811, 47, 771, 1863])).
% 1.44/1.67 tff(1865,plain,
% 1.44/1.67 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1667, 1864, 1659, 1657])).
% 1.44/1.67 tff(1866,plain,
% 1.44/1.67 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1557, 1865, 358])).
% 1.44/1.67 tff(1867,plain,
% 1.44/1.67 (r(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[1866, 1856])).
% 1.44/1.67 tff(1868,plain,
% 1.44/1.67 (r(s(s(s(s(s(elem!1))))), s(s(s(z)))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[409])).
% 1.44/1.67 tff(1869,plain,
% 1.44/1.67 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.44/1.67 inference(symmetry,[status(thm)],[1868])).
% 1.44/1.67 tff(1870,plain,
% 1.44/1.67 ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[1869])).
% 1.44/1.67 tff(1871,plain,
% 1.44/1.67 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[1863, 1870])).
% 1.44/1.67 tff(1872,plain,
% 1.44/1.67 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1626, 1871])).
% 1.44/1.67 tff(1873,plain,
% 1.44/1.67 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[410])).
% 1.44/1.67 tff(1874,plain,
% 1.44/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(1875,plain,
% 1.44/1.67 (((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(1876,plain,
% 1.44/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(elem!1))), s(s(s(s(s(elem!1)))))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[1875])).
% 1.44/1.67 tff(1877,plain,
% 1.44/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[1876, 1874])).
% 1.44/1.67 tff(1878,plain,
% 1.44/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(1879,plain,
% 1.44/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(elem!1))), s(s(s(s(s(elem!1)))))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[1878, 1877])).
% 1.44/1.67 tff(1880,plain,
% 1.44/1.67 (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1879, 183, 1853, 820])).
% 1.44/1.67 tff(1881,plain,
% 1.44/1.67 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[913, 47, 778, 1880])).
% 1.44/1.67 tff(1882,plain,
% 1.44/1.67 (b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[1881, 1873])).
% 1.44/1.67 tff(1883,assumption,(r(s(s(s(s(s(elem!1))))), s(s(z)))), introduced(assumption)).
% 1.44/1.67 tff(1884,assumption,(b(s(s(s(z))), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.44/1.67 tff(1885,assumption,(b(s(s(s(s(s(elem!1))))), s(s(s(z))))), introduced(assumption)).
% 1.44/1.67 tff(1886,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(1887,plain,
% 1.44/1.67 (((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(1888,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[1887])).
% 1.44/1.67 tff(1889,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[1888, 1886])).
% 1.44/1.67 tff(1890,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(1891,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[1890, 1889])).
% 1.44/1.67 tff(1892,plain,
% 1.44/1.67 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1891, 246, 1833, 1885, 1884])).
% 1.44/1.67 tff(1893,plain,
% 1.44/1.67 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(s(s(z))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(s(s(z))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(1894,plain,
% 1.44/1.67 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(s(s(z))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(1895,plain,
% 1.44/1.67 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(s(s(z))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[1894, 1893])).
% 1.44/1.67 tff(1896,plain,
% 1.44/1.67 ((s(s(s(s(s(elem!1))))) = s(s(s(s(z))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1895, 47])).
% 1.44/1.67 tff(1897,plain,
% 1.44/1.67 (b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1896, 1500])).
% 1.44/1.67 tff(1898,plain,
% 1.44/1.67 (r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1897, 1892])).
% 1.44/1.67 tff(1899,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(1900,plain,
% 1.44/1.67 (((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(1901,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[1900])).
% 1.44/1.67 tff(1902,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[1901, 1899])).
% 1.44/1.67 tff(1903,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(1904,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[1903, 1902])).
% 1.44/1.67 tff(1905,plain,
% 1.44/1.67 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1904, 246, 1833, 1885, 1884, 1854])).
% 1.44/1.67 tff(1906,plain,
% 1.44/1.67 (r(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1531, 1905])).
% 1.44/1.67 tff(1907,assumption,(r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))), introduced(assumption)).
% 1.44/1.67 tff(1908,assumption,(r(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 1.44/1.67 tff(1909,plain,
% 1.44/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(1910,plain,
% 1.44/1.67 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(1911,plain,
% 1.44/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(z))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[1910])).
% 1.44/1.67 tff(1912,plain,
% 1.44/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[1911, 1909])).
% 1.44/1.67 tff(1913,plain,
% 1.44/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(1914,plain,
% 1.44/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(z))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[1913, 1912])).
% 1.44/1.67 tff(1915,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1914, 183, 1908, 1907, 1883])).
% 1.44/1.67 tff(1916,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(1917,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1916, 1906, 1898, 1883])).
% 1.44/1.67 tff(1918,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(1919,plain,
% 1.44/1.67 (~r(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1918, 1882, 1854, 1833, 1872])).
% 1.44/1.67 tff(1920,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1919, 1867])).
% 1.44/1.67 tff(1921,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~(z = elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(1922,plain,
% 1.44/1.67 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1921, 1833, 1854, 88, 1659, 1657, 1853])).
% 1.44/1.67 tff(1923,plain,
% 1.44/1.67 (~r(s(s(s(z))), s(z))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[1922, 1852])).
% 1.44/1.67 tff(1924,plain,
% 1.44/1.67 (b(s(s(s(z))), s(z))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[52, 1923])).
% 1.44/1.67 tff(1925,plain,
% 1.44/1.67 (b(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[1924, 1849])).
% 1.44/1.67 tff(1926,plain,
% 1.44/1.67 (b(s(z), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[89])).
% 1.44/1.67 tff(1927,plain,
% 1.44/1.67 (b(s(z), s(s(s(z)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[1926, 1736])).
% 1.44/1.67 tff(1928,plain,
% 1.44/1.67 (r(s(z), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[89])).
% 1.44/1.67 tff(1929,plain,
% 1.44/1.67 (r(s(elem!1), s(s(s(z)))) <=> r(s(z), s(s(s(z))))),
% 1.44/1.67 inference(symmetry,[status(thm)],[1928])).
% 1.44/1.67 tff(1930,plain,
% 1.44/1.67 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(z), s(s(s(z))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[1731, 1929])).
% 1.44/1.67 tff(1931,plain,
% 1.44/1.67 ((~r(s(elem!1), s(s(s(elem!1))))) <=> (~r(s(z), s(s(s(z)))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[1930])).
% 1.44/1.67 tff(1932,assumption,(r(s(elem!1), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.44/1.67 tff(1933,plain,
% 1.44/1.67 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(elem!1)) = s(z))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[90])).
% 1.44/1.67 tff(1934,plain,
% 1.44/1.67 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = s(elem!1))),
% 1.44/1.67 inference(symmetry,[status(thm)],[1933])).
% 1.44/1.67 tff(1935,plain,
% 1.44/1.67 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[1934])).
% 1.44/1.67 tff(1936,plain,
% 1.44/1.67 (~(s(s(elem!1)) = s(elem!1))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[113, 1935])).
% 1.44/1.67 tff(1937,assumption,(b(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 1.44/1.67 tff(1938,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(1939,plain,
% 1.44/1.67 (((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(1940,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[1939])).
% 1.44/1.67 tff(1941,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.67 inference(transitivity,[status(thm)],[1940, 1938])).
% 1.44/1.67 tff(1942,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(1943,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[1942, 1941])).
% 1.44/1.67 tff(1944,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1943, 246, 363, 1937, 1200, 1574, 1657])).
% 1.44/1.67 tff(1945,plain,((~b(s(s(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(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(1946,plain,
% 1.44/1.67 (~b(s(s(elem!1)), s(elem!1))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1945, 1925, 1200, 1574, 1657])).
% 1.44/1.68 tff(1947,plain,
% 1.44/1.68 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1)))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(1948,plain,
% 1.44/1.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1)))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(1949,plain,
% 1.44/1.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[1948, 1947])).
% 1.44/1.68 tff(1950,plain,
% 1.44/1.68 (r(s(s(elem!1)), s(elem!1))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1949, 47, 1946, 1936])).
% 1.44/1.68 tff(1951,assumption,(r(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 1.44/1.68 tff(1952,plain,
% 1.44/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(1953,plain,
% 1.44/1.68 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(1954,plain,
% 1.44/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[1953])).
% 1.44/1.68 tff(1955,plain,
% 1.44/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[1954, 1952])).
% 1.44/1.68 tff(1956,plain,
% 1.44/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(1957,plain,
% 1.44/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[1956, 1955])).
% 1.44/1.68 tff(1958,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1957, 183, 1853, 959, 1951])).
% 1.44/1.68 tff(1959,plain,((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(1960,plain,
% 1.44/1.68 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1959, 1950, 1853])).
% 1.44/1.68 tff(1961,plain,
% 1.44/1.68 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1557, 1960, 358])).
% 1.44/1.68 tff(1962,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(1963,plain,
% 1.44/1.68 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(1964,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[1963])).
% 1.44/1.68 tff(1965,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[1964, 1962])).
% 1.44/1.68 tff(1966,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(1967,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[1966, 1965])).
% 1.44/1.68 tff(1968,plain,
% 1.44/1.68 (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1967, 246, 1961, 1657, 1659])).
% 1.44/1.68 tff(1969,plain,
% 1.44/1.68 (r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[913, 47, 778, 1968])).
% 1.44/1.68 tff(1970,plain,
% 1.44/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(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))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(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))))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(1971,plain,
% 1.44/1.68 (((~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(s(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(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))))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(1972,plain,
% 1.44/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(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)))))))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[1971])).
% 1.44/1.68 tff(1973,plain,
% 1.44/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(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))))))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[1972, 1970])).
% 1.44/1.68 tff(1974,plain,
% 1.44/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(1975,plain,
% 1.44/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(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)))))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[1974, 1973])).
% 1.44/1.68 tff(1976,plain,
% 1.44/1.68 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1975, 183, 1969, 1932])).
% 1.44/1.68 tff(1977,plain,
% 1.44/1.68 (~r(s(z), s(s(s(z))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[1976, 1931])).
% 1.44/1.68 tff(1978,plain,
% 1.44/1.68 (b(s(z), s(s(s(z))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1291, 1977])).
% 1.44/1.68 tff(1979,plain,
% 1.44/1.68 (b(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[1978, 1927])).
% 1.44/1.68 tff(1980,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(1981,plain,
% 1.44/1.68 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(1982,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[1981])).
% 1.44/1.68 tff(1983,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[1982, 1980])).
% 1.44/1.68 tff(1984,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(1985,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[1984, 1983])).
% 1.44/1.68 tff(1986,plain,
% 1.44/1.68 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1985, 246, 1979, 1925, 1834])).
% 1.44/1.68 tff(1987,plain,
% 1.44/1.68 (~b(s(s(s(s(z)))), s(elem!1))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[1986, 1716])).
% 1.44/1.68 tff(1988,plain,
% 1.44/1.68 (r(s(s(s(s(z)))), s(elem!1))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1728, 1987, 1714])).
% 1.44/1.68 tff(1989,plain,
% 1.44/1.68 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[1988, 1706])).
% 1.44/1.68 tff(1990,plain,
% 1.44/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(1991,plain,
% 1.44/1.68 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(1992,plain,
% 1.44/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[1991])).
% 1.44/1.68 tff(1993,plain,
% 1.44/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[1992, 1990])).
% 1.44/1.68 tff(1994,plain,
% 1.44/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(1995,plain,
% 1.44/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[1994, 1993])).
% 1.44/1.68 tff(1996,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1995, 183, 216, 1950, 1989, 1846])).
% 1.44/1.68 tff(1997,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)) | (~(z = elem!1)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(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(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(1998,plain,
% 1.44/1.68 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1997, 1821, 88, 1812, 216, 1799, 1796, 1200, 1574, 1784])).
% 1.44/1.68 tff(1999,plain,
% 1.44/1.68 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1702, 1998])).
% 1.44/1.68 tff(2000,plain,
% 1.44/1.68 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[1999, 1459])).
% 1.44/1.68 tff(2001,assumption,(b(elem!1, s(z))), introduced(assumption)).
% 1.44/1.68 tff(2002,assumption,(b(elem!1, s(s(s(z))))), introduced(assumption)).
% 1.44/1.68 tff(2003,assumption,(b(s(s(s(z))), s(z))), introduced(assumption)).
% 1.44/1.68 tff(2004,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(2005,plain,
% 1.44/1.68 (((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(2006,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[2005])).
% 1.44/1.68 tff(2007,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[2006, 2004])).
% 1.44/1.68 tff(2008,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(2009,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[2008, 2007])).
% 1.44/1.68 tff(2010,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2009, 246, 1044, 2001, 2002, 2003])).
% 1.44/1.68 tff(2011,plain,((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(2012,plain,
% 1.44/1.68 (~b(s(s(s(z))), s(z))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2011, 2002, 1044, 2001])).
% 1.44/1.68 tff(2013,plain,
% 1.44/1.68 (r(s(s(s(z))), s(z))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[52, 2012])).
% 1.44/1.68 tff(2014,plain,
% 1.44/1.68 (r(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[2013, 1431])).
% 1.44/1.68 tff(2015,plain,
% 1.44/1.68 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1862, 183, 1853, 2014])).
% 1.44/1.68 tff(2016,plain,
% 1.44/1.68 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[811, 47, 771, 2015])).
% 1.44/1.68 tff(2017,plain,
% 1.44/1.68 (b(elem!1, s(s(s(elem!1))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[2002, 716])).
% 1.44/1.68 tff(2018,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(2019,plain,
% 1.44/1.68 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(2020,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[2019])).
% 1.44/1.68 tff(2021,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.44/1.69 inference(transitivity,[status(thm)],[2020, 2018])).
% 1.44/1.69 tff(2022,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(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)))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(2023,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[2022, 2021])).
% 1.44/1.69 tff(2024,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2023, 246, 2017, 714, 2016, 1657, 1659])).
% 1.44/1.69 tff(2025,plain,((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~(z = elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(2026,plain,
% 1.44/1.69 (~b(elem!1, s(s(s(z))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2025, 1821, 714, 1799, 1796, 88, 1044, 2001])).
% 1.44/1.69 tff(2027,plain,
% 1.44/1.69 (r(elem!1, s(s(s(z))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[470, 2026, 718])).
% 1.44/1.69 tff(2028,plain,
% 1.44/1.69 (r(elem!1, s(s(s(elem!1))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[2027, 412])).
% 1.44/1.69 tff(2029,plain,
% 1.44/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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)))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(2030,plain,
% 1.44/1.69 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(2031,plain,
% 1.44/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[2030])).
% 1.44/1.69 tff(2032,plain,
% 1.44/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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)))),
% 1.44/1.69 inference(transitivity,[status(thm)],[2031, 2029])).
% 1.44/1.69 tff(2033,plain,
% 1.44/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(2034,plain,
% 1.44/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[2033, 2032])).
% 1.44/1.69 tff(2035,plain,
% 1.44/1.69 ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2034, 183, 2028])).
% 1.44/1.69 tff(2036,plain,
% 1.44/1.69 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2035, 2000])).
% 1.44/1.69 tff(2037,plain,
% 1.44/1.69 ((s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1571, 47, 2036])).
% 1.44/1.69 tff(2038,plain,
% 1.44/1.69 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2037, 1468])).
% 1.44/1.69 tff(2039,plain,
% 1.44/1.69 ((z = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = z)),
% 1.44/1.69 inference(commutativity,[status(thm)],[])).
% 1.44/1.69 tff(2040,plain,
% 1.44/1.69 ((elem!1 = s(s(s(s(elem!1))))) <=> (z = s(s(s(s(elem!1)))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[341])).
% 1.44/1.69 tff(2041,plain,
% 1.44/1.69 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = z)),
% 1.44/1.69 inference(transitivity,[status(thm)],[2040, 2039])).
% 1.44/1.69 tff(2042,plain,
% 1.44/1.69 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.44/1.69 inference(symmetry,[status(thm)],[2041])).
% 1.44/1.69 tff(2043,plain,
% 1.44/1.69 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[2042])).
% 1.44/1.69 tff(2044,plain,
% 1.44/1.69 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[329, 2043])).
% 1.44/1.69 tff(2045,plain,
% 1.44/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(2046,plain,
% 1.44/1.69 (((~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)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1))))))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(2047,plain,
% 1.44/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[2046])).
% 1.44/1.69 tff(2048,plain,
% 1.44/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.44/1.69 inference(transitivity,[status(thm)],[2047, 2045])).
% 1.44/1.69 tff(2049,plain,
% 1.44/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(2050,plain,
% 1.44/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[2049, 2048])).
% 1.44/1.69 tff(2051,plain,
% 1.44/1.69 ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2050, 183, 2028])).
% 1.44/1.69 tff(2052,plain,
% 1.44/1.69 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2051, 2000])).
% 1.44/1.69 tff(2053,plain,
% 1.44/1.69 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(2054,plain,
% 1.44/1.69 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1))))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(2055,plain,
% 1.44/1.69 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1)))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[2054, 2053])).
% 1.44/1.69 tff(2056,plain,
% 1.44/1.69 ((elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2055, 47, 2052])).
% 1.44/1.69 tff(2057,plain,
% 1.44/1.69 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2056, 2044])).
% 1.44/1.69 tff(2058,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(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)))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(2059,plain,
% 1.44/1.69 (((~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(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(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)))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(2060,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), 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))))))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[2059])).
% 1.44/1.69 tff(2061,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), 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)))))))),
% 1.44/1.69 inference(transitivity,[status(thm)],[2060, 2058])).
% 1.44/1.69 tff(2062,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(elem!1)))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(2063,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(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))))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[2062, 2061])).
% 1.44/1.69 tff(2064,plain,
% 1.44/1.69 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2063, 246, 714, 2057, 2038])).
% 1.44/1.69 tff(2065,plain,
% 1.44/1.69 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[2064, 1769])).
% 1.44/1.69 tff(2066,plain,
% 1.44/1.69 (r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1897, 2065])).
% 1.44/1.69 tff(2067,plain,
% 1.44/1.69 (r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[2066, 1767])).
% 1.44/1.69 tff(2068,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(2069,plain,
% 1.44/1.69 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(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)))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(2070,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[2069])).
% 1.44/1.69 tff(2071,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.44/1.69 inference(transitivity,[status(thm)],[2070, 2068])).
% 1.44/1.69 tff(2072,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(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))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(2073,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(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))))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[2072, 2071])).
% 1.44/1.69 tff(2074,plain,
% 1.44/1.69 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2073, 246, 1200, 2057, 2038])).
% 1.44/1.69 tff(2075,plain,
% 1.44/1.69 (~b(s(s(s(s(z)))), s(elem!1))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[2074, 1716])).
% 1.44/1.69 tff(2076,plain,
% 1.44/1.69 (r(s(s(s(s(z)))), s(elem!1))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1728, 2075, 1714])).
% 1.44/1.69 tff(2077,plain,
% 1.44/1.69 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[2076, 1706])).
% 1.44/1.69 tff(2078,plain,
% 1.44/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(2079,plain,
% 1.44/1.69 (((~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(elem!1)))), 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))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(2080,plain,
% 1.44/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(s(elem!1))))), s(s(s(s(elem!1))))))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[2079])).
% 1.44/1.69 tff(2081,plain,
% 1.44/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.44/1.69 inference(transitivity,[status(thm)],[2080, 2078])).
% 1.44/1.69 tff(2082,plain,
% 1.44/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(2083,plain,
% 1.44/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[2082, 2081])).
% 1.44/1.69 tff(2084,plain,
% 1.44/1.69 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2083, 183, 1796, 2077])).
% 1.44/1.69 tff(2085,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2084, 2067])).
% 1.44/1.69 tff(2086,plain,((~r(s(s(s(z))), elem!1)) | (~(z = elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(2087,plain,
% 1.44/1.69 (~r(s(s(s(z))), elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2086, 1765, 88, 1455, 157, 1451, 1448, 1435])).
% 1.44/1.69 tff(2088,plain,
% 1.44/1.69 (b(s(s(s(z))), elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[647, 2087, 554])).
% 1.44/1.69 tff(2089,plain,
% 1.44/1.69 (b(s(s(s(z))), z)),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[2088, 1434])).
% 1.44/1.69 tff(2090,assumption,(b(s(s(s(z))), z)), introduced(assumption)).
% 1.44/1.69 tff(2091,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(2092,plain,
% 1.44/1.69 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(2093,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[2092])).
% 1.44/1.69 tff(2094,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.44/1.69 inference(transitivity,[status(thm)],[2093, 2091])).
% 1.44/1.69 tff(2095,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(2096,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[2095, 2094])).
% 1.44/1.69 tff(2097,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2096, 246, 1056, 236, 2003, 2090])).
% 1.44/1.69 tff(2098,plain,((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(2099,plain,
% 1.44/1.69 (~b(s(s(s(z))), s(z))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2098, 2089, 1432, 1056])).
% 1.44/1.69 tff(2100,plain,
% 1.44/1.69 (r(s(s(s(z))), s(z))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[52, 2099])).
% 1.44/1.69 tff(2101,plain,
% 1.44/1.69 (r(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[2100, 1431])).
% 1.44/1.69 tff(2102,plain,
% 1.44/1.69 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1793, 246, 1765, 1455, 1451])).
% 1.44/1.69 tff(2103,plain,
% 1.44/1.69 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1795, 2102, 1787])).
% 1.44/1.69 tff(2104,plain,
% 1.44/1.69 (b(s(s(s(elem!1))), elem!1)),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[2088, 549])).
% 1.44/1.69 tff(2105,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.44/1.70 inference(rewrite,[status(thm)],[])).
% 1.44/1.70 tff(2106,plain,
% 1.44/1.70 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(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(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(s(s(elem!1))))))),
% 1.44/1.70 inference(rewrite,[status(thm)],[])).
% 1.44/1.70 tff(2107,plain,
% 1.44/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 1.44/1.70 inference(monotonicity,[status(thm)],[2106])).
% 1.44/1.70 tff(2108,plain,
% 1.44/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.44/1.70 inference(transitivity,[status(thm)],[2107, 2105])).
% 1.44/1.70 tff(2109,plain,
% 1.44/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(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(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.44/1.70 inference(quant_inst,[status(thm)],[])).
% 1.44/1.70 tff(2110,plain,
% 1.44/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.44/1.70 inference(modus_ponens,[status(thm)],[2109, 2108])).
% 1.44/1.70 tff(2111,plain,
% 1.44/1.70 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.44/1.70 inference(unit_resolution,[status(thm)],[2110, 246, 1765, 1455, 2104, 1451])).
% 1.44/1.70 tff(2112,plain,
% 1.44/1.70 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.44/1.70 inference(unit_resolution,[status(thm)],[811, 47, 771, 2111])).
% 1.44/1.70 tff(2113,plain,
% 1.44/1.70 ($false),
% 1.44/1.70 inference(unit_resolution,[status(thm)],[1862, 183, 2112, 2103, 2101])).
% 1.44/1.70 tff(2114,plain,(b(s(s(elem!1)), elem!1) | (~(z = elem!1)) | (~b(s(z), z)) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.70 tff(2115,plain,
% 1.44/1.70 (~b(s(z), z)),
% 1.44/1.70 inference(unit_resolution,[status(thm)],[2114, 145, 61, 55])).
% 1.44/1.70 tff(2116,plain,
% 1.44/1.70 (b(s(z), elem!1) <=> b(s(z), z)),
% 1.44/1.70 inference(symmetry,[status(thm)],[1453])).
% 1.44/1.70 tff(2117,plain,
% 1.44/1.70 (b(s(z), z)),
% 1.44/1.70 inference(modus_ponens,[status(thm)],[1044, 2116])).
% 1.44/1.70 tff(2118,assumption,(~b(s(z), z)), introduced(assumption)).
% 1.44/1.70 tff(2119,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2118, 2117])).
% 1.54/1.70 tff(2120,plain,((~(z = elem!1)) | b(s(z), z) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(2121,plain,
% 1.54/1.70 (~b(s(z), elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2120, 2115, 61])).
% 1.54/1.70 tff(2122,plain,
% 1.54/1.70 (r(s(z), elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[1034, 2121, 122])).
% 1.54/1.70 tff(2123,plain,
% 1.54/1.70 (b(elem!1, s(z))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[1425, 143])).
% 1.54/1.70 tff(2124,assumption,(~b(s(s(elem!1)), s(z))), introduced(assumption)).
% 1.54/1.70 tff(2125,assumption,(s(s(elem!1)) = elem!1), introduced(assumption)).
% 1.54/1.70 tff(2126,plain,
% 1.54/1.70 (b(s(s(elem!1)), s(z)) <=> b(elem!1, s(z))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[2125])).
% 1.54/1.70 tff(2127,plain,
% 1.54/1.70 (b(elem!1, s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.54/1.70 inference(symmetry,[status(thm)],[2126])).
% 1.54/1.70 tff(2128,plain,
% 1.54/1.70 (b(s(s(elem!1)), s(z))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[2001, 2127])).
% 1.54/1.70 tff(2129,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2124, 2128])).
% 1.54/1.70 tff(2130,plain,((~(s(s(elem!1)) = elem!1)) | b(s(s(elem!1)), s(z)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(2131,plain,
% 1.54/1.70 (~(s(s(elem!1)) = elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2130, 2124, 2001])).
% 1.54/1.70 tff(2132,plain,
% 1.54/1.70 (r(s(s(elem!1)), elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[156, 2131, 145])).
% 1.54/1.70 tff(2133,plain,
% 1.54/1.70 (r(s(s(elem!1)), s(z))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[197, 2124])).
% 1.54/1.70 tff(2134,plain,
% 1.54/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(2135,plain,
% 1.54/1.70 (((~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(2136,plain,
% 1.54/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[2135])).
% 1.54/1.70 tff(2137,plain,
% 1.54/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)))),
% 1.54/1.70 inference(transitivity,[status(thm)],[2136, 2134])).
% 1.54/1.70 tff(2138,plain,
% 1.54/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(2139,plain,
% 1.54/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[2138, 2137])).
% 1.54/1.70 tff(2140,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2139, 183, 2133, 217, 2132])).
% 1.54/1.70 tff(2141,plain,(b(s(s(elem!1)), s(z)) | (~r(s(z), elem!1)) | b(s(s(elem!1)), elem!1) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(2142,plain,
% 1.54/1.70 (b(s(s(elem!1)), s(z))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2141, 2123, 145, 2122])).
% 1.54/1.70 tff(2143,plain,
% 1.54/1.70 (b(s(s(elem!1)), s(elem!1))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[2142, 1427])).
% 1.54/1.70 tff(2144,plain,
% 1.54/1.70 (b(s(z), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[141])).
% 1.54/1.70 tff(2145,plain,
% 1.54/1.70 (r(s(z), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[141])).
% 1.54/1.70 tff(2146,plain,
% 1.54/1.70 (r(s(elem!1), s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 1.54/1.70 inference(symmetry,[status(thm)],[2145])).
% 1.54/1.70 tff(2147,plain,
% 1.54/1.70 ((~r(s(elem!1), s(s(elem!1)))) <=> (~r(s(z), s(s(elem!1))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[2146])).
% 1.54/1.70 tff(2148,plain,
% 1.54/1.70 (r(s(z), elem!1) <=> r(s(elem!1), elem!1)),
% 1.54/1.70 inference(monotonicity,[status(thm)],[141])).
% 1.54/1.70 tff(2149,plain,
% 1.54/1.70 (r(s(z), z) <=> r(s(z), elem!1)),
% 1.54/1.70 inference(monotonicity,[status(thm)],[61])).
% 1.54/1.70 tff(2150,plain,
% 1.54/1.70 (r(s(z), z) <=> r(s(elem!1), elem!1)),
% 1.54/1.70 inference(transitivity,[status(thm)],[2149, 2148])).
% 1.54/1.70 tff(2151,plain,
% 1.54/1.70 (r(s(z), z)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[1069, 2115])).
% 1.54/1.70 tff(2152,plain,
% 1.54/1.70 (r(s(elem!1), elem!1)),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[2151, 2150])).
% 1.54/1.70 tff(2153,plain,
% 1.54/1.70 ((~(s(s(elem!1)) = z)) <=> (~(s(s(elem!1)) = elem!1))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[135])).
% 1.54/1.70 tff(2154,plain,
% 1.54/1.70 (~(s(s(elem!1)) = elem!1)),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[139, 2153])).
% 1.54/1.70 tff(2155,plain,
% 1.54/1.70 (r(s(s(elem!1)), elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[156, 145, 2154])).
% 1.54/1.70 tff(2156,plain,
% 1.54/1.70 (~r(s(elem!1), s(s(elem!1)))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[373, 183, 2155, 2152])).
% 1.54/1.70 tff(2157,plain,
% 1.54/1.70 (~r(s(z), s(s(elem!1)))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[2156, 2147])).
% 1.54/1.70 tff(2158,plain,
% 1.54/1.70 (b(s(z), s(s(elem!1)))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[233, 2157])).
% 1.54/1.70 tff(2159,plain,
% 1.54/1.70 (b(s(elem!1), s(s(elem!1)))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[2158, 2144])).
% 1.54/1.70 tff(2160,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(2161,plain,
% 1.54/1.70 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(2162,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1)))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[2161])).
% 1.54/1.70 tff(2163,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[2162, 2160])).
% 1.54/1.70 tff(2164,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(2165,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1)))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[2164, 2163])).
% 1.54/1.70 tff(2166,plain,
% 1.54/1.70 (~b(elem!1, s(s(elem!1)))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2165, 246, 2159, 2143, 1426])).
% 1.54/1.70 tff(2167,plain,
% 1.54/1.70 (r(elem!1, s(s(elem!1)))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[1268, 2166, 140])).
% 1.54/1.70 tff(2168,plain,
% 1.54/1.70 (r(z, s(s(elem!1)))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[2167, 132])).
% 1.54/1.70 tff(2169,plain,
% 1.54/1.70 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[357, 61])).
% 1.54/1.70 tff(2170,plain,
% 1.54/1.70 (s(s(z)) = s(s(elem!1))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[141])).
% 1.54/1.70 tff(2171,plain,
% 1.54/1.70 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[2170])).
% 1.54/1.70 tff(2172,plain,
% 1.54/1.70 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.54/1.70 inference(symmetry,[status(thm)],[2171])).
% 1.54/1.70 tff(2173,plain,
% 1.54/1.70 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(z))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[2172])).
% 1.54/1.70 tff(2174,plain,
% 1.54/1.70 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.54/1.70 inference(symmetry,[status(thm)],[2173])).
% 1.54/1.70 tff(2175,plain,
% 1.54/1.70 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = s(s(s(z)))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[76])).
% 1.54/1.70 tff(2176,plain,
% 1.54/1.70 (~(elem!1 = s(s(s(z))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[80, 2175])).
% 1.54/1.70 tff(2177,plain,
% 1.54/1.70 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(z))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[2172])).
% 1.54/1.70 tff(2178,plain,
% 1.54/1.70 ((~b(elem!1, s(s(s(elem!1))))) <=> (~b(elem!1, s(s(s(z)))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[2177])).
% 1.54/1.70 tff(2179,plain,
% 1.54/1.70 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(z))), s(elem!1))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[2172])).
% 1.54/1.70 tff(2180,plain,
% 1.54/1.70 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.54/1.70 inference(symmetry,[status(thm)],[2179])).
% 1.54/1.70 tff(2181,plain,
% 1.54/1.70 ((s(s(s(z))) = s(elem!1)) <=> (s(elem!1) = s(s(s(z))))),
% 1.54/1.70 inference(commutativity,[status(thm)],[])).
% 1.54/1.70 tff(2182,plain,
% 1.54/1.70 ((s(elem!1) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 1.54/1.70 inference(symmetry,[status(thm)],[2181])).
% 1.54/1.70 tff(2183,plain,
% 1.54/1.70 ((s(z) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[141])).
% 1.54/1.70 tff(2184,plain,
% 1.54/1.70 ((s(z) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 1.54/1.70 inference(transitivity,[status(thm)],[2183, 2182])).
% 1.54/1.70 tff(2185,plain,
% 1.54/1.70 ((~(s(z) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[2184])).
% 1.54/1.70 tff(2186,plain,
% 1.54/1.70 (~(s(s(s(z))) = s(elem!1))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[767, 2185])).
% 1.54/1.70 tff(2187,plain,
% 1.54/1.70 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[2171])).
% 1.54/1.70 tff(2188,plain,
% 1.54/1.70 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(z))), s(elem!1))),
% 1.54/1.70 inference(symmetry,[status(thm)],[2187])).
% 1.54/1.70 tff(2189,plain,
% 1.54/1.70 ((~b(s(s(s(elem!1))), s(elem!1))) <=> (~b(s(s(s(z))), s(elem!1)))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[2188])).
% 1.54/1.70 tff(2190,plain,
% 1.54/1.70 (b(z, s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[88])).
% 1.54/1.70 tff(2191,plain,
% 1.54/1.70 (b(elem!1, s(s(s(z)))) <=> b(z, s(s(s(z))))),
% 1.54/1.70 inference(symmetry,[status(thm)],[2190])).
% 1.54/1.70 tff(2192,plain,
% 1.54/1.70 (b(elem!1, s(s(s(elem!1)))) <=> b(z, s(s(s(z))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[715, 2191])).
% 1.54/1.70 tff(2193,plain,
% 1.54/1.70 ((~b(elem!1, s(s(s(elem!1))))) <=> (~b(z, s(s(s(z)))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[2192])).
% 1.54/1.70 tff(2194,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(2195,plain,
% 1.54/1.70 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(2196,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1)))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[2195])).
% 1.54/1.70 tff(2197,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[2196, 2194])).
% 1.54/1.70 tff(2198,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(2199,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[2198, 2197])).
% 1.54/1.70 tff(2200,plain,
% 1.54/1.70 (~b(elem!1, s(s(s(elem!1))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2199, 246, 442, 363, 1937, 1574])).
% 1.54/1.70 tff(2201,plain,
% 1.54/1.70 (~b(z, s(s(s(z))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[2200, 2193])).
% 1.54/1.70 tff(2202,plain,
% 1.54/1.70 ((~b(s(s(s(elem!1))), elem!1)) <=> (~b(s(s(s(z))), elem!1))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[548])).
% 1.54/1.70 tff(2203,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(2204,plain,
% 1.54/1.70 (((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(2205,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1)))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[2204])).
% 1.54/1.70 tff(2206,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[2205, 2203])).
% 1.54/1.70 tff(2207,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(2208,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[2207, 2206])).
% 1.54/1.70 tff(2209,plain,
% 1.54/1.70 (~b(s(s(s(elem!1))), elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2208, 246, 442, 363, 1937, 1574])).
% 1.54/1.70 tff(2210,plain,
% 1.54/1.70 (~b(s(s(s(z))), elem!1)),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[2209, 2202])).
% 1.54/1.70 tff(2211,plain,
% 1.54/1.70 ((~b(elem!1, s(s(s(elem!1))))) <=> (~b(elem!1, s(s(s(z)))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[715])).
% 1.54/1.70 tff(2212,plain,
% 1.54/1.70 (~b(elem!1, s(s(s(z))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[2200, 2211])).
% 1.54/1.70 tff(2213,assumption,(~b(elem!1, s(s(s(z))))), introduced(assumption)).
% 1.54/1.70 tff(2214,assumption,(~b(z, s(s(s(z))))), introduced(assumption)).
% 1.54/1.70 tff(2215,plain,
% 1.54/1.70 ((z = s(s(s(z)))) <=> (s(s(s(z))) = z)),
% 1.54/1.70 inference(commutativity,[status(thm)],[])).
% 1.54/1.70 tff(2216,plain,
% 1.54/1.70 ((s(s(s(z))) = z) <=> (z = s(s(s(z))))),
% 1.54/1.70 inference(symmetry,[status(thm)],[2215])).
% 1.54/1.70 tff(2217,plain,
% 1.54/1.70 ((~(s(s(s(z))) = z)) <=> (~(z = s(s(s(z)))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[2216])).
% 1.54/1.70 tff(2218,plain,
% 1.54/1.70 (~(z = s(s(s(z))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[80, 2217])).
% 1.54/1.70 tff(2219,plain,
% 1.54/1.70 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z)))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(2220,plain,
% 1.54/1.71 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z)))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(2221,plain,
% 1.54/1.71 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[2220, 2219])).
% 1.54/1.71 tff(2222,plain,
% 1.54/1.71 ((z = s(s(s(z)))) | r(z, s(s(s(z))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2221, 47, 2214])).
% 1.54/1.71 tff(2223,plain,
% 1.54/1.71 (r(z, s(s(s(z))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2222, 2218])).
% 1.54/1.71 tff(2224,plain,
% 1.54/1.71 (r(z, s(s(s(z)))) <=> r(z, elem!1)),
% 1.54/1.71 inference(monotonicity,[status(thm)],[1673])).
% 1.54/1.71 tff(2225,plain,
% 1.54/1.71 (r(z, elem!1) <=> r(z, s(s(s(z))))),
% 1.54/1.71 inference(symmetry,[status(thm)],[2224])).
% 1.54/1.71 tff(2226,plain,
% 1.54/1.71 ((~r(z, elem!1)) <=> (~r(z, s(s(s(z)))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2225])).
% 1.54/1.71 tff(2227,plain,
% 1.54/1.71 (~r(z, s(s(s(z))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[56, 2226])).
% 1.54/1.71 tff(2228,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[429, 2227])).
% 1.54/1.71 tff(2229,plain,((~(s(s(s(z))) = elem!1)) | (~r(z, s(s(s(z))))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(2230,plain,
% 1.54/1.71 (~(s(s(s(z))) = elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2229, 2223, 56])).
% 1.54/1.71 tff(2231,plain,
% 1.54/1.71 (r(s(s(s(z))), elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[647, 2230, 1])).
% 1.54/1.71 tff(2232,assumption,(~r(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.54/1.71 tff(2233,plain,
% 1.54/1.71 (~(elem!1 = z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1447, 1056, 1445])).
% 1.54/1.71 tff(2234,plain,
% 1.54/1.71 (~(z = elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1440, 2233])).
% 1.54/1.71 tff(2235,plain,
% 1.54/1.71 (b(z, elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[60, 2234, 56])).
% 1.54/1.71 tff(2236,plain,
% 1.54/1.71 ((~(s(s(s(z))) = elem!1)) <=> (~(elem!1 = s(s(s(z)))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[73])).
% 1.54/1.71 tff(2237,plain,
% 1.54/1.71 (b(z, s(s(s(z)))) <=> b(z, elem!1)),
% 1.54/1.71 inference(monotonicity,[status(thm)],[1673])).
% 1.54/1.71 tff(2238,plain,
% 1.54/1.71 (b(z, elem!1) <=> b(z, s(s(s(z))))),
% 1.54/1.71 inference(symmetry,[status(thm)],[2237])).
% 1.54/1.71 tff(2239,assumption,(b(z, elem!1)), introduced(assumption)).
% 1.54/1.71 tff(2240,plain,
% 1.54/1.71 (b(z, s(s(s(z))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[2239, 2238])).
% 1.54/1.71 tff(2241,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2214, 2240])).
% 1.54/1.71 tff(2242,plain,((~(s(s(s(z))) = elem!1)) | b(z, s(s(s(z)))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(2243,plain,
% 1.54/1.71 (~(s(s(s(z))) = elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2242, 2235, 2214])).
% 1.54/1.71 tff(2244,plain,
% 1.54/1.71 (~(elem!1 = s(s(s(z))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[2243, 2236])).
% 1.54/1.71 tff(2245,plain,
% 1.54/1.71 (r(elem!1, s(s(s(z))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[470, 2244, 2213])).
% 1.54/1.71 tff(2246,assumption,(r(elem!1, z)), introduced(assumption)).
% 1.54/1.71 tff(2247,plain,
% 1.54/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(2248,plain,
% 1.54/1.71 (((~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(2249,plain,
% 1.54/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2248])).
% 1.54/1.71 tff(2250,plain,
% 1.54/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[2249, 2247])).
% 1.54/1.71 tff(2251,plain,
% 1.54/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(elem!1, z)))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(2252,plain,
% 1.54/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[2251, 2250])).
% 1.54/1.71 tff(2253,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2252, 183, 2246, 413, 429])).
% 1.54/1.71 tff(2254,plain,((~r(z, s(s(s(z))))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(2255,plain,
% 1.54/1.71 (~r(elem!1, z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2254, 2223, 2245])).
% 1.54/1.71 tff(2256,plain,
% 1.54/1.71 (b(elem!1, z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1143, 2255, 2233])).
% 1.54/1.71 tff(2257,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(2258,plain,
% 1.54/1.71 (((~b(elem!1, z)) | (~b(s(z), 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))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(2259,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z)))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2258])).
% 1.54/1.71 tff(2260,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[2259, 2257])).
% 1.54/1.71 tff(2261,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(2262,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z)))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[2261, 2260])).
% 1.54/1.71 tff(2263,plain,
% 1.54/1.71 (~b(elem!1, s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2262, 246, 2235, 2256, 1056])).
% 1.54/1.71 tff(2264,plain,
% 1.54/1.71 (r(s(s(s(z))), elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[647, 2243, 1])).
% 1.54/1.71 tff(2265,plain,
% 1.54/1.71 (~r(elem!1, s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1023, 430, 634])).
% 1.54/1.71 tff(2266,plain,
% 1.54/1.71 (s(s(s(z))) = s(s(elem!1))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[121, 6])).
% 1.54/1.71 tff(2267,plain,
% 1.54/1.71 (r(s(s(s(z))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2266])).
% 1.54/1.71 tff(2268,plain,
% 1.54/1.71 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(z))), elem!1)),
% 1.54/1.71 inference(symmetry,[status(thm)],[2267])).
% 1.54/1.71 tff(2269,plain,
% 1.54/1.71 ((~r(s(s(elem!1)), elem!1)) <=> (~r(s(s(s(z))), elem!1))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2268])).
% 1.54/1.71 tff(2270,plain,
% 1.54/1.71 (~r(s(s(s(z))), elem!1)),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[2232, 2269])).
% 1.54/1.71 tff(2271,plain,
% 1.54/1.71 (r(s(s(s(z))), s(z)) <=> r(s(s(s(z))), elem!1)),
% 1.54/1.71 inference(monotonicity,[status(thm)],[6])).
% 1.54/1.71 tff(2272,plain,
% 1.54/1.71 (r(s(s(s(z))), elem!1)),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[430, 2271])).
% 1.54/1.71 tff(2273,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2272, 2270])).
% 1.54/1.71 tff(2274,plain,((~(s(z) = elem!1)) | r(s(s(elem!1)), elem!1) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(2275,plain,
% 1.54/1.71 (~(s(z) = elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2274, 430, 2232])).
% 1.54/1.71 tff(2276,plain,
% 1.54/1.71 (s(z) = elem!1),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[202, 4])).
% 1.54/1.71 tff(2277,assumption,(~(s(z) = elem!1)), introduced(assumption)).
% 1.54/1.71 tff(2278,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2277, 2276])).
% 1.54/1.71 tff(2279,plain,((~(elem!1 = s(z))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(2280,plain,
% 1.54/1.71 (~(elem!1 = s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2279, 2275])).
% 1.54/1.71 tff(2281,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[214, 2280, 2265, 210])).
% 1.54/1.71 tff(2282,plain,((~r(s(s(s(z))), s(z))) | b(elem!1, s(z)) | (~r(s(s(s(z))), elem!1)) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(2283,plain,
% 1.54/1.71 (~r(s(s(s(z))), s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2282, 2263, 2264, 2232])).
% 1.54/1.71 tff(2284,plain,
% 1.54/1.71 (b(s(s(s(z))), s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[52, 2283])).
% 1.54/1.71 tff(2285,plain,
% 1.54/1.71 (b(s(s(s(z))), s(z)) <=> b(s(s(s(z))), elem!1)),
% 1.54/1.71 inference(monotonicity,[status(thm)],[6])).
% 1.54/1.71 tff(2286,plain,
% 1.54/1.71 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(z))),
% 1.54/1.71 inference(symmetry,[status(thm)],[2285])).
% 1.54/1.71 tff(2287,plain,
% 1.54/1.71 ((~b(s(s(s(z))), elem!1)) <=> (~b(s(s(s(z))), s(z)))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2286])).
% 1.54/1.71 tff(2288,plain,
% 1.54/1.71 (~b(s(s(s(z))), s(z))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[1, 2287])).
% 1.54/1.71 tff(2289,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2003, 2288])).
% 1.54/1.71 tff(2290,plain,((~(s(z) = elem!1)) | (~b(s(s(s(z))), s(z))) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(2291,plain,
% 1.54/1.71 (~(s(z) = elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2290, 2284, 1])).
% 1.54/1.71 tff(2292,assumption,(elem!1 = s(s(s(z)))), introduced(assumption)).
% 1.54/1.71 tff(2293,plain,
% 1.54/1.71 (b(elem!1, s(z)) <=> b(s(s(s(z))), s(z))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2292])).
% 1.54/1.71 tff(2294,plain,
% 1.54/1.71 (b(s(s(s(z))), s(z)) <=> b(elem!1, s(z))),
% 1.54/1.71 inference(symmetry,[status(thm)],[2293])).
% 1.54/1.71 tff(2295,plain,
% 1.54/1.71 (b(elem!1, s(z))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[2003, 2294])).
% 1.54/1.71 tff(2296,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[210, 2295])).
% 1.54/1.71 tff(2297,plain,((~(elem!1 = s(s(s(z))))) | b(elem!1, s(z)) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(2298,plain,
% 1.54/1.71 (~(elem!1 = s(s(s(z))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2297, 210, 2003])).
% 1.54/1.71 tff(2299,plain,
% 1.54/1.71 (~(s(s(s(z))) = elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1677, 2298])).
% 1.54/1.71 tff(2300,plain,
% 1.54/1.71 (r(s(s(s(z))), elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[647, 2299, 1])).
% 1.54/1.71 tff(2301,plain,
% 1.54/1.71 (r(s(z), elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1034, 2277, 1445])).
% 1.54/1.71 tff(2302,plain,
% 1.54/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(2303,plain,
% 1.54/1.71 (((~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(2304,plain,
% 1.54/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2303])).
% 1.54/1.71 tff(2305,plain,
% 1.54/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.54/1.71 inference(transitivity,[status(thm)],[2304, 2302])).
% 1.54/1.71 tff(2306,plain,
% 1.54/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(2307,plain,
% 1.54/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[2306, 2305])).
% 1.54/1.71 tff(2308,plain,
% 1.54/1.71 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2307, 183, 217, 333])).
% 1.54/1.71 tff(2309,plain,
% 1.54/1.71 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(z)) | b(s(s(s(s(s(elem!1))))), s(z)) | r(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(elem!1))))) = s(z)) | b(s(s(s(s(s(elem!1))))), s(z)) | r(s(s(s(s(s(elem!1))))), s(z)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(2310,plain,
% 1.54/1.71 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(z)) | b(s(s(s(s(s(elem!1))))), s(z)) | r(s(s(s(s(s(elem!1))))), s(z)))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(2311,plain,
% 1.54/1.71 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(z)) | b(s(s(s(s(s(elem!1))))), s(z)) | r(s(s(s(s(s(elem!1))))), s(z))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[2310, 2309])).
% 1.54/1.71 tff(2312,plain,
% 1.54/1.71 (b(s(s(s(s(s(elem!1))))), s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2311, 47, 331, 2308])).
% 1.54/1.71 tff(2313,plain,
% 1.54/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(2314,plain,
% 1.54/1.71 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(2315,plain,
% 1.54/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2314])).
% 1.54/1.71 tff(2316,plain,
% 1.54/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.54/1.71 inference(transitivity,[status(thm)],[2315, 2313])).
% 1.54/1.71 tff(2317,plain,
% 1.54/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(2318,plain,
% 1.54/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[2317, 2316])).
% 1.54/1.71 tff(2319,plain,
% 1.54/1.71 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2318, 183, 634, 333])).
% 1.54/1.71 tff(2320,plain,
% 1.54/1.71 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1626, 2319])).
% 1.54/1.71 tff(2321,plain,
% 1.54/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(2322,plain,
% 1.54/1.71 (((~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(2323,plain,
% 1.54/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), elem!1))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2322])).
% 1.54/1.71 tff(2324,plain,
% 1.54/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 1.54/1.71 inference(transitivity,[status(thm)],[2323, 2321])).
% 1.54/1.71 tff(2325,plain,
% 1.54/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(2326,plain,
% 1.54/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), elem!1))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[2325, 2324])).
% 1.54/1.71 tff(2327,plain,
% 1.54/1.71 (~r(s(z), s(s(s(z))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2326, 183, 217, 634])).
% 1.54/1.71 tff(2328,plain,
% 1.54/1.71 (b(s(z), s(s(s(z))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1291, 2327])).
% 1.54/1.71 tff(2329,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(2330,plain,
% 1.54/1.71 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(2331,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z)))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2330])).
% 1.54/1.71 tff(2332,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[2331, 2329])).
% 1.54/1.71 tff(2333,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(2334,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z)))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[2333, 2332])).
% 1.54/1.71 tff(2335,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2334, 246, 1056, 2328, 2003, 2320, 2312])).
% 1.54/1.71 tff(2336,plain,((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(2337,plain,
% 1.54/1.71 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2336, 2301, 1056, 2300, 2003])).
% 1.54/1.71 tff(2338,plain,
% 1.54/1.71 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[86, 2337, 69])).
% 1.54/1.71 tff(2339,plain,
% 1.54/1.71 (~(elem!1 = s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2279, 2277])).
% 1.54/1.71 tff(2340,plain,
% 1.54/1.71 (r(elem!1, s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[214, 2339, 210])).
% 1.54/1.71 tff(2341,plain,
% 1.54/1.71 (~r(s(z), s(s(s(z))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2326, 183, 2301, 2300])).
% 1.54/1.71 tff(2342,plain,
% 1.54/1.71 (b(s(z), s(s(s(z))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1291, 2341])).
% 1.54/1.71 tff(2343,plain,
% 1.54/1.71 (r(elem!1, s(s(s(z))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[470, 2298, 2213])).
% 1.54/1.71 tff(2344,plain,
% 1.54/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(elem!1, z)) | (~r(elem!1, s(z))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(2345,plain,
% 1.54/1.72 (((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z))) <=> ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(elem!1, s(z))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(2346,plain,
% 1.54/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(elem!1, s(z)))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[2345])).
% 1.54/1.72 tff(2347,plain,
% 1.54/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(elem!1, z)) | (~r(elem!1, s(z))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[2346, 2344])).
% 1.54/1.72 tff(2348,plain,
% 1.54/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z)))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(2349,plain,
% 1.54/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(elem!1, z)) | (~r(elem!1, s(z)))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[2348, 2347])).
% 1.54/1.72 tff(2350,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2349, 183, 2246, 474, 171])).
% 1.54/1.72 tff(2351,plain,((~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(2352,plain,
% 1.54/1.72 (~r(elem!1, z)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2351, 171, 474])).
% 1.54/1.72 tff(2353,plain,
% 1.54/1.72 (b(elem!1, z)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1143, 2352, 1438])).
% 1.54/1.72 tff(2354,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(2355,plain,
% 1.54/1.72 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(2356,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[2355])).
% 1.54/1.72 tff(2357,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.54/1.72 inference(transitivity,[status(thm)],[2356, 2354])).
% 1.54/1.72 tff(2358,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(2359,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[2358, 2357])).
% 1.54/1.72 tff(2360,plain,
% 1.54/1.72 (~b(s(s(s(s(s(elem!1))))), z)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2359, 246, 2239, 1051, 714])).
% 1.54/1.72 tff(2361,plain,
% 1.54/1.72 (r(s(s(s(s(s(elem!1))))), z)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1601, 2360])).
% 1.54/1.72 tff(2362,assumption,(b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.54/1.72 tff(2363,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(2364,plain,
% 1.54/1.72 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(2365,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[2364])).
% 1.54/1.72 tff(2366,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))),
% 1.54/1.72 inference(transitivity,[status(thm)],[2365, 2363])).
% 1.54/1.72 tff(2367,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(2368,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[2367, 2366])).
% 1.54/1.72 tff(2369,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2368, 246, 2239, 1051, 2362, 1100])).
% 1.54/1.72 tff(2370,plain,((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(2371,plain,
% 1.54/1.72 (~b(s(s(elem!1)), z)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2370, 2362, 2239, 1051])).
% 1.54/1.72 tff(2372,plain,
% 1.54/1.72 (r(s(s(elem!1)), z)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[523, 2371])).
% 1.54/1.72 tff(2373,plain,
% 1.54/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(2374,plain,
% 1.54/1.72 (((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(2375,plain,
% 1.54/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[2374])).
% 1.54/1.72 tff(2376,plain,
% 1.54/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[2375, 2373])).
% 1.54/1.72 tff(2377,plain,
% 1.54/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(2378,plain,
% 1.54/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[2377, 2376])).
% 1.54/1.72 tff(2379,plain,
% 1.54/1.72 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2378, 183, 2372, 2361])).
% 1.54/1.72 tff(2380,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(2381,plain,
% 1.54/1.72 (((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(2382,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[2381])).
% 1.54/1.72 tff(2383,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.54/1.72 inference(transitivity,[status(thm)],[2382, 2380])).
% 1.54/1.72 tff(2384,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(2385,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[2384, 2383])).
% 1.54/1.72 tff(2386,plain,
% 1.54/1.72 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2385, 246, 2239, 1051, 2362, 714])).
% 1.54/1.72 tff(2387,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[361, 47, 1555, 2386, 2379])).
% 1.54/1.72 tff(2388,plain,((~b(s(s(elem!1)), elem!1)) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(elem!1))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(2389,plain,
% 1.54/1.72 (~b(s(s(elem!1)), elem!1)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2388, 2353, 2239, 1555, 714])).
% 1.54/1.72 tff(2390,plain,
% 1.54/1.72 (s(s(elem!1)) = elem!1),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[156, 2389, 2232])).
% 1.54/1.72 tff(2391,plain,
% 1.54/1.72 (elem!1 = s(s(elem!1))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[2390, 134])).
% 1.54/1.72 tff(2392,assumption,(elem!1 = s(s(elem!1))), introduced(assumption)).
% 1.54/1.72 tff(2393,assumption,(s(s(s(s(z)))) = elem!1), introduced(assumption)).
% 1.54/1.72 tff(2394,plain,
% 1.54/1.72 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.54/1.72 inference(transitivity,[status(thm)],[2393, 2392])).
% 1.54/1.72 tff(2395,plain,
% 1.54/1.72 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[2394])).
% 1.54/1.72 tff(2396,plain,
% 1.54/1.72 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(z)))))),
% 1.54/1.72 inference(symmetry,[status(thm)],[2395])).
% 1.54/1.72 tff(2397,plain,
% 1.54/1.72 (s(elem!1) = s(s(s(z)))),
% 1.54/1.72 inference(transitivity,[status(thm)],[108, 2396, 1491])).
% 1.54/1.72 tff(2398,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1749, 2397])).
% 1.54/1.72 tff(2399,plain,((~(elem!1 = s(s(elem!1)))) | (s(elem!1) = s(s(s(z)))) | (~(s(s(s(s(z)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(2400,plain,
% 1.54/1.72 (~(s(s(s(s(z)))) = elem!1)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2399, 2391, 1749])).
% 1.54/1.72 tff(2401,assumption,(b(s(z), s(s(s(z))))), introduced(assumption)).
% 1.54/1.72 tff(2402,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(2403,plain,
% 1.54/1.72 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(2404,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[2403])).
% 1.54/1.72 tff(2405,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[2404, 2402])).
% 1.54/1.72 tff(2406,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(2407,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[2406, 2405])).
% 1.54/1.72 tff(2408,plain,
% 1.54/1.72 (~b(s(s(s(s(z)))), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2407, 246, 1056, 2401, 2003, 1833])).
% 1.54/1.72 tff(2409,plain,
% 1.54/1.72 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(2410,plain,
% 1.54/1.72 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z)))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(2411,plain,
% 1.54/1.72 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[2410, 2409])).
% 1.54/1.72 tff(2412,plain,
% 1.54/1.72 (r(s(s(s(s(z)))), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2411, 47, 1713, 2408])).
% 1.54/1.72 tff(2413,plain,
% 1.54/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(2414,plain,
% 1.54/1.72 (((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(2415,plain,
% 1.54/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[2414])).
% 1.54/1.72 tff(2416,plain,
% 1.54/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.54/1.72 inference(transitivity,[status(thm)],[2415, 2413])).
% 1.54/1.72 tff(2417,plain,
% 1.54/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(2418,plain,
% 1.54/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[2417, 2416])).
% 1.54/1.72 tff(2419,plain,
% 1.54/1.72 (~r(s(s(s(s(z)))), z)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2418, 183, 171, 2412])).
% 1.54/1.72 tff(2420,plain,
% 1.54/1.72 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(z)))) = z))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(2421,plain,
% 1.54/1.72 (~(s(s(s(s(z)))) = z)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2420, 33])).
% 1.54/1.72 tff(2422,plain,
% 1.54/1.72 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(2423,plain,
% 1.54/1.72 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(2424,plain,
% 1.54/1.72 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z)),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[2423, 2422])).
% 1.54/1.72 tff(2425,plain,
% 1.54/1.72 (b(s(s(s(s(z)))), z)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2424, 47, 2421, 2419])).
% 1.54/1.72 tff(2426,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(2427,plain,
% 1.54/1.72 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(2428,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[2427])).
% 1.54/1.72 tff(2429,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 1.54/1.73 inference(transitivity,[status(thm)],[2428, 2426])).
% 1.54/1.73 tff(2430,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(2431,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[2430, 2429])).
% 1.54/1.73 tff(2432,plain,
% 1.54/1.73 (~b(s(s(s(s(z)))), elem!1)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2431, 246, 2239, 1051, 2425])).
% 1.54/1.73 tff(2433,plain,
% 1.54/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(2434,plain,
% 1.54/1.73 (((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(2435,plain,
% 1.54/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[2434])).
% 1.54/1.73 tff(2436,plain,
% 1.54/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.54/1.73 inference(transitivity,[status(thm)],[2435, 2433])).
% 1.54/1.73 tff(2437,plain,
% 1.54/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(2438,plain,
% 1.54/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[2437, 2436])).
% 1.54/1.73 tff(2439,plain,
% 1.54/1.73 (~r(s(s(s(s(z)))), elem!1)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2438, 183, 474, 2412])).
% 1.54/1.73 tff(2440,plain,
% 1.54/1.73 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(2441,plain,
% 1.54/1.73 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(2442,plain,
% 1.54/1.73 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1)),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[2441, 2440])).
% 1.54/1.73 tff(2443,plain,
% 1.54/1.73 ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2442, 47, 2439])).
% 1.54/1.73 tff(2444,plain,
% 1.54/1.73 (s(s(s(s(z)))) = elem!1),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2443, 2432])).
% 1.54/1.73 tff(2445,plain,
% 1.54/1.73 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[2444])).
% 1.54/1.73 tff(2446,plain,
% 1.54/1.73 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.73 inference(symmetry,[status(thm)],[2445])).
% 1.54/1.73 tff(2447,plain,
% 1.54/1.73 ((~b(elem!1, s(s(s(z))))) <=> (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[2446])).
% 1.54/1.73 tff(2448,plain,
% 1.54/1.73 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[2213, 2447])).
% 1.54/1.73 tff(2449,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1833, 2448])).
% 1.54/1.73 tff(2450,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | b(elem!1, s(s(s(z)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(2451,plain,
% 1.54/1.73 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2450, 2353, 2239, 2213, 171, 474, 1056, 2401, 2003])).
% 1.54/1.73 tff(2452,plain,
% 1.54/1.73 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1702, 2451])).
% 1.54/1.73 tff(2453,plain,
% 1.54/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(2454,plain,
% 1.54/1.73 (((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(2455,plain,
% 1.54/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[2454])).
% 1.54/1.73 tff(2456,plain,
% 1.54/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.54/1.73 inference(transitivity,[status(thm)],[2455, 2453])).
% 1.54/1.73 tff(2457,plain,
% 1.54/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(2458,plain,
% 1.54/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[2457, 2456])).
% 1.54/1.73 tff(2459,plain,
% 1.54/1.73 (~r(s(s(s(s(z)))), elem!1)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2458, 183, 474, 413, 2452])).
% 1.54/1.73 tff(2460,plain,
% 1.54/1.73 ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2442, 47, 2459])).
% 1.54/1.73 tff(2461,plain,
% 1.54/1.73 (b(s(s(s(s(z)))), elem!1)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2460, 2400])).
% 1.54/1.73 tff(2462,plain,
% 1.54/1.73 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(2463,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[2462])).
% 1.54/1.73 tff(2464,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 1.54/1.73 inference(transitivity,[status(thm)],[2463, 2426])).
% 1.54/1.73 tff(2465,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(2466,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[2465, 2464])).
% 1.54/1.73 tff(2467,plain,
% 1.54/1.73 (~b(s(s(s(s(z)))), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2466, 246, 2239, 2353, 2461])).
% 1.54/1.73 tff(2468,plain,
% 1.54/1.73 (r(s(s(s(s(z)))), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2424, 47, 2421, 2467])).
% 1.54/1.73 tff(2469,plain,
% 1.54/1.73 (s(s(s(elem!1))) = s(elem!1)),
% 1.54/1.73 inference(monotonicity,[status(thm)],[2390])).
% 1.54/1.73 tff(2470,plain,
% 1.54/1.73 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[2469])).
% 1.54/1.73 tff(2471,plain,
% 1.54/1.73 (s(s(s(s(elem!1)))) = elem!1),
% 1.54/1.73 inference(transitivity,[status(thm)],[2470, 2390])).
% 1.54/1.73 tff(2472,plain,
% 1.54/1.73 (s(s(s(s(s(elem!1))))) = s(elem!1)),
% 1.54/1.73 inference(monotonicity,[status(thm)],[2471])).
% 1.54/1.73 tff(2473,plain,
% 1.54/1.73 (r(z, s(s(s(s(s(elem!1)))))) <=> r(z, s(elem!1))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[2472])).
% 1.54/1.73 tff(2474,plain,
% 1.54/1.73 ((z = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = z)),
% 1.54/1.73 inference(commutativity,[status(thm)],[])).
% 1.54/1.73 tff(2475,plain,
% 1.54/1.73 ((s(s(s(s(s(elem!1))))) = z) <=> (z = s(s(s(s(s(elem!1))))))),
% 1.54/1.73 inference(symmetry,[status(thm)],[2474])).
% 1.54/1.73 tff(2476,plain,
% 1.54/1.73 ((~(s(s(s(s(s(elem!1))))) = z)) <=> (~(z = s(s(s(s(s(elem!1)))))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[2475])).
% 1.54/1.73 tff(2477,plain,
% 1.54/1.73 (~(z = s(s(s(s(s(elem!1))))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[65, 2476])).
% 1.54/1.73 tff(2478,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(2479,plain,
% 1.54/1.73 (((~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(elem!1)))))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(2480,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[2479])).
% 1.54/1.73 tff(2481,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.54/1.73 inference(transitivity,[status(thm)],[2480, 2478])).
% 1.54/1.73 tff(2482,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(2483,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[2482, 2481])).
% 1.54/1.73 tff(2484,plain,
% 1.54/1.73 (~b(z, s(s(s(s(s(elem!1))))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2483, 246, 2239, 2353, 714])).
% 1.54/1.73 tff(2485,plain,
% 1.54/1.73 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(elem!1)))))) | b(z, s(s(s(s(s(elem!1)))))) | r(z, 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(elem!1)))))) | b(z, s(s(s(s(s(elem!1)))))) | r(z, s(s(s(s(s(elem!1)))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(2486,plain,
% 1.54/1.73 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(elem!1)))))) | b(z, s(s(s(s(s(elem!1)))))) | r(z, s(s(s(s(s(elem!1)))))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(2487,plain,
% 1.54/1.73 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(elem!1)))))) | b(z, s(s(s(s(s(elem!1)))))) | r(z, s(s(s(s(s(elem!1))))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[2486, 2485])).
% 1.54/1.73 tff(2488,plain,
% 1.54/1.73 ((z = s(s(s(s(s(elem!1)))))) | r(z, s(s(s(s(s(elem!1))))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2487, 47, 2484])).
% 1.54/1.73 tff(2489,plain,
% 1.54/1.73 (r(z, s(s(s(s(s(elem!1))))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2488, 2477])).
% 1.54/1.73 tff(2490,plain,
% 1.54/1.73 (r(z, s(elem!1))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[2489, 2473])).
% 1.54/1.73 tff(2491,plain,
% 1.54/1.73 (s(elem!1) = s(s(s(s(s(elem!1)))))),
% 1.54/1.73 inference(symmetry,[status(thm)],[2472])).
% 1.54/1.73 tff(2492,plain,
% 1.54/1.73 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[2491])).
% 1.54/1.73 tff(2493,plain,
% 1.54/1.73 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 1.54/1.73 inference(symmetry,[status(thm)],[2492])).
% 1.54/1.73 tff(2494,plain,
% 1.54/1.73 ((~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[2493])).
% 1.54/1.73 tff(2495,plain,
% 1.54/1.73 (~(s(s(s(s(z)))) = s(elem!1))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[1501, 2494])).
% 1.54/1.73 tff(2496,plain,
% 1.54/1.73 (b(s(s(s(s(s(elem!1))))), elem!1) <=> b(s(elem!1), elem!1)),
% 1.54/1.73 inference(monotonicity,[status(thm)],[2472])).
% 1.54/1.73 tff(2497,plain,
% 1.54/1.73 (b(s(elem!1), elem!1)),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[714, 2496])).
% 1.54/1.73 tff(2498,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(2499,plain,
% 1.54/1.73 (((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1)))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(2500,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[2499])).
% 1.54/1.73 tff(2501,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[2500, 2498])).
% 1.54/1.73 tff(2502,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(2503,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[2502, 2501])).
% 1.54/1.73 tff(2504,plain,
% 1.54/1.73 (~b(s(s(s(s(z)))), s(elem!1))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2503, 246, 2239, 2353, 2497, 2461])).
% 1.54/1.73 tff(2505,plain,
% 1.54/1.73 (r(s(s(s(s(z)))), s(elem!1))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1728, 2504, 2495])).
% 1.54/1.73 tff(2506,plain,
% 1.54/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(2507,plain,
% 1.54/1.73 (((~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(2508,plain,
% 1.54/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[2507])).
% 1.54/1.74 tff(2509,plain,
% 1.54/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z)))),
% 1.54/1.74 inference(transitivity,[status(thm)],[2508, 2506])).
% 1.54/1.74 tff(2510,plain,
% 1.54/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(2511,plain,
% 1.54/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[2510, 2509])).
% 1.54/1.74 tff(2512,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2511, 183, 171, 2505, 2490, 2468])).
% 1.54/1.74 tff(2513,plain,((~r(z, s(z))) | (~b(z, elem!1)) | (s(elem!1) = s(s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | r(s(s(elem!1)), elem!1) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | b(elem!1, s(s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(2514,plain,
% 1.54/1.74 (~r(z, s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2513, 2338, 1749, 2239, 2232, 1555, 2340, 2343, 2213, 1056, 2342, 2003, 2233])).
% 1.54/1.74 tff(2515,plain,
% 1.54/1.74 (b(z, s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[169, 2514])).
% 1.54/1.74 tff(2516,plain,
% 1.54/1.74 (~r(s(s(s(z))), s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1023, 474, 634])).
% 1.54/1.74 tff(2517,plain,
% 1.54/1.74 (b(s(s(s(z))), s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[52, 2516])).
% 1.54/1.74 tff(2518,plain,
% 1.54/1.74 (~r(s(z), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1163, 2246, 474])).
% 1.54/1.74 tff(2519,plain,
% 1.54/1.74 (b(s(z), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1069, 2518])).
% 1.54/1.74 tff(2520,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(2521,plain,
% 1.54/1.74 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(2522,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[2521])).
% 1.54/1.74 tff(2523,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[2522, 2520])).
% 1.54/1.74 tff(2524,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(2525,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[2524, 2523])).
% 1.54/1.74 tff(2526,plain,
% 1.54/1.74 (~b(s(s(s(z))), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2525, 246, 2239, 2519, 236, 2517])).
% 1.54/1.74 tff(2527,plain,
% 1.54/1.74 (r(s(s(s(z))), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[993, 47, 80, 2526])).
% 1.54/1.74 tff(2528,plain,
% 1.54/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(2529,plain,
% 1.54/1.74 (((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(2530,plain,
% 1.54/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[2529])).
% 1.54/1.74 tff(2531,plain,
% 1.54/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))),
% 1.54/1.74 inference(transitivity,[status(thm)],[2530, 2528])).
% 1.54/1.74 tff(2532,plain,
% 1.54/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(2533,plain,
% 1.54/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[2532, 2531])).
% 1.54/1.74 tff(2534,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2533, 183, 2246, 634, 2527])).
% 1.54/1.74 tff(2535,plain,((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(2536,plain,
% 1.54/1.74 (~r(elem!1, z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2535, 2515, 2300, 2239, 2340])).
% 1.54/1.74 tff(2537,plain,
% 1.54/1.74 (b(elem!1, z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1143, 2536, 2233])).
% 1.54/1.74 tff(2538,plain,
% 1.54/1.74 (~b(s(s(elem!1)), elem!1)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2388, 2537, 2239, 1555, 2338])).
% 1.54/1.74 tff(2539,plain,
% 1.54/1.74 (s(s(elem!1)) = elem!1),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[156, 2538, 2232])).
% 1.54/1.74 tff(2540,plain,
% 1.54/1.74 (s(s(s(elem!1))) = s(elem!1)),
% 1.54/1.74 inference(monotonicity,[status(thm)],[2539])).
% 1.54/1.74 tff(2541,plain,
% 1.54/1.74 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[2540])).
% 1.54/1.74 tff(2542,plain,
% 1.54/1.74 (s(s(s(s(elem!1)))) = elem!1),
% 1.54/1.74 inference(transitivity,[status(thm)],[2541, 2539])).
% 1.54/1.74 tff(2543,plain,
% 1.54/1.74 (s(s(s(s(s(elem!1))))) = s(elem!1)),
% 1.54/1.74 inference(monotonicity,[status(thm)],[2542])).
% 1.54/1.74 tff(2544,plain,
% 1.54/1.74 (b(s(s(s(s(s(elem!1))))), elem!1) <=> b(s(elem!1), elem!1)),
% 1.54/1.74 inference(monotonicity,[status(thm)],[2543])).
% 1.54/1.74 tff(2545,plain,
% 1.54/1.74 (b(s(elem!1), elem!1)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[2338, 2544])).
% 1.54/1.74 tff(2546,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(2547,plain,
% 1.54/1.74 (((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1)))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(2548,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1)))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[2547])).
% 1.54/1.74 tff(2549,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[2548, 2546])).
% 1.54/1.74 tff(2550,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(2551,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1)))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[2550, 2549])).
% 1.54/1.74 tff(2552,plain,
% 1.54/1.74 (~b(z, s(elem!1))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2551, 246, 2239, 2537, 2545])).
% 1.54/1.74 tff(2553,plain,
% 1.54/1.74 ((z = s(elem!1)) <=> (s(elem!1) = z)),
% 1.54/1.74 inference(commutativity,[status(thm)],[])).
% 1.54/1.74 tff(2554,plain,
% 1.54/1.74 ((s(elem!1) = z) <=> (z = s(elem!1))),
% 1.54/1.74 inference(symmetry,[status(thm)],[2553])).
% 1.54/1.74 tff(2555,plain,
% 1.54/1.74 ((~(s(elem!1) = z)) <=> (~(z = s(elem!1)))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[2554])).
% 1.54/1.74 tff(2556,plain,
% 1.54/1.74 (~(z = s(elem!1))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[111, 2555])).
% 1.54/1.74 tff(2557,plain,
% 1.54/1.74 (((~![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)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(2558,plain,
% 1.54/1.74 ((~![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)))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(2559,plain,
% 1.54/1.74 ((~![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))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[2558, 2557])).
% 1.54/1.74 tff(2560,plain,
% 1.54/1.74 ((z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2559, 47])).
% 1.54/1.74 tff(2561,plain,
% 1.54/1.74 (b(z, s(elem!1)) | r(z, s(elem!1))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2560, 2556])).
% 1.54/1.74 tff(2562,plain,
% 1.54/1.74 (r(z, s(elem!1))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2561, 2552])).
% 1.54/1.74 tff(2563,plain,
% 1.54/1.74 (s(elem!1) = s(s(s(s(s(elem!1)))))),
% 1.54/1.74 inference(symmetry,[status(thm)],[2543])).
% 1.54/1.74 tff(2564,plain,
% 1.54/1.74 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[2563])).
% 1.54/1.74 tff(2565,plain,
% 1.54/1.74 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 1.54/1.74 inference(symmetry,[status(thm)],[2564])).
% 1.54/1.74 tff(2566,plain,
% 1.54/1.74 ((~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[2565])).
% 1.54/1.74 tff(2567,plain,
% 1.54/1.74 (~(s(s(s(s(z)))) = s(elem!1))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[1501, 2566])).
% 1.54/1.74 tff(2568,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(2569,plain,
% 1.54/1.74 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(2570,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[2569])).
% 1.54/1.74 tff(2571,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.54/1.74 inference(transitivity,[status(thm)],[2570, 2568])).
% 1.54/1.74 tff(2572,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(2573,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[2572, 2571])).
% 1.54/1.74 tff(2574,plain,
% 1.54/1.74 (~b(s(elem!1), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2573, 246, 2239, 2537, 2515, 2545])).
% 1.54/1.74 tff(2575,assumption,(~r(s(elem!1), z)), introduced(assumption)).
% 1.54/1.74 tff(2576,assumption,(~b(s(elem!1), z)), introduced(assumption)).
% 1.54/1.74 tff(2577,plain,
% 1.54/1.74 (((~![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))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(2578,plain,
% 1.54/1.74 ((~![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))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(2579,plain,
% 1.54/1.74 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[2578, 2577])).
% 1.54/1.74 tff(2580,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2579, 47, 111, 2576, 2575])).
% 1.54/1.74 tff(2581,plain,(r(s(elem!1), z) | b(s(elem!1), z)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(2582,plain,
% 1.54/1.74 (r(s(elem!1), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2581, 2574])).
% 1.54/1.74 tff(2583,plain,
% 1.54/1.74 (~b(s(s(s(z))), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2098, 2515, 1056, 2003])).
% 1.54/1.74 tff(2584,plain,
% 1.54/1.74 (r(s(s(s(z))), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[995, 2583])).
% 1.54/1.74 tff(2585,plain,
% 1.54/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(z))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(2586,plain,
% 1.54/1.74 (((~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z)))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(z))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(2587,plain,
% 1.54/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(z)))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[2586])).
% 1.54/1.74 tff(2588,plain,
% 1.54/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(z))))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[2587, 2585])).
% 1.54/1.74 tff(2589,plain,
% 1.54/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(2590,plain,
% 1.54/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(z)))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[2589, 2588])).
% 1.54/1.74 tff(2591,plain,
% 1.54/1.74 (~r(s(elem!1), s(s(s(z))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2590, 183, 2300, 2584, 2582])).
% 1.54/1.74 tff(2592,plain,
% 1.54/1.74 (b(s(elem!1), s(s(s(z))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1754, 2591, 1749])).
% 1.54/1.74 tff(2593,assumption,(r(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 1.54/1.74 tff(2594,plain,
% 1.54/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(2595,plain,
% 1.54/1.74 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(2596,plain,
% 1.54/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[2595])).
% 1.54/1.74 tff(2597,plain,
% 1.54/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.54/1.74 inference(transitivity,[status(thm)],[2596, 2594])).
% 1.54/1.74 tff(2598,plain,
% 1.54/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(2599,plain,
% 1.54/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[2598, 2597])).
% 1.54/1.74 tff(2600,plain,
% 1.54/1.74 (~r(s(s(s(s(z)))), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2599, 183, 2223, 2593])).
% 1.54/1.74 tff(2601,plain,
% 1.54/1.74 (b(s(s(s(s(z)))), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2424, 47, 2421, 2600])).
% 1.54/1.74 tff(2602,plain,
% 1.54/1.74 (~(elem!1 = s(s(s(z))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2297, 2003, 210])).
% 1.54/1.74 tff(2603,plain,
% 1.54/1.74 (r(elem!1, s(s(s(z))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[470, 2602, 2213])).
% 1.54/1.74 tff(2604,plain,
% 1.54/1.74 (~r(elem!1, z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2254, 2223, 2603])).
% 1.54/1.74 tff(2605,plain,
% 1.54/1.74 (b(elem!1, z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1143, 2604, 2233])).
% 1.54/1.74 tff(2606,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(2607,plain,
% 1.54/1.74 (((~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(2608,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[2607])).
% 1.54/1.74 tff(2609,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 1.54/1.75 inference(transitivity,[status(thm)],[2608, 2606])).
% 1.54/1.75 tff(2610,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(2611,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[2610, 2609])).
% 1.54/1.75 tff(2612,plain,
% 1.54/1.75 (~b(s(s(s(s(z)))), elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2611, 246, 2605, 1056, 236, 2601])).
% 1.54/1.75 tff(2613,plain,
% 1.54/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(2614,plain,
% 1.54/1.75 (((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(2615,plain,
% 1.54/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[2614])).
% 1.54/1.75 tff(2616,plain,
% 1.54/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.54/1.75 inference(transitivity,[status(thm)],[2615, 2613])).
% 1.54/1.75 tff(2617,plain,
% 1.54/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(2618,plain,
% 1.54/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[2617, 2616])).
% 1.54/1.75 tff(2619,plain,
% 1.54/1.75 (~r(s(s(s(s(z)))), elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2618, 183, 2603, 2593])).
% 1.54/1.75 tff(2620,plain,
% 1.54/1.75 ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2442, 47, 2619])).
% 1.54/1.75 tff(2621,plain,
% 1.54/1.75 (s(s(s(s(z)))) = elem!1),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2620, 2612])).
% 1.54/1.75 tff(2622,plain,
% 1.54/1.75 ((s(s(s(s(z)))) = s(z)) <=> (elem!1 = s(z))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[2621])).
% 1.54/1.75 tff(2623,plain,
% 1.54/1.75 ((s(s(s(s(z)))) = s(z)) <=> (s(z) = elem!1)),
% 1.54/1.75 inference(transitivity,[status(thm)],[2622, 4])).
% 1.54/1.75 tff(2624,plain,
% 1.54/1.75 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(z) = elem!1))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[2623])).
% 1.54/1.75 tff(2625,plain,
% 1.54/1.75 (~(s(z) = elem!1)),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[1713, 2624])).
% 1.54/1.75 tff(2626,plain,
% 1.54/1.75 (r(s(z), elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1034, 2625, 1445])).
% 1.54/1.75 tff(2627,plain,
% 1.54/1.75 (~(s(s(s(z))) = elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1677, 2602])).
% 1.54/1.75 tff(2628,plain,
% 1.54/1.75 (r(s(s(s(z))), elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[647, 2627, 1])).
% 1.54/1.75 tff(2629,plain,
% 1.54/1.75 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2336, 2003, 1056, 2628, 2626])).
% 1.54/1.75 tff(2630,plain,
% 1.54/1.75 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[86, 2629, 69])).
% 1.54/1.75 tff(2631,plain,
% 1.54/1.75 (b(z, s(s(s(s(z))))) <=> b(z, elem!1)),
% 1.54/1.75 inference(monotonicity,[status(thm)],[2621])).
% 1.54/1.75 tff(2632,plain,
% 1.54/1.75 ((z = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = z)),
% 1.54/1.75 inference(commutativity,[status(thm)],[])).
% 1.54/1.75 tff(2633,plain,
% 1.54/1.75 ((s(s(s(s(z)))) = z) <=> (z = s(s(s(s(z)))))),
% 1.54/1.75 inference(symmetry,[status(thm)],[2632])).
% 1.54/1.75 tff(2634,plain,
% 1.54/1.75 ((~(s(s(s(s(z)))) = z)) <=> (~(z = s(s(s(s(z))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[2633])).
% 1.54/1.75 tff(2635,plain,
% 1.54/1.75 (~(z = s(s(s(s(z)))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[2421, 2634])).
% 1.54/1.75 tff(2636,plain,
% 1.54/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(2637,plain,
% 1.54/1.75 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(2638,plain,
% 1.54/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z))))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[2637])).
% 1.54/1.75 tff(2639,plain,
% 1.54/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[2638, 2636])).
% 1.54/1.75 tff(2640,plain,
% 1.54/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(2641,plain,
% 1.54/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z))))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[2640, 2639])).
% 1.54/1.75 tff(2642,plain,
% 1.54/1.75 (~r(z, s(s(s(s(z)))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2641, 183, 2223, 2593])).
% 1.54/1.75 tff(2643,plain,
% 1.54/1.75 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(2644,plain,
% 1.54/1.75 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z))))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(2645,plain,
% 1.54/1.75 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[2644, 2643])).
% 1.54/1.75 tff(2646,plain,
% 1.54/1.75 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z)))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2645, 47, 2642])).
% 1.54/1.75 tff(2647,plain,
% 1.54/1.75 (b(z, s(s(s(s(z)))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2646, 2635])).
% 1.54/1.75 tff(2648,plain,
% 1.54/1.75 (b(z, elem!1)),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[2647, 2631])).
% 1.54/1.75 tff(2649,plain,
% 1.54/1.75 (~b(s(s(s(s(s(elem!1))))), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2359, 246, 2648, 2605, 2630])).
% 1.54/1.75 tff(2650,plain,
% 1.54/1.75 (r(s(s(s(s(s(elem!1))))), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1601, 2649])).
% 1.54/1.75 tff(2651,plain,
% 1.54/1.75 ((~(elem!1 = s(s(elem!1)))) <=> (~(s(s(elem!1)) = elem!1))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[133])).
% 1.54/1.75 tff(2652,plain,
% 1.54/1.75 (~(elem!1 = s(s(elem!1)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2399, 2621, 1749])).
% 1.54/1.75 tff(2653,plain,
% 1.54/1.75 (~(s(s(elem!1)) = elem!1)),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[2652, 2651])).
% 1.54/1.75 tff(2654,plain,
% 1.54/1.75 (b(s(s(elem!1)), elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[156, 2653, 2232])).
% 1.54/1.75 tff(2655,plain,
% 1.54/1.75 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2385, 246, 2648, 2605, 2654, 2630])).
% 1.54/1.75 tff(2656,plain,
% 1.54/1.75 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[361, 47, 1555, 2655])).
% 1.54/1.75 tff(2657,plain,
% 1.54/1.75 (~b(s(s(elem!1)), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2370, 2654, 2605, 2648])).
% 1.54/1.75 tff(2658,plain,
% 1.54/1.75 (r(s(s(elem!1)), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[523, 2657])).
% 1.54/1.75 tff(2659,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2378, 183, 2658, 2656, 2650])).
% 1.54/1.75 tff(2660,plain,((~b(s(s(s(z))), s(z))) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | (s(s(s(s(s(elem!1))))) = elem!1) | (~b(s(z), z)) | r(s(s(elem!1)), elem!1) | (s(elem!1) = s(s(s(z)))) | b(s(z), elem!1) | (~b(z, s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | b(z, s(s(s(z)))) | b(s(s(s(z))), elem!1) | b(elem!1, s(s(s(z)))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(2661,plain,
% 1.54/1.75 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2660, 2515, 69, 1056, 2232, 1749, 1445, 2003, 1555, 2214, 1, 2213, 210])).
% 1.54/1.75 tff(2662,plain,
% 1.54/1.75 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1702, 2661])).
% 1.54/1.75 tff(2663,plain,
% 1.54/1.75 ((~(s(elem!1) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[2182])).
% 1.54/1.75 tff(2664,plain,
% 1.54/1.75 (~(s(s(s(z))) = s(elem!1))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[1749, 2663])).
% 1.54/1.75 tff(2665,plain,
% 1.54/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(2666,plain,
% 1.54/1.75 (((~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), s(elem!1)))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(2667,plain,
% 1.54/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[2666])).
% 1.54/1.75 tff(2668,plain,
% 1.54/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z)))),
% 1.54/1.75 inference(transitivity,[status(thm)],[2667, 2665])).
% 1.54/1.75 tff(2669,plain,
% 1.54/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(2670,plain,
% 1.54/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), z))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[2669, 2668])).
% 1.54/1.75 tff(2671,plain,
% 1.54/1.75 (~r(s(s(s(z))), s(elem!1))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2670, 183, 2584, 2582])).
% 1.54/1.75 tff(2672,plain,
% 1.54/1.75 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1)) | r(s(s(s(z))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1)) | r(s(s(s(z))), s(elem!1)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(2673,plain,
% 1.54/1.75 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1)) | r(s(s(s(z))), s(elem!1)))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(2674,plain,
% 1.54/1.75 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1)) | r(s(s(s(z))), s(elem!1))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[2673, 2672])).
% 1.54/1.75 tff(2675,plain,
% 1.54/1.75 ((s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1)) | r(s(s(s(z))), s(elem!1))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2674, 47])).
% 1.54/1.75 tff(2676,plain,
% 1.54/1.75 (b(s(s(s(z))), s(elem!1))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2675, 2671, 2664])).
% 1.54/1.75 tff(2677,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(2678,plain,
% 1.54/1.75 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1)))) <=> ((~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(2679,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[2678])).
% 1.54/1.75 tff(2680,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[2679, 2677])).
% 1.54/1.75 tff(2681,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(2682,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[2681, 2680])).
% 1.54/1.75 tff(2683,plain,
% 1.54/1.75 (~b(s(s(s(s(z)))), s(elem!1))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2682, 246, 2545, 2676, 2662, 2592])).
% 1.54/1.75 tff(2684,plain,
% 1.54/1.75 (r(s(s(s(s(z)))), s(elem!1))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1728, 2683, 2567])).
% 1.54/1.75 tff(2685,plain,
% 1.54/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(2686,plain,
% 1.54/1.75 (((~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(2687,plain,
% 1.54/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[2686])).
% 1.54/1.75 tff(2688,plain,
% 1.54/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z)))),
% 1.54/1.75 inference(transitivity,[status(thm)],[2687, 2685])).
% 1.54/1.75 tff(2689,plain,
% 1.54/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(2690,plain,
% 1.54/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[2689, 2688])).
% 1.54/1.75 tff(2691,plain,
% 1.54/1.75 (~r(s(s(s(s(z)))), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2690, 183, 2223, 2684, 2562])).
% 1.54/1.75 tff(2692,plain,
% 1.54/1.75 (~b(s(s(s(s(z)))), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2407, 246, 1056, 2342, 2003, 2662])).
% 1.54/1.75 tff(2693,plain,
% 1.54/1.75 (r(s(s(s(s(z)))), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2411, 47, 1713, 2692])).
% 1.54/1.75 tff(2694,plain,
% 1.54/1.75 (~r(s(s(s(s(z)))), elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2438, 183, 2340, 2693])).
% 1.54/1.75 tff(2695,plain,
% 1.54/1.75 (elem!1 = s(s(elem!1))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[2539, 134])).
% 1.54/1.76 tff(2696,plain,
% 1.54/1.76 (~(s(s(s(s(z)))) = elem!1)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2399, 2695, 1749])).
% 1.54/1.76 tff(2697,plain,
% 1.54/1.76 (b(s(s(s(s(z)))), elem!1)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2442, 47, 2696, 2694])).
% 1.54/1.76 tff(2698,plain,
% 1.54/1.76 (~b(s(s(s(s(z)))), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2466, 246, 2239, 2537, 2697])).
% 1.54/1.76 tff(2699,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2424, 47, 2421, 2698, 2691])).
% 1.54/1.76 tff(2700,plain,((s(z) = elem!1) | (~b(z, elem!1)) | (s(elem!1) = s(s(s(z)))) | b(z, s(s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | r(s(s(elem!1)), elem!1) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | (s(s(s(s(s(elem!1))))) = elem!1) | b(s(z), elem!1) | b(s(s(s(z))), elem!1) | b(elem!1, s(s(s(z)))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(2701,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2700, 2291, 2284, 1749, 2214, 1056, 2263, 2232, 1555, 69, 1445, 1, 2213, 2235])).
% 1.54/1.76 tff(2702,plain,((~b(s(z), z)) | (s(elem!1) = s(s(s(z)))) | b(z, s(s(s(z)))) | r(s(s(elem!1)), elem!1) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | (s(s(s(s(s(elem!1))))) = elem!1) | b(s(z), elem!1) | b(s(s(s(z))), elem!1) | b(elem!1, s(s(s(z)))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(2703,plain,
% 1.54/1.76 (~b(s(z), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2702, 2232, 2214, 1749, 1555, 69, 1445, 1, 2213, 56])).
% 1.54/1.76 tff(2704,plain,
% 1.54/1.76 (r(s(z), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1069, 2703])).
% 1.54/1.76 tff(2705,plain,
% 1.54/1.76 (r(s(z), elem!1)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1034, 2275, 1445])).
% 1.54/1.76 tff(2706,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(2707,plain,
% 1.54/1.76 (((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(2708,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[2707])).
% 1.54/1.76 tff(2709,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[2708, 2706])).
% 1.54/1.76 tff(2710,plain,
% 1.54/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(2711,plain,
% 1.54/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[2710, 2709])).
% 1.54/1.76 tff(2712,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2711, 183, 2705, 634, 430])).
% 1.54/1.76 tff(2713,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)) | b(s(z), elem!1) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(2714,plain,
% 1.54/1.76 (~r(s(s(s(z))), s(z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2713, 2231, 1445, 2232])).
% 1.54/1.76 tff(2715,plain,
% 1.54/1.76 (b(s(s(s(z))), s(z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[52, 2714])).
% 1.54/1.76 tff(2716,plain,
% 1.54/1.76 (~(s(z) = elem!1)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2290, 2715, 1])).
% 1.54/1.76 tff(2717,plain,
% 1.54/1.76 (r(s(z), elem!1)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1034, 2716, 1445])).
% 1.54/1.76 tff(2718,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, z)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(2719,plain,
% 1.54/1.76 (((~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1))) <=> ((~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, z)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(2720,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, z))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[2719])).
% 1.54/1.76 tff(2721,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, z)))),
% 1.54/1.76 inference(transitivity,[status(thm)],[2720, 2718])).
% 1.54/1.76 tff(2722,plain,
% 1.54/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1)))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(2723,plain,
% 1.54/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, z))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[2722, 2721])).
% 1.54/1.76 tff(2724,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2723, 183, 2246, 1114, 217])).
% 1.54/1.76 tff(2725,plain,((~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(2726,plain,
% 1.54/1.76 (~r(elem!1, z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2725, 2717, 2704])).
% 1.54/1.76 tff(2727,plain,
% 1.54/1.76 (b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.54/1.76 inference(symmetry,[status(thm)],[1768])).
% 1.54/1.76 tff(2728,plain,
% 1.54/1.76 ((~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(s(z))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[1766])).
% 1.54/1.76 tff(2729,plain,
% 1.54/1.76 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[1457, 410])).
% 1.54/1.76 tff(2730,plain,
% 1.54/1.76 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.54/1.76 inference(symmetry,[status(thm)],[2729])).
% 1.54/1.76 tff(2731,plain,
% 1.54/1.76 (r(elem!1, s(s(s(z))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[429, 426])).
% 1.54/1.76 tff(2732,plain,
% 1.54/1.76 (b(s(s(elem!1)), elem!1)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[156, 150, 2232])).
% 1.54/1.76 tff(2733,plain,
% 1.54/1.76 (r(s(z), elem!1) <=> r(s(elem!1), elem!1)),
% 1.54/1.76 inference(monotonicity,[status(thm)],[89])).
% 1.54/1.76 tff(2734,plain,
% 1.54/1.76 (r(s(elem!1), elem!1)),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[217, 2733])).
% 1.54/1.76 tff(2735,plain,
% 1.54/1.76 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(z))), s(elem!1))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[410])).
% 1.54/1.76 tff(2736,plain,
% 1.54/1.76 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.54/1.76 inference(symmetry,[status(thm)],[2735])).
% 1.54/1.76 tff(2737,plain,
% 1.54/1.76 (b(s(s(s(z))), s(elem!1))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[2003, 1848])).
% 1.54/1.76 tff(2738,plain,
% 1.54/1.76 (b(s(s(s(elem!1))), s(elem!1))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[2737, 2736])).
% 1.54/1.76 tff(2739,plain,
% 1.54/1.76 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(z))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[410])).
% 1.54/1.76 tff(2740,plain,
% 1.54/1.76 (b(s(elem!1), s(s(s(z)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.54/1.76 inference(symmetry,[status(thm)],[2739])).
% 1.54/1.76 tff(2741,plain,
% 1.54/1.76 (b(s(elem!1), s(s(s(z))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[2328, 1926])).
% 1.54/1.76 tff(2742,plain,
% 1.54/1.76 (b(s(elem!1), s(s(s(elem!1))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[2741, 2740])).
% 1.54/1.76 tff(2743,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(2744,plain,
% 1.54/1.76 (((~r(s(elem!1), elem!1)) | (~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)))) <=> ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(2745,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~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))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[2744])).
% 1.54/1.76 tff(2746,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~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))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.54/1.76 inference(transitivity,[status(thm)],[2745, 2743])).
% 1.54/1.76 tff(2747,plain,
% 1.54/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~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))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(2748,plain,
% 1.54/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[2747, 2746])).
% 1.54/1.76 tff(2749,plain,
% 1.54/1.76 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2748, 183, 333, 367])).
% 1.54/1.76 tff(2750,plain,
% 1.54/1.76 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1795, 2749, 1787])).
% 1.54/1.76 tff(2751,assumption,(b(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 1.54/1.76 tff(2752,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(2753,plain,
% 1.54/1.76 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(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(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(2754,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[2753])).
% 1.54/1.76 tff(2755,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[2754, 2752])).
% 1.54/1.76 tff(2756,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(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(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(2757,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[2756, 2755])).
% 1.54/1.76 tff(2758,plain,
% 1.54/1.76 (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2757, 246, 2751, 1937, 2750])).
% 1.54/1.76 tff(2759,plain,
% 1.54/1.76 (r(s(s(s(z))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 1.54/1.76 inference(symmetry,[status(thm)],[555])).
% 1.54/1.76 tff(2760,plain,
% 1.54/1.76 (r(s(s(s(elem!1))), elem!1)),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[634, 2759])).
% 1.54/1.76 tff(2761,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(2762,plain,
% 1.54/1.76 (((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(2763,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(s(s(elem!1))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(elem!1))), s(s(s(s(s(elem!1)))))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[2762])).
% 1.54/1.76 tff(2764,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(s(s(elem!1))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[2763, 2761])).
% 1.54/1.76 tff(2765,plain,
% 1.54/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(s(s(elem!1))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(2766,plain,
% 1.54/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[2765, 2764])).
% 1.54/1.76 tff(2767,plain,
% 1.54/1.76 ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2766, 183, 333])).
% 1.54/1.76 tff(2768,plain,
% 1.54/1.76 (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2767, 2760])).
% 1.54/1.76 tff(2769,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[913, 47, 778, 2768, 2758])).
% 1.54/1.76 tff(2770,plain,((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~(z = elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(2771,plain,
% 1.54/1.76 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2770, 2742, 2738, 634, 88, 2734])).
% 1.54/1.76 tff(2772,plain,
% 1.54/1.76 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[86, 2771, 69])).
% 1.54/1.76 tff(2773,plain,
% 1.54/1.76 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[2593, 1459])).
% 1.54/1.76 tff(2774,plain,
% 1.54/1.76 ((~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))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2034, 183])).
% 1.54/1.76 tff(2775,plain,
% 1.54/1.76 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2774, 2773, 414])).
% 1.54/1.76 tff(2776,plain,
% 1.54/1.76 ((s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1571, 47, 2775])).
% 1.54/1.76 tff(2777,plain,
% 1.54/1.76 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2776, 1468])).
% 1.54/1.76 tff(2778,plain,
% 1.54/1.76 ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2050, 183])).
% 1.54/1.76 tff(2779,plain,
% 1.54/1.76 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2778, 2773, 414])).
% 1.54/1.76 tff(2780,plain,
% 1.54/1.76 ((elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2055, 47, 2779])).
% 1.54/1.76 tff(2781,plain,
% 1.54/1.76 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2780, 2044])).
% 1.54/1.76 tff(2782,plain,
% 1.54/1.76 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2063, 246, 714, 2781, 2777])).
% 1.54/1.76 tff(2783,plain,
% 1.54/1.76 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[2782, 1769])).
% 1.54/1.76 tff(2784,plain,
% 1.54/1.76 (r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1897, 2783])).
% 1.54/1.76 tff(2785,plain,
% 1.54/1.76 (r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[2784, 1767])).
% 1.54/1.76 tff(2786,plain,
% 1.54/1.76 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 1.54/1.76 inference(commutativity,[status(thm)],[])).
% 1.54/1.76 tff(2787,plain,
% 1.54/1.76 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[1457, 94])).
% 1.54/1.76 tff(2788,plain,
% 1.54/1.76 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[2787, 2786])).
% 1.54/1.76 tff(2789,plain,
% 1.54/1.76 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.54/1.76 inference(symmetry,[status(thm)],[2788])).
% 1.54/1.76 tff(2790,plain,
% 1.54/1.76 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[2789])).
% 1.54/1.76 tff(2791,plain,
% 1.54/1.76 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1526, 2790])).
% 1.54/1.76 tff(2792,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(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(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(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(elem!1)))), s(s(elem!1)))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(2793,plain,
% 1.54/1.76 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(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(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(elem!1)))), s(s(elem!1)))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(2794,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(elem!1)))), s(s(elem!1))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[2793])).
% 1.54/1.76 tff(2795,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(elem!1)))), s(s(elem!1)))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[2794, 2792])).
% 1.54/1.76 tff(2796,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(2797,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(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(elem!1)))), s(s(elem!1))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[2796, 2795])).
% 1.54/1.76 tff(2798,plain,
% 1.54/1.76 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2797, 246, 2362, 2781, 2777])).
% 1.54/1.77 tff(2799,plain,
% 1.54/1.77 ((s(s(s(s(elem!1)))) = s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1844, 47, 2798])).
% 1.54/1.77 tff(2800,plain,
% 1.54/1.77 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2799, 2791])).
% 1.54/1.77 tff(2801,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~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(X1, 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(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(2802,plain,
% 1.54/1.77 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(2803,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[2802])).
% 1.54/1.77 tff(2804,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[2803, 2801])).
% 1.54/1.77 tff(2805,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(2806,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[2805, 2804])).
% 1.54/1.77 tff(2807,plain,
% 1.54/1.77 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2806, 246, 2362, 714, 2781, 2777])).
% 1.54/1.77 tff(2808,plain,
% 1.54/1.77 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[361, 47, 1555, 2807])).
% 1.54/1.77 tff(2809,plain,
% 1.54/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(2810,plain,
% 1.54/1.77 (((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), 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(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(2811,plain,
% 1.54/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[2810])).
% 1.54/1.77 tff(2812,plain,
% 1.54/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[2811, 2809])).
% 1.54/1.77 tff(2813,plain,
% 1.54/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(2814,plain,
% 1.54/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[2813, 2812])).
% 1.54/1.77 tff(2815,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2814, 183, 2808, 2800, 2785])).
% 1.54/1.77 tff(2816,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~(z = elem!1)) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(2817,plain,
% 1.54/1.77 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2816, 88, 1555, 2772, 2732, 2731])).
% 1.54/1.77 tff(2818,plain,
% 1.54/1.77 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1702, 2817])).
% 1.54/1.77 tff(2819,plain,
% 1.54/1.77 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[2818, 2730])).
% 1.54/1.77 tff(2820,plain,
% 1.54/1.77 ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1985, 246, 2742, 2738])).
% 1.54/1.77 tff(2821,plain,
% 1.54/1.77 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2820, 2819])).
% 1.54/1.77 tff(2822,plain,
% 1.54/1.77 (~b(s(s(s(s(z)))), s(elem!1))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[2821, 1716])).
% 1.54/1.77 tff(2823,plain,
% 1.54/1.77 (r(s(s(s(s(z)))), s(elem!1))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1728, 2822, 1714])).
% 1.54/1.77 tff(2824,plain,
% 1.54/1.77 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[2823, 1706])).
% 1.54/1.77 tff(2825,plain,
% 1.54/1.77 ((s(elem!1) = elem!1) <=> (elem!1 = s(elem!1))),
% 1.54/1.77 inference(commutativity,[status(thm)],[])).
% 1.54/1.77 tff(2826,plain,
% 1.54/1.77 ((s(elem!1) = z) <=> (s(elem!1) = elem!1)),
% 1.54/1.77 inference(monotonicity,[status(thm)],[88])).
% 1.54/1.77 tff(2827,plain,
% 1.54/1.77 ((s(elem!1) = z) <=> (elem!1 = s(elem!1))),
% 1.54/1.77 inference(transitivity,[status(thm)],[2826, 2825])).
% 1.54/1.77 tff(2828,plain,
% 1.54/1.77 ((~(s(elem!1) = z)) <=> (~(elem!1 = s(elem!1)))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[2827])).
% 1.54/1.77 tff(2829,plain,
% 1.54/1.77 (~(elem!1 = s(elem!1))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[111, 2828])).
% 1.54/1.77 tff(2830,assumption,(r(s(s(s(s(elem!1)))), s(elem!1))), introduced(assumption)).
% 1.54/1.77 tff(2831,plain,
% 1.54/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(2832,plain,
% 1.54/1.77 (((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1))))))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(2833,plain,
% 1.54/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[2832])).
% 1.54/1.77 tff(2834,plain,
% 1.54/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[2833, 2831])).
% 1.54/1.77 tff(2835,plain,
% 1.54/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(2836,plain,
% 1.54/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[2835, 2834])).
% 1.54/1.77 tff(2837,plain,
% 1.54/1.77 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2836, 183, 601, 2830])).
% 1.54/1.77 tff(2838,plain,
% 1.54/1.77 ((elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2055, 47, 2837])).
% 1.54/1.77 tff(2839,plain,
% 1.54/1.77 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2838, 2044])).
% 1.54/1.77 tff(2840,plain,
% 1.54/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(2841,plain,
% 1.54/1.77 (((~r(elem!1, s(elem!1))) | (~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))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(2842,plain,
% 1.54/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~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)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[2841])).
% 1.54/1.77 tff(2843,plain,
% 1.54/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~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)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[2842, 2840])).
% 1.54/1.77 tff(2844,plain,
% 1.54/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~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)))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(2845,plain,
% 1.54/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[2844, 2843])).
% 1.54/1.77 tff(2846,plain,
% 1.54/1.77 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2845, 183, 601, 2830])).
% 1.54/1.77 tff(2847,plain,
% 1.54/1.77 ((s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1571, 47, 2846])).
% 1.54/1.77 tff(2848,plain,
% 1.54/1.77 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2847, 1468])).
% 1.54/1.77 tff(2849,plain,
% 1.54/1.77 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2063, 246, 714, 2848, 2839])).
% 1.54/1.77 tff(2850,plain,
% 1.54/1.77 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[2849, 1769])).
% 1.54/1.77 tff(2851,plain,
% 1.54/1.77 (r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1897, 2850])).
% 1.54/1.77 tff(2852,plain,
% 1.54/1.77 (r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[2851, 1767])).
% 1.54/1.77 tff(2853,plain,
% 1.54/1.77 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2797, 246, 2362, 2848, 2839])).
% 1.54/1.77 tff(2854,plain,
% 1.54/1.77 ((s(s(s(s(elem!1)))) = s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1844, 47, 2853])).
% 1.54/1.77 tff(2855,plain,
% 1.54/1.77 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2854, 2791])).
% 1.54/1.77 tff(2856,plain,
% 1.54/1.77 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2806, 246, 2362, 714, 2848, 2839])).
% 1.54/1.77 tff(2857,plain,
% 1.54/1.77 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[361, 47, 1555, 2856])).
% 1.54/1.77 tff(2858,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2814, 183, 2857, 2855, 2852])).
% 1.54/1.77 tff(2859,plain,((~r(elem!1, s(elem!1))) | (~(z = elem!1)) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(2860,plain,
% 1.54/1.77 (~r(elem!1, s(elem!1))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2859, 88, 1555, 2732, 2772, 2824])).
% 1.54/1.77 tff(2861,plain,
% 1.54/1.77 (((~![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)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(2862,plain,
% 1.54/1.77 ((~![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)))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(2863,plain,
% 1.54/1.77 ((~![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))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[2862, 2861])).
% 1.54/1.77 tff(2864,plain,
% 1.54/1.77 ((elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2863, 47])).
% 1.54/1.77 tff(2865,plain,
% 1.54/1.77 (b(elem!1, s(elem!1))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2864, 2860, 2829])).
% 1.54/1.77 tff(2866,assumption,(b(s(s(s(s(s(elem!1))))), s(elem!1))), introduced(assumption)).
% 1.54/1.77 tff(2867,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), 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))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(2868,plain,
% 1.54/1.77 (((~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(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1))) <=> ((~b(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))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(2869,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[2868])).
% 1.54/1.77 tff(2870,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[2869, 2867])).
% 1.54/1.77 tff(2871,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), 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(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(2872,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[2871, 2870])).
% 1.54/1.77 tff(2873,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2872, 246, 2751, 714, 1937, 2866, 1574])).
% 1.54/1.77 tff(2874,plain,((~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(2875,plain,
% 1.54/1.77 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2874, 2742, 2772, 2738, 2865])).
% 1.54/1.77 tff(2876,plain,
% 1.54/1.77 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1795, 2875, 1787])).
% 1.54/1.77 tff(2877,plain,
% 1.54/1.77 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2083, 183, 2876, 2824])).
% 1.54/1.77 tff(2878,plain,
% 1.54/1.77 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[2877, 2728])).
% 1.54/1.77 tff(2879,plain,
% 1.54/1.77 (b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1897, 2878])).
% 1.54/1.77 tff(2880,plain,
% 1.54/1.77 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[2879, 2727])).
% 1.54/1.77 tff(2881,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(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(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(2882,plain,
% 1.54/1.77 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), 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(s(elem!1))))), 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(elem!1, s(elem!1))) | (~b(s(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(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(2883,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(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(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[2882])).
% 1.54/1.77 tff(2884,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(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(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[2883, 2881])).
% 1.54/1.77 tff(2885,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), 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(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(2886,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(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))))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[2885, 2884])).
% 1.54/1.77 tff(2887,plain,
% 1.54/1.77 ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2886, 246, 2742, 2772, 2865, 2819])).
% 1.54/1.77 tff(2888,plain,
% 1.54/1.77 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2887, 2880])).
% 1.54/1.77 tff(2889,plain,
% 1.54/1.77 ((s(s(s(s(elem!1)))) = elem!1) | r(s(s(s(s(elem!1)))), elem!1)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1571, 47, 2888])).
% 1.54/1.77 tff(2890,plain,
% 1.54/1.77 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2889, 1468])).
% 1.54/1.77 tff(2891,plain,
% 1.54/1.77 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 1.54/1.77 inference(commutativity,[status(thm)],[])).
% 1.54/1.77 tff(2892,plain,
% 1.54/1.77 ((s(elem!1) = s(s(s(s(elem!1))))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[1457])).
% 1.54/1.77 tff(2893,plain,
% 1.54/1.77 ((s(elem!1) = s(s(s(s(elem!1))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 1.54/1.77 inference(transitivity,[status(thm)],[2892, 2891])).
% 1.54/1.77 tff(2894,plain,
% 1.54/1.77 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 1.54/1.77 inference(symmetry,[status(thm)],[2893])).
% 1.54/1.77 tff(2895,plain,
% 1.54/1.77 ((~(s(s(s(s(z)))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(elem!1))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[2894])).
% 1.54/1.77 tff(2896,plain,
% 1.54/1.77 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[1714, 2895])).
% 1.54/1.77 tff(2897,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), 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(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(2898,plain,
% 1.54/1.77 (((~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(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(elem!1))), 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)))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(2899,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[2898])).
% 1.54/1.78 tff(2900,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[2899, 2897])).
% 1.54/1.78 tff(2901,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), 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(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(2902,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), 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(s(elem!1))))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[2901, 2900])).
% 1.54/1.78 tff(2903,plain,
% 1.54/1.78 ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[2902, 246, 2742, 2738])).
% 1.54/1.78 tff(2904,plain,
% 1.54/1.78 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[2903, 2819])).
% 1.54/1.78 tff(2905,plain,
% 1.54/1.78 (((~![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))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(2906,plain,
% 1.54/1.78 ((~![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))))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(2907,plain,
% 1.54/1.78 ((~![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)))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[2906, 2905])).
% 1.54/1.78 tff(2908,plain,
% 1.54/1.78 ((s(elem!1) = s(s(s(s(elem!1))))) | r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[2907, 47, 2904])).
% 1.54/1.78 tff(2909,plain,
% 1.54/1.78 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[2908, 2896])).
% 1.54/1.78 tff(2910,plain,
% 1.54/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(2911,plain,
% 1.54/1.78 (((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(2912,plain,
% 1.54/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[2911])).
% 1.54/1.78 tff(2913,plain,
% 1.54/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[2912, 2910])).
% 1.54/1.78 tff(2914,plain,
% 1.54/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(2915,plain,
% 1.54/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1))))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[2914, 2913])).
% 1.54/1.78 tff(2916,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[2915, 183, 2734, 2909, 2890])).
% 1.54/1.78 tff(2917,plain,((~(z = elem!1)) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | (s(s(s(s(s(elem!1))))) = elem!1) | (~r(s(s(s(z))), elem!1)) | r(s(s(elem!1)), elem!1) | (~b(s(s(s(z))), s(z))) | (~r(s(z), elem!1)) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(2918,plain,
% 1.54/1.78 (~(z = elem!1)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[2917, 2231, 69, 1555, 2232, 2715, 2717, 2223])).
% 1.54/1.78 tff(2919,plain,
% 1.54/1.78 (~(elem!1 = z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1041, 2918])).
% 1.54/1.78 tff(2920,plain,
% 1.54/1.78 (b(elem!1, z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1143, 2919, 2726])).
% 1.54/1.78 tff(2921,plain,
% 1.54/1.78 (b(z, elem!1)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[60, 2918, 56])).
% 1.54/1.78 tff(2922,plain,
% 1.54/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(2923,plain,
% 1.54/1.78 (((~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(2924,plain,
% 1.54/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[2923])).
% 1.54/1.78 tff(2925,plain,
% 1.54/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.54/1.78 inference(transitivity,[status(thm)],[2924, 2922])).
% 1.54/1.78 tff(2926,plain,
% 1.54/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(2927,plain,
% 1.54/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[2926, 2925])).
% 1.54/1.78 tff(2928,plain,
% 1.54/1.78 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[2927, 183, 1114, 217, 333])).
% 1.54/1.78 tff(2929,plain,
% 1.54/1.78 (b(s(s(s(s(s(elem!1))))), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[2311, 47, 331, 2928])).
% 1.54/1.78 tff(2930,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(2931,plain,
% 1.54/1.78 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z)))) <=> ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(2932,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z)))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[2931])).
% 1.54/1.78 tff(2933,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[2932, 2930])).
% 1.54/1.78 tff(2934,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(2935,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z)))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[2934, 2933])).
% 1.54/1.78 tff(2936,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[2935, 246, 2328, 2003, 2320, 2929])).
% 1.54/1.78 tff(2937,plain,((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(2938,plain,
% 1.54/1.78 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[2937, 2715, 2231, 2704, 2717])).
% 1.54/1.78 tff(2939,plain,
% 1.54/1.78 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[86, 2938, 69])).
% 1.54/1.78 tff(2940,plain,
% 1.54/1.78 (~b(s(s(elem!1)), elem!1)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[2388, 2939, 2921, 1555, 2920])).
% 1.54/1.78 tff(2941,plain,
% 1.54/1.78 (s(s(elem!1)) = elem!1),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[156, 2940, 2232])).
% 1.54/1.78 tff(2942,plain,
% 1.54/1.78 (s(s(s(elem!1))) = s(elem!1)),
% 1.54/1.78 inference(monotonicity,[status(thm)],[2941])).
% 1.54/1.78 tff(2943,plain,
% 1.54/1.78 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[2942])).
% 1.54/1.78 tff(2944,plain,
% 1.54/1.78 (s(s(s(s(elem!1)))) = elem!1),
% 1.54/1.78 inference(transitivity,[status(thm)],[2943, 2941])).
% 1.54/1.78 tff(2945,plain,
% 1.54/1.78 (s(s(s(s(s(elem!1))))) = s(elem!1)),
% 1.54/1.78 inference(monotonicity,[status(thm)],[2944])).
% 1.54/1.78 tff(2946,plain,
% 1.54/1.78 (b(s(s(s(s(s(elem!1))))), elem!1) <=> b(s(elem!1), elem!1)),
% 1.54/1.78 inference(monotonicity,[status(thm)],[2945])).
% 1.54/1.78 tff(2947,plain,
% 1.54/1.78 (b(s(elem!1), elem!1)),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[2939, 2946])).
% 1.54/1.78 tff(2948,plain,
% 1.54/1.78 (~b(z, s(elem!1))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[2551, 246, 2921, 2920, 2947])).
% 1.54/1.78 tff(2949,plain,
% 1.54/1.78 (r(z, s(elem!1))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[2561, 2948])).
% 1.54/1.78 tff(2950,plain,
% 1.54/1.78 (s(elem!1) = s(s(s(s(s(elem!1)))))),
% 1.54/1.78 inference(symmetry,[status(thm)],[2945])).
% 1.54/1.78 tff(2951,plain,
% 1.54/1.78 ((s(z) = s(elem!1)) <=> (s(z) = s(s(s(s(s(elem!1))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[2950])).
% 1.54/1.78 tff(2952,plain,
% 1.54/1.78 ((s(z) = s(elem!1)) <=> (s(s(s(s(s(elem!1))))) = s(z))),
% 1.54/1.78 inference(transitivity,[status(thm)],[2951, 317])).
% 1.54/1.78 tff(2953,plain,
% 1.54/1.78 ((s(s(s(s(s(elem!1))))) = s(z)) <=> (s(z) = s(elem!1))),
% 1.54/1.78 inference(symmetry,[status(thm)],[2952])).
% 1.54/1.78 tff(2954,plain,
% 1.54/1.78 ((~(s(s(s(s(s(elem!1))))) = s(z))) <=> (~(s(z) = s(elem!1)))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[2953])).
% 1.54/1.78 tff(2955,plain,
% 1.54/1.78 (~(s(z) = s(elem!1))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[331, 2954])).
% 1.54/1.78 tff(2956,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(2957,plain,
% 1.54/1.78 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(2958,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[2957])).
% 1.54/1.78 tff(2959,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.54/1.78 inference(transitivity,[status(thm)],[2958, 2956])).
% 1.54/1.78 tff(2960,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(2961,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[2960, 2959])).
% 1.54/1.78 tff(2962,plain,
% 1.54/1.78 (~b(s(elem!1), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[2961, 246, 2921, 2920, 2947])).
% 1.54/1.78 tff(2963,plain,
% 1.54/1.78 (r(s(elem!1), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[2581, 2962])).
% 1.54/1.78 tff(2964,plain,
% 1.54/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(2965,plain,
% 1.54/1.78 (((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1)))) <=> ((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(2966,plain,
% 1.54/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1)))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[2965])).
% 1.54/1.78 tff(2967,plain,
% 1.54/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[2966, 2964])).
% 1.54/1.78 tff(2968,plain,
% 1.54/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(2969,plain,
% 1.54/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1)))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[2968, 2967])).
% 1.54/1.78 tff(2970,plain,
% 1.54/1.78 (~r(s(z), s(elem!1))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[2969, 183, 2704, 2963])).
% 1.54/1.78 tff(2971,plain,
% 1.54/1.78 (((~![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)))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(2972,plain,
% 1.54/1.78 ((~![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)))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(2973,plain,
% 1.54/1.78 ((~![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))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[2972, 2971])).
% 1.54/1.78 tff(2974,plain,
% 1.54/1.78 ((s(z) = s(elem!1)) | b(s(z), s(elem!1))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[2973, 47, 2970])).
% 1.54/1.78 tff(2975,plain,
% 1.54/1.78 (b(s(z), s(elem!1))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[2974, 2955])).
% 1.54/1.78 tff(2976,plain,
% 1.54/1.78 ((s(elem!1) = s(z)) <=> (s(s(s(s(s(elem!1))))) = s(z))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[2950])).
% 1.54/1.78 tff(2977,plain,
% 1.54/1.78 ((s(s(s(s(s(elem!1))))) = s(z)) <=> (s(elem!1) = s(z))),
% 1.54/1.78 inference(symmetry,[status(thm)],[2976])).
% 1.54/1.78 tff(2978,plain,
% 1.54/1.78 ((~(s(s(s(s(s(elem!1))))) = s(z))) <=> (~(s(elem!1) = s(z)))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[2977])).
% 1.54/1.78 tff(2979,plain,
% 1.54/1.78 (~(s(elem!1) = s(z))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[331, 2978])).
% 1.54/1.79 tff(2980,plain,
% 1.54/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(2981,plain,
% 1.54/1.79 (((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(2982,plain,
% 1.54/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[2981])).
% 1.54/1.79 tff(2983,plain,
% 1.54/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 1.54/1.79 inference(transitivity,[status(thm)],[2982, 2980])).
% 1.54/1.79 tff(2984,plain,
% 1.54/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(2985,plain,
% 1.54/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[2984, 2983])).
% 1.54/1.79 tff(2986,plain,
% 1.54/1.79 (~r(s(elem!1), s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[2985, 183, 2704, 2963])).
% 1.54/1.79 tff(2987,plain,
% 1.54/1.79 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z)))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(2988,plain,
% 1.54/1.79 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z)))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(2989,plain,
% 1.54/1.79 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[2988, 2987])).
% 1.54/1.79 tff(2990,plain,
% 1.54/1.79 ((s(elem!1) = s(z)) | b(s(elem!1), s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[2989, 47, 2986])).
% 1.54/1.79 tff(2991,plain,
% 1.54/1.79 (b(s(elem!1), s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[2990, 2979])).
% 1.54/1.79 tff(2992,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(2993,plain,
% 1.54/1.79 (((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(2994,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z)))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[2993])).
% 1.54/1.79 tff(2995,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[2994, 2992])).
% 1.54/1.79 tff(2996,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(2997,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z)))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[2996, 2995])).
% 1.54/1.79 tff(2998,plain,
% 1.54/1.79 (~b(s(s(s(z))), s(elem!1))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[2997, 246, 2715, 2991, 2975])).
% 1.54/1.79 tff(2999,plain,
% 1.54/1.79 (r(s(s(s(z))), s(elem!1))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[2675, 2998, 2664])).
% 1.54/1.79 tff(3000,plain,
% 1.54/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(3001,plain,
% 1.54/1.79 (((~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(3002,plain,
% 1.54/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1)))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3001])).
% 1.54/1.79 tff(3003,plain,
% 1.54/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[3002, 3000])).
% 1.54/1.79 tff(3004,plain,
% 1.54/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(s(s(z))))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(3005,plain,
% 1.54/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1)))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[3004, 3003])).
% 1.54/1.79 tff(3006,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3005, 183, 2223, 2999, 2949])).
% 1.54/1.79 tff(3007,plain,(r(s(s(elem!1)), elem!1) | (s(elem!1) = s(s(s(z)))) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | (s(s(s(s(s(elem!1))))) = elem!1) | r(z, elem!1) | b(s(z), elem!1) | b(s(s(s(z))), elem!1) | b(z, s(s(s(z)))) | b(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(3008,plain,
% 1.54/1.79 (r(s(s(elem!1)), elem!1)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3007, 1749, 1555, 69, 56, 1445, 1, 2214, 2213])).
% 1.54/1.79 tff(3009,plain,
% 1.54/1.79 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1637, 183, 3008, 2231])).
% 1.54/1.79 tff(3010,plain,
% 1.54/1.79 (s(s(s(z))) = elem!1),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[2292, 74])).
% 1.54/1.79 tff(3011,assumption,(~(s(s(s(z))) = elem!1)), introduced(assumption)).
% 1.54/1.79 tff(3012,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3011, 3010])).
% 1.54/1.79 tff(3013,plain,((~(elem!1 = s(s(s(z))))) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(3014,plain,
% 1.54/1.79 (~(elem!1 = s(s(s(z))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3013, 2230])).
% 1.54/1.79 tff(3015,plain,
% 1.54/1.79 (r(elem!1, s(s(s(z))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[470, 3014, 2213])).
% 1.54/1.79 tff(3016,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[2711, 183, 217, 634, 430])).
% 1.54/1.79 tff(3017,plain,((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(3018,plain,
% 1.54/1.79 (~r(s(z), elem!1)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3017, 430, 634])).
% 1.54/1.79 tff(3019,plain,
% 1.54/1.79 (s(z) = elem!1),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1034, 3018, 1445])).
% 1.54/1.79 tff(3020,plain,
% 1.54/1.79 (s(s(s(z))) = s(s(elem!1))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[121, 3019])).
% 1.54/1.79 tff(3021,plain,
% 1.54/1.79 (b(s(elem!1), s(s(s(z)))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3020])).
% 1.54/1.79 tff(3022,plain,
% 1.54/1.79 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(s(z))))),
% 1.54/1.79 inference(symmetry,[status(thm)],[3021])).
% 1.54/1.79 tff(3023,plain,
% 1.54/1.79 ((~b(s(elem!1), s(s(elem!1)))) <=> (~b(s(elem!1), s(s(s(z)))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3022])).
% 1.54/1.79 tff(3024,plain,
% 1.54/1.79 ((s(s(s(z))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 1.54/1.79 inference(commutativity,[status(thm)],[])).
% 1.54/1.79 tff(3025,plain,
% 1.54/1.79 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3020])).
% 1.54/1.79 tff(3026,plain,
% 1.54/1.79 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.54/1.79 inference(symmetry,[status(thm)],[3025])).
% 1.54/1.79 tff(3027,plain,
% 1.54/1.79 (s(s(elem!1)) = s(s(s(z)))),
% 1.54/1.79 inference(symmetry,[status(thm)],[3020])).
% 1.54/1.79 tff(3028,plain,
% 1.54/1.79 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(s(s(z)))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3027, 3026])).
% 1.54/1.79 tff(3029,plain,
% 1.54/1.79 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[3028, 3024])).
% 1.54/1.79 tff(3030,plain,
% 1.54/1.79 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 1.54/1.79 inference(symmetry,[status(thm)],[3029])).
% 1.54/1.79 tff(3031,plain,
% 1.54/1.79 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3030])).
% 1.54/1.79 tff(3032,plain,
% 1.54/1.79 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[1697, 3031])).
% 1.54/1.79 tff(3033,plain,
% 1.54/1.79 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(s(z)))) = elem!1)),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3026])).
% 1.54/1.79 tff(3034,plain,
% 1.54/1.79 ((s(s(s(s(z)))) = elem!1) <=> (s(s(s(elem!1))) = elem!1)),
% 1.54/1.79 inference(symmetry,[status(thm)],[3033])).
% 1.54/1.79 tff(3035,plain,
% 1.54/1.79 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3034])).
% 1.54/1.79 tff(3036,plain,
% 1.54/1.79 ((s(s(s(s(z)))) = s(z)) <=> (s(s(s(s(z)))) = elem!1)),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3019])).
% 1.54/1.79 tff(3037,plain,
% 1.54/1.79 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3036])).
% 1.54/1.79 tff(3038,plain,
% 1.54/1.79 (~(s(s(s(s(z)))) = elem!1)),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[1713, 3037])).
% 1.54/1.79 tff(3039,plain,
% 1.54/1.79 (~(s(s(s(elem!1))) = elem!1)),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[3038, 3035])).
% 1.54/1.79 tff(3040,plain,
% 1.54/1.79 (r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))) <=> r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3026])).
% 1.54/1.79 tff(3041,plain,
% 1.54/1.79 (r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))) <=> r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.54/1.79 inference(symmetry,[status(thm)],[3040])).
% 1.54/1.79 tff(3042,plain,
% 1.54/1.79 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3026])).
% 1.54/1.79 tff(3043,plain,
% 1.54/1.79 ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) <=> (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3042])).
% 1.54/1.79 tff(3044,plain,
% 1.54/1.79 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3027])).
% 1.54/1.79 tff(3045,plain,
% 1.54/1.79 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.54/1.79 inference(symmetry,[status(thm)],[3044])).
% 1.54/1.79 tff(3046,plain,
% 1.54/1.79 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3025])).
% 1.54/1.79 tff(3047,plain,
% 1.54/1.79 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3025, 3020])).
% 1.54/1.79 tff(3048,plain,
% 1.54/1.79 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.79 inference(symmetry,[status(thm)],[3047])).
% 1.54/1.79 tff(3049,plain,
% 1.54/1.79 ((~r(s(s(s(elem!1))), s(s(elem!1)))) <=> (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3048])).
% 1.54/1.79 tff(3050,plain,
% 1.54/1.79 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3020])).
% 1.54/1.79 tff(3051,plain,
% 1.54/1.79 (r(elem!1, s(s(elem!1)))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[413, 3050])).
% 1.54/1.79 tff(3052,plain,
% 1.54/1.79 (r(z, s(s(s(z)))) <=> r(z, s(s(elem!1)))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3020])).
% 1.54/1.79 tff(3053,plain,
% 1.54/1.79 (r(z, s(s(elem!1)))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[429, 3052])).
% 1.54/1.79 tff(3054,plain,
% 1.54/1.79 (~r(elem!1, z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[2254, 413, 429])).
% 1.54/1.79 tff(3055,plain,
% 1.54/1.79 (~(z = elem!1)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[115, 3020])).
% 1.54/1.79 tff(3056,plain,
% 1.54/1.79 (~(elem!1 = z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1041, 3055])).
% 1.54/1.79 tff(3057,plain,
% 1.54/1.79 (b(elem!1, z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1143, 3056, 3054])).
% 1.54/1.79 tff(3058,plain,
% 1.54/1.79 (~r(z, s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[438, 430, 429])).
% 1.54/1.79 tff(3059,plain,
% 1.54/1.79 (b(z, s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[169, 3058])).
% 1.54/1.79 tff(3060,plain,
% 1.54/1.79 (b(z, s(z)) <=> b(z, elem!1)),
% 1.54/1.79 inference(monotonicity,[status(thm)],[6])).
% 1.54/1.79 tff(3061,plain,
% 1.54/1.79 (b(z, elem!1) <=> b(z, s(z))),
% 1.54/1.79 inference(symmetry,[status(thm)],[3060])).
% 1.54/1.79 tff(3062,plain,
% 1.54/1.79 ((~b(z, elem!1)) <=> (~b(z, s(z)))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3061])).
% 1.54/1.79 tff(3063,plain,
% 1.54/1.79 (~b(z, s(z))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[55, 3062])).
% 1.54/1.79 tff(3064,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[236, 3063])).
% 1.54/1.79 tff(3065,plain,((~(s(z) = elem!1)) | (~b(z, s(z))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(3066,plain,
% 1.54/1.79 (b(z, elem!1)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3065, 3019, 3059])).
% 1.54/1.79 tff(3067,plain,
% 1.54/1.79 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.54/1.79 inference(commutativity,[status(thm)],[])).
% 1.54/1.79 tff(3068,plain,
% 1.54/1.79 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[97])).
% 1.54/1.79 tff(3069,plain,
% 1.54/1.79 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.54/1.79 inference(symmetry,[status(thm)],[3068])).
% 1.54/1.79 tff(3070,plain,
% 1.54/1.79 ((elem!1 = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(s(z)))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3069])).
% 1.54/1.79 tff(3071,plain,
% 1.54/1.79 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.54/1.79 inference(transitivity,[status(thm)],[3070, 3067])).
% 1.54/1.79 tff(3072,plain,
% 1.54/1.79 ((s(s(s(s(z)))) = elem!1) <=> (elem!1 = s(s(s(elem!1))))),
% 1.54/1.79 inference(symmetry,[status(thm)],[3071])).
% 1.54/1.79 tff(3073,plain,
% 1.54/1.79 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3072])).
% 1.54/1.79 tff(3074,assumption,(~(s(s(s(s(z)))) = elem!1)), introduced(assumption)).
% 1.54/1.79 tff(3075,plain,
% 1.54/1.79 (~(elem!1 = s(s(s(elem!1))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[3074, 3073])).
% 1.54/1.79 tff(3076,assumption,(r(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 1.54/1.79 tff(3077,plain,
% 1.54/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(3078,plain,
% 1.54/1.79 (((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(3079,plain,
% 1.54/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3078])).
% 1.54/1.79 tff(3080,plain,
% 1.54/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))),
% 1.54/1.79 inference(transitivity,[status(thm)],[3079, 3077])).
% 1.54/1.79 tff(3081,plain,
% 1.54/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(3082,plain,
% 1.54/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[3081, 3080])).
% 1.54/1.79 tff(3083,plain,
% 1.54/1.79 (~r(s(s(s(elem!1))), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3082, 183, 266, 3076])).
% 1.54/1.79 tff(3084,plain,
% 1.54/1.79 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = z) | b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = z) | b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(3085,plain,
% 1.54/1.79 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = z) | b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(3086,plain,
% 1.54/1.79 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = z) | b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z)),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[3085, 3084])).
% 1.54/1.79 tff(3087,plain,
% 1.54/1.79 (b(s(s(s(elem!1))), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3086, 47, 355, 3083])).
% 1.54/1.79 tff(3088,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(3089,plain,
% 1.54/1.79 (((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(3090,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(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(X1, 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(elem!1))))) | (~b(s(s(s(elem!1))), z))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3089])).
% 1.54/1.79 tff(3091,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(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(X1, 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(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 1.54/1.79 inference(transitivity,[status(thm)],[3090, 3088])).
% 1.54/1.79 tff(3092,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(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))))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(3093,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[3092, 3091])).
% 1.54/1.79 tff(3094,plain,
% 1.54/1.79 (~b(elem!1, s(s(s(elem!1))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3093, 246, 2239, 1051, 3087])).
% 1.54/1.79 tff(3095,plain,
% 1.54/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(3096,plain,
% 1.54/1.79 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(3097,plain,
% 1.54/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1)))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3096])).
% 1.54/1.79 tff(3098,plain,
% 1.54/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[3097, 3095])).
% 1.54/1.79 tff(3099,plain,
% 1.54/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(3100,plain,
% 1.54/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1)))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[3099, 3098])).
% 1.54/1.79 tff(3101,plain,
% 1.54/1.79 (~r(elem!1, s(s(s(elem!1))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3100, 183, 602, 3076])).
% 1.54/1.79 tff(3102,plain,
% 1.54/1.79 (((~![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)))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(3103,plain,
% 1.54/1.79 ((~![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)))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(3104,plain,
% 1.54/1.79 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[3103, 3102])).
% 1.54/1.79 tff(3105,plain,
% 1.54/1.79 ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3104, 47, 3101])).
% 1.54/1.79 tff(3106,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3105, 3094, 3075])).
% 1.54/1.79 tff(3107,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (s(s(s(s(z)))) = elem!1) | (~(s(s(s(z))) = s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(3108,plain,
% 1.54/1.79 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3107, 3066, 3057, 3038, 3020, 3053, 3051])).
% 1.54/1.79 tff(3109,plain,
% 1.54/1.79 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[3108, 3049])).
% 1.54/1.79 tff(3110,plain,
% 1.54/1.79 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1702, 3109])).
% 1.54/1.79 tff(3111,plain,
% 1.54/1.79 (b(s(s(s(elem!1))), s(s(s(z))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[3110, 3046])).
% 1.54/1.79 tff(3112,plain,
% 1.54/1.79 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[3111, 3045])).
% 1.54/1.79 tff(3113,plain,
% 1.54/1.79 (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[1555, 1536])).
% 1.54/1.79 tff(3114,plain,
% 1.54/1.79 ((s(s(s(z))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(z))))),
% 1.54/1.79 inference(commutativity,[status(thm)],[])).
% 1.54/1.79 tff(3115,plain,
% 1.54/1.79 ((s(s(s(s(s(elem!1))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(elem!1))))))),
% 1.54/1.79 inference(symmetry,[status(thm)],[3114])).
% 1.54/1.79 tff(3116,plain,
% 1.54/1.79 ((~(s(s(s(s(s(elem!1))))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(s(s(s(elem!1)))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3115])).
% 1.54/1.79 tff(3117,plain,
% 1.54/1.79 (~(s(s(s(z))) = s(s(s(s(s(elem!1))))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[1622, 3116])).
% 1.54/1.79 tff(3118,plain,
% 1.54/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(3119,plain,
% 1.54/1.79 (((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(3120,plain,
% 1.54/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[3119])).
% 1.64/1.80 tff(3121,plain,
% 1.64/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.64/1.80 inference(transitivity,[status(thm)],[3120, 3118])).
% 1.64/1.80 tff(3122,plain,
% 1.64/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(3123,plain,
% 1.64/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[3122, 3121])).
% 1.64/1.80 tff(3124,plain,
% 1.64/1.80 (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3123, 183, 634, 333])).
% 1.64/1.80 tff(3125,plain,
% 1.64/1.80 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(z))), s(s(s(s(s(elem!1)))))) | r(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(z))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(z))), s(s(s(s(s(elem!1)))))) | r(s(s(s(z))), s(s(s(s(s(elem!1)))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(3126,plain,
% 1.64/1.80 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(z))), s(s(s(s(s(elem!1)))))) | r(s(s(s(z))), s(s(s(s(s(elem!1)))))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(3127,plain,
% 1.64/1.80 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(z))), s(s(s(s(s(elem!1)))))) | r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[3126, 3125])).
% 1.64/1.80 tff(3128,plain,
% 1.64/1.80 ((s(s(s(z))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3127, 47, 3124])).
% 1.64/1.80 tff(3129,plain,
% 1.64/1.80 (b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3128, 3117])).
% 1.64/1.80 tff(3130,plain,
% 1.64/1.80 (b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1548, 3113])).
% 1.64/1.80 tff(3131,plain,
% 1.64/1.80 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[361, 47, 1555, 340])).
% 1.64/1.80 tff(3132,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(3133,plain,
% 1.64/1.80 (((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(z)))))) <=> ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(3134,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[3133])).
% 1.64/1.80 tff(3135,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[3134, 3132])).
% 1.64/1.80 tff(3136,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(3137,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[3136, 3135])).
% 1.64/1.80 tff(3138,plain,
% 1.64/1.80 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3137, 246, 3131, 3130, 3129])).
% 1.64/1.80 tff(3139,plain,
% 1.64/1.80 (s(s(elem!1)) = s(s(s(z)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[454, 3138, 1638])).
% 1.64/1.80 tff(3140,plain,
% 1.64/1.80 (inj_0(s(s(elem!1))) = inj_0(s(s(s(z))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[3139])).
% 1.64/1.80 tff(3141,plain,
% 1.64/1.80 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 1.64/1.80 inference(symmetry,[status(thm)],[3140])).
% 1.64/1.80 tff(3142,plain,
% 1.64/1.80 (s(s(z)) = s(elem!1)),
% 1.64/1.80 inference(transitivity,[status(thm)],[25, 3141, 92])).
% 1.64/1.80 tff(3143,plain,
% 1.64/1.80 (b(s(s(z)), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[3142])).
% 1.64/1.80 tff(3144,plain,
% 1.64/1.80 (b(s(elem!1), s(s(s(z)))) <=> b(s(s(z)), s(s(s(z))))),
% 1.64/1.80 inference(symmetry,[status(thm)],[3143])).
% 1.64/1.80 tff(3145,plain,
% 1.64/1.80 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(z))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[3139])).
% 1.64/1.80 tff(3146,plain,
% 1.64/1.80 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 1.64/1.80 inference(symmetry,[status(thm)],[3145])).
% 1.64/1.80 tff(3147,plain,
% 1.64/1.80 ((~b(elem!1, s(s(s(z))))) <=> (~b(elem!1, s(s(elem!1))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[3146])).
% 1.64/1.80 tff(3148,plain,
% 1.64/1.80 (~b(elem!1, s(s(elem!1)))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[2213, 3147])).
% 1.64/1.80 tff(3149,plain,
% 1.64/1.80 ((s(s(elem!1)) = elem!1) <=> (s(s(s(z))) = elem!1)),
% 1.64/1.80 inference(monotonicity,[status(thm)],[3139])).
% 1.64/1.80 tff(3150,plain,
% 1.64/1.80 ((s(s(elem!1)) = elem!1) <=> (elem!1 = s(s(s(z))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[3149, 73])).
% 1.64/1.80 tff(3151,plain,
% 1.64/1.80 ((elem!1 = s(s(s(z)))) <=> (s(s(elem!1)) = elem!1)),
% 1.64/1.80 inference(symmetry,[status(thm)],[3150])).
% 1.64/1.80 tff(3152,plain,
% 1.64/1.80 (s(elem!1) = s(s(z))),
% 1.64/1.80 inference(transitivity,[status(thm)],[108, 3140, 24])).
% 1.64/1.80 tff(3153,plain,
% 1.64/1.80 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[3152])).
% 1.64/1.80 tff(3154,plain,
% 1.64/1.80 (elem!1 = inj_0(s(elem!1))),
% 1.64/1.80 inference(symmetry,[status(thm)],[343])).
% 1.64/1.80 tff(3155,plain,
% 1.64/1.80 (elem!1 = s(z)),
% 1.64/1.80 inference(transitivity,[status(thm)],[3154, 3153, 1486])).
% 1.64/1.80 tff(3156,plain,
% 1.64/1.80 ((elem!1 = s(s(s(z)))) <=> (s(z) = s(s(s(z))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[3155])).
% 1.64/1.80 tff(3157,plain,
% 1.64/1.80 ((s(z) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 1.64/1.80 inference(symmetry,[status(thm)],[3156])).
% 1.64/1.80 tff(3158,plain,
% 1.64/1.80 ((s(z) = s(s(s(z)))) <=> (elem!1 = s(s(elem!1)))),
% 1.64/1.80 inference(transitivity,[status(thm)],[3157, 3151, 134])).
% 1.64/1.80 tff(3159,plain,
% 1.64/1.80 ((~(s(z) = s(s(s(z))))) <=> (~(elem!1 = s(s(elem!1))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[3158])).
% 1.64/1.80 tff(3160,plain,
% 1.64/1.80 (~(elem!1 = s(s(elem!1)))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[767, 3159])).
% 1.64/1.80 tff(3161,plain,
% 1.64/1.80 (r(elem!1, s(s(elem!1)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1268, 3160, 3148])).
% 1.64/1.80 tff(3162,plain,
% 1.64/1.80 (inj_0(s(s(elem!1))) = inj_0(s(s(s(z))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[418])).
% 1.64/1.80 tff(3163,plain,
% 1.64/1.80 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 1.64/1.80 inference(symmetry,[status(thm)],[3162])).
% 1.64/1.80 tff(3164,plain,
% 1.64/1.80 (s(s(z)) = s(elem!1)),
% 1.64/1.80 inference(transitivity,[status(thm)],[25, 3163, 92])).
% 1.64/1.80 tff(3165,plain,
% 1.64/1.80 (b(z, s(s(z))) <=> b(z, s(elem!1))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[3164])).
% 1.64/1.80 tff(3166,plain,
% 1.64/1.80 (b(z, s(elem!1)) <=> b(z, s(s(z)))),
% 1.64/1.80 inference(symmetry,[status(thm)],[3165])).
% 1.64/1.80 tff(3167,plain,
% 1.64/1.80 (r(z, s(s(z))) <=> r(z, s(elem!1))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[3164])).
% 1.64/1.80 tff(3168,plain,
% 1.64/1.80 ((~r(z, s(s(z)))) <=> (~r(z, s(elem!1)))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[3167])).
% 1.64/1.80 tff(3169,plain,
% 1.64/1.80 (r(s(s(z)), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[3164])).
% 1.64/1.80 tff(3170,plain,
% 1.64/1.80 (r(s(elem!1), s(s(s(z)))) <=> r(s(s(z)), s(s(s(z))))),
% 1.64/1.80 inference(symmetry,[status(thm)],[3169])).
% 1.64/1.80 tff(3171,assumption,(r(s(elem!1), s(s(s(z))))), introduced(assumption)).
% 1.64/1.80 tff(3172,plain,
% 1.64/1.80 (r(s(s(z)), s(s(s(z))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[3171, 3170])).
% 1.64/1.80 tff(3173,plain,
% 1.64/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(3174,plain,
% 1.64/1.80 (((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(3175,plain,
% 1.64/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z))))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[3174])).
% 1.64/1.80 tff(3176,plain,
% 1.64/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[3175, 3173])).
% 1.64/1.80 tff(3177,plain,
% 1.64/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(3178,plain,
% 1.64/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[3177, 3176])).
% 1.64/1.80 tff(3179,plain,
% 1.64/1.80 (~r(z, s(s(z)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3178, 183, 429, 3172])).
% 1.64/1.80 tff(3180,plain,
% 1.64/1.80 (~r(z, s(elem!1))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[3179, 3168])).
% 1.64/1.80 tff(3181,plain,
% 1.64/1.80 (b(z, s(elem!1))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[2561, 3180])).
% 1.64/1.80 tff(3182,plain,
% 1.64/1.80 (b(z, s(s(z)))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[3181, 3166])).
% 1.64/1.80 tff(3183,plain,
% 1.64/1.80 (s(elem!1) = s(s(z))),
% 1.64/1.80 inference(transitivity,[status(thm)],[108, 3162, 24])).
% 1.64/1.80 tff(3184,plain,
% 1.64/1.80 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[3183])).
% 1.64/1.80 tff(3185,plain,
% 1.64/1.80 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 1.64/1.80 inference(symmetry,[status(thm)],[3184])).
% 1.64/1.80 tff(3186,plain,
% 1.64/1.80 (s(z) = elem!1),
% 1.64/1.80 inference(transitivity,[status(thm)],[1523, 3185, 343])).
% 1.64/1.80 tff(3187,plain,
% 1.64/1.80 (b(s(z), s(s(z))) <=> b(elem!1, s(elem!1))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[3186, 3164])).
% 1.64/1.80 tff(3188,plain,
% 1.64/1.80 (b(elem!1, s(elem!1)) <=> b(s(z), s(s(z)))),
% 1.64/1.80 inference(symmetry,[status(thm)],[3187])).
% 1.64/1.80 tff(3189,assumption,(elem!1 = s(elem!1)), introduced(assumption)).
% 1.64/1.80 tff(3190,plain,
% 1.64/1.80 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[3164])).
% 1.64/1.80 tff(3191,plain,
% 1.64/1.80 (s(z) = s(s(z))),
% 1.64/1.80 inference(transitivity,[status(thm)],[1523, 3190, 343, 3189, 108, 3162, 24])).
% 1.64/1.80 tff(3192,plain,
% 1.64/1.80 (inj_0(s(z)) = inj_0(s(s(z)))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[3191])).
% 1.64/1.80 tff(3193,plain,
% 1.64/1.80 (inj_0(s(s(z))) = inj_0(s(z))),
% 1.64/1.80 inference(symmetry,[status(thm)],[3192])).
% 1.64/1.80 tff(3194,plain,
% 1.64/1.80 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 1.64/1.80 inference(symmetry,[status(thm)],[3190])).
% 1.64/1.80 tff(3195,plain,
% 1.64/1.80 (s(elem!1) = elem!1),
% 1.64/1.80 inference(symmetry,[status(thm)],[3189])).
% 1.64/1.80 tff(3196,plain,
% 1.64/1.80 (s(s(z)) = z),
% 1.64/1.80 inference(transitivity,[status(thm)],[25, 3163, 92, 3195, 3154, 3194, 3193, 20])).
% 1.64/1.80 tff(3197,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[35, 3196])).
% 1.64/1.80 tff(3198,plain,((~(elem!1 = s(elem!1))) | (~(s(s(elem!1)) = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.80 tff(3199,plain,
% 1.64/1.80 (~(elem!1 = s(elem!1))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3198, 418])).
% 1.64/1.80 tff(3200,plain,
% 1.64/1.80 (r(s(elem!1), s(s(elem!1))) <=> r(s(elem!1), s(s(s(z))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[418])).
% 1.64/1.80 tff(3201,plain,
% 1.64/1.80 (r(s(elem!1), s(s(s(z)))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.64/1.80 inference(symmetry,[status(thm)],[3200])).
% 1.64/1.80 tff(3202,plain,
% 1.64/1.80 (r(s(elem!1), s(s(elem!1)))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[3171, 3201])).
% 1.64/1.80 tff(3203,plain,
% 1.64/1.80 (~r(elem!1, s(elem!1))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1217, 3202, 602])).
% 1.64/1.80 tff(3204,plain,
% 1.64/1.80 (b(elem!1, s(elem!1))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[2864, 3203, 3199])).
% 1.64/1.80 tff(3205,plain,
% 1.64/1.80 (b(s(z), s(s(z)))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[3204, 3188])).
% 1.64/1.80 tff(3206,plain,
% 1.64/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(3207,plain,
% 1.64/1.80 (((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(3208,plain,
% 1.64/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[3207])).
% 1.64/1.80 tff(3209,plain,
% 1.64/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 1.64/1.80 inference(transitivity,[status(thm)],[3208, 3206])).
% 1.64/1.80 tff(3210,plain,
% 1.64/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z)))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(3211,plain,
% 1.64/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[3210, 3209])).
% 1.64/1.80 tff(3212,plain,
% 1.64/1.80 (~r(s(s(z)), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3211, 183, 429, 3172])).
% 1.64/1.80 tff(3213,plain,
% 1.64/1.80 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(3214,plain,
% 1.64/1.80 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(3215,plain,
% 1.64/1.80 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z)),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[3214, 3213])).
% 1.64/1.80 tff(3216,plain,
% 1.64/1.80 (b(s(s(z)), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3215, 47, 35, 3212])).
% 1.64/1.80 tff(3217,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(3218,plain,
% 1.64/1.80 (((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(3219,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[3218])).
% 1.64/1.80 tff(3220,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.64/1.80 inference(transitivity,[status(thm)],[3219, 3217])).
% 1.64/1.80 tff(3221,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(3222,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[3221, 3220])).
% 1.64/1.80 tff(3223,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3222, 246, 236, 3216, 3205, 3182])).
% 1.64/1.80 tff(3224,plain,((~r(s(elem!1), s(s(s(z))))) | (~b(z, s(z))) | (~(s(s(elem!1)) = s(s(s(z))))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.80 tff(3225,plain,
% 1.64/1.80 (~r(s(elem!1), s(s(s(z))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3224, 3139, 236, 3161, 429])).
% 1.64/1.80 tff(3226,plain,
% 1.64/1.80 (b(s(elem!1), s(s(s(z))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1754, 3225, 1749])).
% 1.64/1.80 tff(3227,plain,
% 1.64/1.80 (b(s(s(z)), s(s(s(z))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[3226, 3144])).
% 1.64/1.80 tff(3228,assumption,(s(s(s(s(s(elem!1))))) = s(elem!1)), introduced(assumption)).
% 1.64/1.80 tff(3229,plain,
% 1.64/1.80 (s(s(s(s(s(elem!1))))) = s(s(z))),
% 1.64/1.80 inference(transitivity,[status(thm)],[3228, 108, 3162, 24])).
% 1.64/1.80 tff(3230,plain,
% 1.64/1.80 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(z)))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[3229])).
% 1.64/1.80 tff(3231,plain,
% 1.64/1.80 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.64/1.80 inference(symmetry,[status(thm)],[3230])).
% 1.64/1.80 tff(3232,plain,
% 1.64/1.80 (s(z) = s(s(s(s(elem!1))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[1523, 3231, 325])).
% 1.64/1.80 tff(3233,plain,
% 1.64/1.80 (inj_0(s(z)) = inj_0(s(s(s(s(elem!1)))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[3232])).
% 1.64/1.80 tff(3234,plain,
% 1.64/1.80 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(z))),
% 1.64/1.80 inference(symmetry,[status(thm)],[3233])).
% 1.64/1.80 tff(3235,plain,
% 1.64/1.80 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[418])).
% 1.64/1.80 tff(3236,plain,
% 1.64/1.80 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.64/1.80 inference(symmetry,[status(thm)],[3235])).
% 1.64/1.80 tff(3237,plain,
% 1.64/1.80 (s(s(s(s(z)))) = z),
% 1.64/1.80 inference(transitivity,[status(thm)],[3236, 352, 3234, 20])).
% 1.64/1.80 tff(3238,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[2421, 3237])).
% 1.64/1.80 tff(3239,plain,((~(s(s(s(s(s(elem!1))))) = s(elem!1))) | (~(s(s(elem!1)) = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.80 tff(3240,plain,
% 1.64/1.80 (~(s(s(s(s(s(elem!1))))) = s(elem!1))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3239, 3139])).
% 1.64/1.80 tff(3241,plain,
% 1.64/1.80 (b(s(s(s(s(s(elem!1))))), s(s(z))) <=> b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[3142])).
% 1.64/1.80 tff(3242,plain,
% 1.64/1.80 ((~b(s(s(s(s(s(elem!1))))), s(s(z)))) <=> (~b(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[3241])).
% 1.64/1.80 tff(3243,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(3244,plain,
% 1.64/1.80 (((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z))))) <=> ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(3245,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[3244])).
% 1.64/1.81 tff(3246,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[3245, 3243])).
% 1.64/1.81 tff(3247,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(3248,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[3247, 3246])).
% 1.64/1.81 tff(3249,plain,
% 1.64/1.81 (~b(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3248, 246, 2320, 3129, 3227])).
% 1.64/1.81 tff(3250,plain,
% 1.64/1.81 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[3249, 3242])).
% 1.64/1.81 tff(3251,plain,
% 1.64/1.81 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1795, 3250, 3240])).
% 1.64/1.81 tff(3252,plain,
% 1.64/1.81 (r(s(s(s(s(s(elem!1))))), s(s(z))) <=> r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[3164])).
% 1.64/1.81 tff(3253,plain,
% 1.64/1.81 (r(s(s(s(s(s(elem!1))))), s(elem!1)) <=> r(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.64/1.81 inference(symmetry,[status(thm)],[3252])).
% 1.64/1.81 tff(3254,plain,
% 1.64/1.81 (r(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[1853, 3253])).
% 1.64/1.81 tff(3255,assumption,(~r(s(s(s(s(s(elem!1))))), s(s(z)))), introduced(assumption)).
% 1.64/1.81 tff(3256,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3255, 3254])).
% 1.64/1.81 tff(3257,plain,(r(s(s(s(s(s(elem!1))))), s(s(z))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~(s(s(elem!1)) = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(3258,plain,
% 1.64/1.81 (r(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3257, 3251, 3139])).
% 1.64/1.81 tff(3259,plain,
% 1.64/1.81 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1918, 3258, 2320, 3129, 3227])).
% 1.64/1.81 tff(3260,plain,
% 1.64/1.81 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1702, 3259])).
% 1.64/1.81 tff(3261,plain,
% 1.64/1.81 (~r(s(s(s(s(z)))), z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[2599, 183, 429, 3260])).
% 1.64/1.81 tff(3262,plain,
% 1.64/1.81 (b(s(s(s(s(z)))), z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[2424, 47, 2421, 3261])).
% 1.64/1.81 tff(3263,plain,
% 1.64/1.81 (b(elem!1, s(s(s(z)))) <=> b(s(z), s(s(s(z))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[3155])).
% 1.64/1.81 tff(3264,plain,
% 1.64/1.81 ((~b(elem!1, s(s(s(z))))) <=> (~b(s(z), s(s(s(z)))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[3263])).
% 1.64/1.81 tff(3265,plain,
% 1.64/1.81 (~b(s(z), s(s(s(z))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[2213, 3264])).
% 1.64/1.81 tff(3266,plain,
% 1.64/1.81 (r(s(z), s(s(s(z))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1291, 3265])).
% 1.64/1.81 tff(3267,plain,
% 1.64/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(3268,plain,
% 1.64/1.81 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(3269,plain,
% 1.64/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[3268])).
% 1.64/1.81 tff(3270,plain,
% 1.64/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[3269, 3267])).
% 1.64/1.81 tff(3271,plain,
% 1.64/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(3272,plain,
% 1.64/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[3271, 3270])).
% 1.64/1.81 tff(3273,plain,
% 1.64/1.81 (~r(s(s(s(s(z)))), s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3272, 183, 3266, 3260])).
% 1.64/1.81 tff(3274,plain,
% 1.64/1.81 (b(s(s(s(s(z)))), s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[2411, 47, 1713, 3273])).
% 1.64/1.81 tff(3275,plain,
% 1.64/1.81 (b(elem!1, z) <=> b(s(z), z)),
% 1.64/1.81 inference(monotonicity,[status(thm)],[3155])).
% 1.64/1.81 tff(3276,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(3277,plain,
% 1.64/1.81 (((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(3278,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1)))))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[3277])).
% 1.64/1.81 tff(3279,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[3278, 3276])).
% 1.64/1.81 tff(3280,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(3281,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1)))))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[3280, 3279])).
% 1.64/1.81 tff(3282,plain,
% 1.64/1.81 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3281, 246, 3131, 3130, 3129])).
% 1.64/1.81 tff(3283,plain,
% 1.64/1.81 (s(s(s(z))) = s(s(elem!1))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[689, 3282, 1647])).
% 1.64/1.81 tff(3284,plain,
% 1.64/1.81 (~(z = elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[115, 3283])).
% 1.64/1.81 tff(3285,plain,
% 1.64/1.81 (~(elem!1 = z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1041, 3284])).
% 1.64/1.81 tff(3286,plain,
% 1.64/1.81 ((~(s(z) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[3157])).
% 1.64/1.81 tff(3287,plain,
% 1.64/1.81 (~(elem!1 = s(s(s(z))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[767, 3286])).
% 1.64/1.81 tff(3288,plain,
% 1.64/1.81 (r(elem!1, s(s(s(z))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[470, 3287, 2213])).
% 1.64/1.81 tff(3289,plain,
% 1.64/1.81 (~r(elem!1, z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[2254, 3288, 429])).
% 1.64/1.81 tff(3290,plain,
% 1.64/1.81 (b(elem!1, z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1143, 3289, 3285])).
% 1.64/1.81 tff(3291,plain,
% 1.64/1.81 (b(s(z), z)),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[3290, 3275])).
% 1.64/1.81 tff(3292,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(3293,plain,
% 1.64/1.81 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(3294,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[3293])).
% 1.64/1.81 tff(3295,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.64/1.81 inference(transitivity,[status(thm)],[3294, 3292])).
% 1.64/1.81 tff(3296,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(3297,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[3296, 3295])).
% 1.64/1.81 tff(3298,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3297, 246, 3291, 236, 3274, 3262])).
% 1.64/1.81 tff(3299,plain,((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~b(z, s(z))) | (~r(z, s(s(s(z))))) | (s(elem!1) = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(3300,plain,
% 1.64/1.81 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3299, 3059, 429, 1749, 2213, 1555, 634, 216])).
% 1.64/1.81 tff(3301,plain,
% 1.64/1.81 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[86, 3300, 69])).
% 1.64/1.81 tff(3302,plain,
% 1.64/1.81 (~b(z, s(s(s(s(s(elem!1))))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[2483, 246, 3066, 3057, 3301])).
% 1.64/1.81 tff(3303,plain,
% 1.64/1.81 ((z = s(s(s(s(s(elem!1)))))) | r(z, s(s(s(s(s(elem!1))))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[2487, 47, 3302])).
% 1.64/1.81 tff(3304,plain,
% 1.64/1.81 (r(z, s(s(s(s(s(elem!1))))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3303, 2477])).
% 1.64/1.81 tff(3305,assumption,(r(z, s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.64/1.81 tff(3306,assumption,(r(s(s(elem!1)), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.64/1.81 tff(3307,plain,
% 1.64/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(3308,plain,
% 1.64/1.81 (((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(3309,plain,
% 1.64/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[3308])).
% 1.64/1.81 tff(3310,plain,
% 1.64/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[3309, 3307])).
% 1.64/1.81 tff(3311,plain,
% 1.64/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(elem!1)))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(3312,plain,
% 1.64/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[3311, 3310])).
% 1.64/1.81 tff(3313,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3312, 183, 266, 3306, 3305])).
% 1.64/1.81 tff(3314,plain,((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(3315,plain,
% 1.64/1.81 (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3314, 3053, 3304])).
% 1.64/1.81 tff(3316,plain,
% 1.64/1.81 ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1547, 47, 3315])).
% 1.64/1.81 tff(3317,plain,
% 1.64/1.81 (b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3316, 3113])).
% 1.64/1.81 tff(3318,plain,
% 1.64/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(3319,plain,
% 1.64/1.81 (((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(elem!1)))))))) <=> ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(3320,plain,
% 1.64/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[3319])).
% 1.64/1.81 tff(3321,plain,
% 1.64/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[3320, 3318])).
% 1.64/1.81 tff(3322,plain,
% 1.64/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(elem!1))))))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(3323,plain,
% 1.64/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[3322, 3321])).
% 1.64/1.81 tff(3324,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3323, 183, 266, 959, 3305])).
% 1.64/1.81 tff(3325,plain,((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(3326,plain,
% 1.64/1.81 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3325, 3053, 3304])).
% 1.64/1.81 tff(3327,plain,
% 1.64/1.81 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[361, 47, 1555, 3326])).
% 1.64/1.81 tff(3328,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(3329,plain,
% 1.64/1.82 (((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(3330,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[3329])).
% 1.64/1.82 tff(3331,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.64/1.82 inference(transitivity,[status(thm)],[3330, 3328])).
% 1.64/1.82 tff(3332,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(3333,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[3332, 3331])).
% 1.64/1.82 tff(3334,plain,
% 1.64/1.82 (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3333, 246, 3301, 3327, 3317, 3112])).
% 1.64/1.82 tff(3335,plain,
% 1.64/1.82 (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[3334, 3043])).
% 1.64/1.82 tff(3336,plain,
% 1.64/1.82 (r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1506, 3335])).
% 1.64/1.82 tff(3337,plain,
% 1.64/1.82 (r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[3336, 3041])).
% 1.64/1.82 tff(3338,plain,
% 1.64/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(3339,plain,
% 1.64/1.82 (((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(3340,plain,
% 1.64/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[3339])).
% 1.64/1.82 tff(3341,plain,
% 1.64/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[3340, 3338])).
% 1.64/1.82 tff(3342,plain,
% 1.64/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(3343,plain,
% 1.64/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[3342, 3341])).
% 1.64/1.82 tff(3344,plain,
% 1.64/1.82 ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3343, 183, 3053, 3304])).
% 1.64/1.82 tff(3345,plain,
% 1.64/1.82 (~r(s(s(s(elem!1))), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3344, 3337])).
% 1.64/1.82 tff(3346,plain,
% 1.64/1.82 (b(s(s(s(elem!1))), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3086, 47, 355, 3345])).
% 1.64/1.82 tff(3347,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(3348,plain,
% 1.64/1.82 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(3349,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[3348])).
% 1.64/1.82 tff(3350,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 1.64/1.82 inference(transitivity,[status(thm)],[3349, 3347])).
% 1.64/1.82 tff(3351,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(3352,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[3351, 3350])).
% 1.64/1.82 tff(3353,plain,
% 1.64/1.82 (~b(s(s(s(elem!1))), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3352, 246, 3066, 3057, 3346])).
% 1.64/1.82 tff(3354,plain,
% 1.64/1.82 (((~![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))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(3355,plain,
% 1.64/1.82 ((~![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))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(3356,plain,
% 1.64/1.82 ((~![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)),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[3355, 3354])).
% 1.64/1.82 tff(3357,plain,
% 1.64/1.82 ((s(s(s(elem!1))) = elem!1) | r(s(s(s(elem!1))), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3356, 47, 3353])).
% 1.64/1.82 tff(3358,plain,
% 1.64/1.82 (r(s(s(s(elem!1))), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3357, 3039])).
% 1.64/1.82 tff(3359,plain,
% 1.64/1.82 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1372, 183, 216, 3358])).
% 1.64/1.82 tff(3360,plain,
% 1.64/1.82 ((s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1820, 47, 3359])).
% 1.64/1.82 tff(3361,plain,
% 1.64/1.82 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3360, 3032])).
% 1.64/1.82 tff(3362,plain,
% 1.64/1.82 (elem!1 = s(z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[9, 3019])).
% 1.64/1.82 tff(3363,plain,
% 1.64/1.82 (s(s(z)) = s(elem!1)),
% 1.64/1.82 inference(monotonicity,[status(thm)],[3019])).
% 1.64/1.82 tff(3364,plain,
% 1.64/1.82 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[3363, 3025])).
% 1.64/1.82 tff(3365,plain,
% 1.64/1.82 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 1.64/1.82 inference(symmetry,[status(thm)],[3364])).
% 1.64/1.82 tff(3366,plain,
% 1.64/1.82 ((~r(s(elem!1), s(s(s(elem!1))))) <=> (~r(s(s(z)), s(s(s(s(z))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[3365])).
% 1.64/1.82 tff(3367,plain,
% 1.64/1.82 (r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[3025])).
% 1.64/1.82 tff(3368,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(3369,plain,
% 1.64/1.82 (((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), 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(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(3370,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[3369])).
% 1.64/1.82 tff(3371,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[3370, 3368])).
% 1.64/1.82 tff(3372,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(3373,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[3372, 3371])).
% 1.64/1.82 tff(3374,plain,
% 1.64/1.82 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3373, 246, 3327, 3317, 3112])).
% 1.64/1.82 tff(3375,plain,
% 1.64/1.82 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[3069])).
% 1.64/1.82 tff(3376,plain,
% 1.64/1.82 (b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.64/1.82 inference(symmetry,[status(thm)],[3375])).
% 1.64/1.82 tff(3377,assumption,(b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))), introduced(assumption)).
% 1.64/1.82 tff(3378,plain,
% 1.64/1.82 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[3377, 3376])).
% 1.64/1.82 tff(3379,assumption,(~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))), introduced(assumption)).
% 1.64/1.82 tff(3380,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3379, 3378])).
% 1.64/1.82 tff(3381,plain,(b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~(s(s(s(z))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(3382,plain,
% 1.64/1.82 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3381, 3374, 3020])).
% 1.64/1.82 tff(3383,plain,
% 1.64/1.82 (r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1897, 3382])).
% 1.64/1.82 tff(3384,plain,
% 1.64/1.82 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[3383, 3367])).
% 1.64/1.82 tff(3385,plain,
% 1.64/1.82 ((elem!1 = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(s(z)))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[3026])).
% 1.64/1.82 tff(3386,plain,
% 1.64/1.82 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.64/1.82 inference(transitivity,[status(thm)],[3385, 3067])).
% 1.64/1.82 tff(3387,plain,
% 1.64/1.82 ((s(s(s(s(z)))) = elem!1) <=> (elem!1 = s(s(s(elem!1))))),
% 1.64/1.82 inference(symmetry,[status(thm)],[3386])).
% 1.64/1.82 tff(3388,plain,
% 1.64/1.82 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[3387])).
% 1.64/1.82 tff(3389,plain,
% 1.64/1.82 (~(elem!1 = s(s(s(elem!1))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[3038, 3388])).
% 1.64/1.82 tff(3390,plain,
% 1.64/1.82 (~b(elem!1, s(s(s(elem!1))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3093, 246, 3066, 3057, 3346])).
% 1.64/1.82 tff(3391,plain,
% 1.64/1.82 ((elem!1 = s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3104, 47, 3390])).
% 1.64/1.82 tff(3392,plain,
% 1.64/1.82 (r(elem!1, s(s(s(elem!1))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3391, 3389])).
% 1.64/1.82 tff(3393,plain,
% 1.64/1.82 ((s(s(s(z))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 1.64/1.82 inference(symmetry,[status(thm)],[417])).
% 1.64/1.82 tff(3394,plain,
% 1.64/1.82 (s(s(elem!1)) = s(s(s(z)))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[3020, 3393])).
% 1.64/1.82 tff(3395,plain,
% 1.64/1.82 (~(s(s(s(s(s(elem!1))))) = s(elem!1))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3239, 3394])).
% 1.64/1.82 tff(3396,plain,
% 1.64/1.82 (~(elem!1 = s(elem!1))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3198, 3394])).
% 1.64/1.82 tff(3397,plain,
% 1.64/1.82 (~(elem!1 = s(s(s(s(s(elem!1))))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[69, 125])).
% 1.64/1.82 tff(3398,plain,
% 1.64/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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))))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(3399,plain,
% 1.64/1.82 (((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(3400,plain,
% 1.64/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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)))))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[3399])).
% 1.64/1.82 tff(3401,plain,
% 1.64/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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))))))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[3400, 3398])).
% 1.64/1.82 tff(3402,plain,
% 1.64/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(3403,plain,
% 1.64/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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)))))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[3402, 3401])).
% 1.64/1.82 tff(3404,plain,
% 1.64/1.82 (~r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3403, 183, 3384, 3392])).
% 1.64/1.82 tff(3405,plain,
% 1.64/1.82 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(elem!1)))))) | b(elem!1, s(s(s(s(s(elem!1)))))) | r(elem!1, s(s(s(s(s(elem!1)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(s(elem!1)))))) | b(elem!1, s(s(s(s(s(elem!1)))))) | r(elem!1, s(s(s(s(s(elem!1)))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(3406,plain,
% 1.64/1.82 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(elem!1)))))) | b(elem!1, s(s(s(s(s(elem!1)))))) | r(elem!1, s(s(s(s(s(elem!1)))))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(3407,plain,
% 1.64/1.82 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(s(elem!1)))))) | b(elem!1, s(s(s(s(s(elem!1)))))) | r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[3406, 3405])).
% 1.64/1.82 tff(3408,plain,
% 1.64/1.82 ((elem!1 = s(s(s(s(s(elem!1)))))) | b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3407, 47, 3404])).
% 1.64/1.82 tff(3409,plain,
% 1.64/1.82 (b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3408, 3397])).
% 1.64/1.82 tff(3410,assumption,(~(s(s(s(s(s(elem!1))))) = s(elem!1))), introduced(assumption)).
% 1.64/1.82 tff(3411,plain,
% 1.64/1.82 (~(s(elem!1) = s(s(s(s(s(elem!1))))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[3410, 1802])).
% 1.64/1.82 tff(3412,assumption,(r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))), introduced(assumption)).
% 1.64/1.82 tff(3413,plain,
% 1.64/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(3414,plain,
% 1.64/1.82 (((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(3415,plain,
% 1.64/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(elem!1)))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[3414])).
% 1.64/1.82 tff(3416,plain,
% 1.64/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[3415, 3413])).
% 1.64/1.82 tff(3417,plain,
% 1.64/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(3418,plain,
% 1.64/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[3417, 3416])).
% 1.64/1.82 tff(3419,plain,
% 1.64/1.82 (~r(s(elem!1), s(s(s(s(s(elem!1))))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3418, 183, 3412, 1348])).
% 1.64/1.82 tff(3420,plain,
% 1.64/1.82 ((s(elem!1) = s(s(s(s(s(elem!1)))))) | b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[395, 47, 3419])).
% 1.64/1.82 tff(3421,plain,
% 1.64/1.82 (b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3420, 3411])).
% 1.64/1.82 tff(3422,assumption,(b(elem!1, s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.64/1.82 tff(3423,plain,
% 1.64/1.82 ((elem!1 = s(elem!1)) <=> (s(elem!1) = elem!1)),
% 1.64/1.82 inference(symmetry,[status(thm)],[2825])).
% 1.64/1.82 tff(3424,plain,
% 1.64/1.82 ((~(elem!1 = s(elem!1))) <=> (~(s(elem!1) = elem!1))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[3423])).
% 1.64/1.82 tff(3425,assumption,(~(elem!1 = s(elem!1))), introduced(assumption)).
% 1.64/1.82 tff(3426,plain,
% 1.64/1.82 (~(s(elem!1) = elem!1)),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[3425, 3424])).
% 1.64/1.82 tff(3427,assumption,(r(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.64/1.82 tff(3428,plain,
% 1.64/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(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))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(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))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(3429,plain,
% 1.64/1.82 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1))) <=> ((~r(elem!1, s(s(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))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(3430,plain,
% 1.64/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(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)))))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[3429])).
% 1.64/1.83 tff(3431,plain,
% 1.64/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(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))))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[3430, 3428])).
% 1.64/1.83 tff(3432,plain,
% 1.64/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(3433,plain,
% 1.64/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(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)))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[3432, 3431])).
% 1.64/1.83 tff(3434,plain,
% 1.64/1.83 (~r(s(elem!1), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[3433, 183, 602, 1348, 3427])).
% 1.64/1.83 tff(3435,plain,
% 1.64/1.83 (((~![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))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(3436,plain,
% 1.64/1.83 ((~![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))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(3437,plain,
% 1.64/1.83 ((~![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)),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[3436, 3435])).
% 1.64/1.83 tff(3438,plain,
% 1.64/1.83 ((s(elem!1) = elem!1) | b(s(elem!1), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[3437, 47, 3434])).
% 1.64/1.83 tff(3439,plain,
% 1.64/1.83 (b(s(elem!1), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[3438, 3426])).
% 1.64/1.83 tff(3440,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(3441,plain,
% 1.64/1.83 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(3442,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1)))))))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[3441])).
% 1.64/1.83 tff(3443,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[3442, 3440])).
% 1.64/1.83 tff(3444,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), elem!1)))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(3445,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1)))))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[3444, 3443])).
% 1.64/1.83 tff(3446,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[3445, 246, 1051, 714, 3439, 3422, 3421])).
% 1.64/1.83 tff(3447,plain,((~r(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (elem!1 = s(elem!1)) | (s(s(s(s(s(elem!1))))) = s(elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(3448,plain,
% 1.64/1.83 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[3447, 3057, 3301, 3409, 3396, 3395, 3051, 3392, 3384])).
% 1.64/1.83 tff(3449,plain,
% 1.64/1.83 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[3448, 3366])).
% 1.64/1.83 tff(3450,plain,
% 1.64/1.83 (b(s(s(z)), s(s(s(s(z)))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1531, 3449])).
% 1.64/1.83 tff(3451,plain,
% 1.64/1.83 (s(z) = elem!1),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[2279, 202])).
% 1.64/1.83 tff(3452,plain,
% 1.64/1.83 (s(s(s(z))) = s(s(elem!1))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[121, 3451])).
% 1.64/1.83 tff(3453,plain,
% 1.64/1.83 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[3452])).
% 1.64/1.83 tff(3454,plain,
% 1.64/1.83 (s(elem!1) = s(s(z))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[202])).
% 1.64/1.83 tff(3455,plain,
% 1.64/1.83 (s(s(z)) = s(elem!1)),
% 1.64/1.83 inference(symmetry,[status(thm)],[3454])).
% 1.64/1.83 tff(3456,plain,
% 1.64/1.83 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[3455, 3453])).
% 1.64/1.83 tff(3457,assumption,(b(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 1.64/1.83 tff(3458,plain,
% 1.64/1.83 (b(s(elem!1), s(s(s(elem!1))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[3457, 3456])).
% 1.64/1.83 tff(3459,assumption,(~b(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 1.64/1.83 tff(3460,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[3459, 3458])).
% 1.64/1.83 tff(3461,plain,((~b(s(s(z)), s(s(s(s(z)))))) | b(s(elem!1), s(s(s(elem!1)))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(3462,plain,
% 1.64/1.83 (b(s(elem!1), s(s(s(elem!1))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[3461, 3450, 3362])).
% 1.64/1.83 tff(3463,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(3464,plain,
% 1.64/1.83 (((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(3465,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[3464])).
% 1.64/1.83 tff(3466,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[3465, 3463])).
% 1.64/1.83 tff(3467,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(3468,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[3467, 3466])).
% 1.64/1.83 tff(3469,plain,
% 1.64/1.83 (~b(s(elem!1), s(s(elem!1)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[3468, 246, 3462, 3317, 3112, 3361])).
% 1.64/1.83 tff(3470,plain,
% 1.64/1.83 (~b(s(elem!1), s(s(s(z))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[3469, 3023])).
% 1.64/1.83 tff(3471,plain,
% 1.64/1.83 (~r(s(elem!1), s(s(s(z))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[3224, 3394, 3059, 3051, 429])).
% 1.64/1.83 tff(3472,plain,
% 1.64/1.83 (b(s(elem!1), s(s(s(z))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1754, 3471, 1749])).
% 1.64/1.83 tff(3473,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[3472, 3470])).
% 1.64/1.83 tff(3474,plain,((~r(s(s(s(z))), s(z))) | (s(s(s(s(s(elem!1))))) = elem!1) | (~r(s(s(elem!1)), elem!1)) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | (s(elem!1) = s(s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | b(s(z), elem!1) | (~r(s(s(s(z))), elem!1)) | b(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(3475,plain,
% 1.64/1.83 (~r(s(s(s(z))), s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[3474, 3008, 69, 1555, 1749, 2223, 3015, 1445, 2231, 2213])).
% 1.64/1.83 tff(3476,plain,
% 1.64/1.83 (b(s(s(s(z))), s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[52, 3475])).
% 1.64/1.83 tff(3477,plain,
% 1.64/1.83 (~(s(z) = elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[2290, 3476, 1])).
% 1.64/1.83 tff(3478,plain,
% 1.64/1.83 (r(s(z), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1034, 3477, 1445])).
% 1.64/1.83 tff(3479,plain,
% 1.64/1.83 (~r(s(z), s(s(elem!1)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[223, 183, 3478, 3008])).
% 1.64/1.83 tff(3480,plain,
% 1.64/1.83 (b(s(z), s(s(elem!1)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[233, 3479])).
% 1.64/1.83 tff(3481,plain,
% 1.64/1.83 (~r(s(s(elem!1)), s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[2139, 183, 3478, 3008])).
% 1.64/1.83 tff(3482,plain,
% 1.64/1.83 (b(s(s(elem!1)), s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[197, 3481])).
% 1.64/1.83 tff(3483,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(3484,plain,
% 1.64/1.83 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z)))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(3485,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[3484])).
% 1.64/1.83 tff(3486,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[3485, 3483])).
% 1.64/1.83 tff(3487,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(3488,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[3487, 3486])).
% 1.64/1.83 tff(3489,plain,
% 1.64/1.83 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[3488, 246, 3482, 3480, 3476])).
% 1.64/1.83 tff(3490,plain,
% 1.64/1.83 (s(s(elem!1)) = s(s(s(z)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[454, 3489, 3009])).
% 1.64/1.83 tff(3491,plain,
% 1.64/1.83 (inj_0(s(s(elem!1))) = inj_0(s(s(s(z))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[3490])).
% 1.64/1.83 tff(3492,plain,
% 1.64/1.83 (s(elem!1) = s(s(z))),
% 1.64/1.83 inference(transitivity,[status(thm)],[108, 3491, 24])).
% 1.64/1.83 tff(3493,plain,
% 1.64/1.83 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[3492])).
% 1.64/1.83 tff(3494,plain,
% 1.64/1.83 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 1.64/1.83 inference(symmetry,[status(thm)],[3493])).
% 1.64/1.83 tff(3495,plain,
% 1.64/1.83 (s(z) = elem!1),
% 1.64/1.83 inference(transitivity,[status(thm)],[1523, 3494, 343])).
% 1.64/1.83 tff(3496,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[3477, 3495])).
% 1.64/1.83 tff(3497,plain,((s(elem!1) = s(s(s(z)))) | b(s(z), elem!1) | b(s(s(s(z))), elem!1) | (s(s(s(s(s(elem!1))))) = elem!1) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | b(elem!1, s(s(s(z)))) | r(z, elem!1) | b(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(3498,plain,
% 1.64/1.83 (s(elem!1) = s(s(s(z)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[3497, 2214, 1, 69, 1555, 2213, 56, 1445])).
% 1.64/1.83 tff(3499,plain,
% 1.64/1.83 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[3498])).
% 1.64/1.83 tff(3500,plain,
% 1.64/1.83 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.64/1.83 inference(symmetry,[status(thm)],[3499])).
% 1.64/1.83 tff(3501,plain,
% 1.64/1.83 (s(s(z)) = elem!1),
% 1.64/1.83 inference(transitivity,[status(thm)],[25, 3500, 343])).
% 1.64/1.83 tff(3502,plain,
% 1.64/1.83 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[3498])).
% 1.64/1.83 tff(3503,plain,
% 1.64/1.83 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.64/1.83 inference(symmetry,[status(thm)],[3502])).
% 1.64/1.83 tff(3504,plain,
% 1.64/1.83 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(elem!1)), elem!1)),
% 1.64/1.83 inference(monotonicity,[status(thm)],[3503, 3501])).
% 1.64/1.83 tff(3505,plain,
% 1.64/1.83 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(z)))), s(s(z)))),
% 1.64/1.83 inference(symmetry,[status(thm)],[3504])).
% 1.64/1.83 tff(3506,plain,
% 1.64/1.83 (elem!1 = s(s(z))),
% 1.64/1.83 inference(transitivity,[status(thm)],[3154, 3499, 24])).
% 1.64/1.83 tff(3507,plain,
% 1.64/1.83 ((s(s(elem!1)) = elem!1) <=> (s(s(s(s(z)))) = s(s(z)))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[3502, 3506])).
% 1.64/1.83 tff(3508,plain,
% 1.64/1.83 ((s(s(elem!1)) = elem!1) <=> (s(s(z)) = s(s(s(s(z)))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[3507, 2786])).
% 1.64/1.83 tff(3509,plain,
% 1.64/1.83 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(elem!1)) = elem!1)),
% 1.64/1.83 inference(symmetry,[status(thm)],[3508])).
% 1.64/1.83 tff(3510,plain,
% 1.64/1.83 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(elem!1)) = elem!1))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[3509])).
% 1.64/1.83 tff(3511,plain,
% 1.64/1.83 (~(s(s(elem!1)) = elem!1)),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[1526, 3510])).
% 1.64/1.83 tff(3512,plain,
% 1.64/1.83 ((s(s(z)) = z) <=> (elem!1 = z)),
% 1.64/1.83 inference(monotonicity,[status(thm)],[3501])).
% 1.64/1.83 tff(3513,plain,
% 1.64/1.83 ((s(s(z)) = z) <=> (z = elem!1)),
% 1.64/1.83 inference(transitivity,[status(thm)],[3512, 1037])).
% 1.64/1.83 tff(3514,plain,
% 1.64/1.83 ((~(s(s(z)) = z)) <=> (~(z = elem!1))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[3513])).
% 1.64/1.83 tff(3515,plain,
% 1.64/1.83 (~(z = elem!1)),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[35, 3514])).
% 1.64/1.83 tff(3516,plain,
% 1.64/1.83 (b(z, elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[60, 3515, 56])).
% 1.64/1.83 tff(3517,plain,
% 1.64/1.83 ((s(s(z)) = z) <=> (elem!1 = z)),
% 1.64/1.83 inference(transitivity,[status(thm)],[3513, 1436])).
% 1.64/1.83 tff(3518,plain,
% 1.64/1.83 ((~(s(s(z)) = z)) <=> (~(elem!1 = z))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[3517])).
% 1.64/1.83 tff(3519,plain,
% 1.64/1.83 (~(elem!1 = z)),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[35, 3518])).
% 1.64/1.83 tff(3520,plain,
% 1.64/1.83 (~(s(s(s(z))) = elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[2242, 3516, 2214])).
% 1.64/1.83 tff(3521,plain,
% 1.64/1.83 (~(elem!1 = s(s(s(z))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[3013, 3520])).
% 1.64/1.83 tff(3522,plain,
% 1.64/1.83 (r(elem!1, s(s(s(z))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[470, 3521, 2213])).
% 1.64/1.83 tff(3523,plain,
% 1.64/1.83 (r(z, s(elem!1)) <=> r(z, s(s(s(z))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[3498])).
% 1.64/1.83 tff(3524,plain,
% 1.64/1.83 (b(z, s(elem!1)) <=> b(z, s(s(s(z))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[3498])).
% 1.64/1.83 tff(3525,plain,
% 1.64/1.83 (b(z, s(s(s(z)))) <=> b(z, s(elem!1))),
% 1.64/1.83 inference(symmetry,[status(thm)],[3524])).
% 1.64/1.83 tff(3526,plain,
% 1.64/1.83 ((~b(z, s(s(s(z))))) <=> (~b(z, s(elem!1)))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[3525])).
% 1.64/1.83 tff(3527,plain,
% 1.64/1.83 (~b(z, s(elem!1))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[2214, 3526])).
% 1.64/1.83 tff(3528,plain,
% 1.64/1.83 (r(z, s(elem!1))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[2561, 3527])).
% 1.64/1.83 tff(3529,plain,
% 1.64/1.83 (r(z, s(s(s(z))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[3528, 3523])).
% 1.64/1.83 tff(3530,plain,
% 1.64/1.83 (~r(elem!1, z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[2254, 3529, 3522])).
% 1.64/1.83 tff(3531,plain,
% 1.64/1.83 (b(elem!1, z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1143, 3530, 3519])).
% 1.64/1.83 tff(3532,plain,
% 1.64/1.83 (r(s(s(s(z))), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[647, 3520, 1])).
% 1.64/1.83 tff(3533,plain,
% 1.64/1.83 ((s(s(s(z))) = s(s(elem!1))) <=> (s(s(s(z))) = s(s(s(s(z)))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[3502])).
% 1.64/1.83 tff(3534,plain,
% 1.64/1.83 ((s(s(s(z))) = s(s(elem!1))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[3533, 3024])).
% 1.64/1.83 tff(3535,plain,
% 1.64/1.83 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 1.64/1.83 inference(symmetry,[status(thm)],[3534])).
% 1.64/1.83 tff(3536,plain,
% 1.64/1.83 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(elem!1))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[3535])).
% 1.64/1.83 tff(3537,plain,
% 1.64/1.83 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[1697, 3536])).
% 1.64/1.83 tff(3538,plain,
% 1.64/1.83 (~(s(z) = elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[121, 3537])).
% 1.64/1.83 tff(3539,plain,
% 1.64/1.83 (r(s(z), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1034, 3538, 1445])).
% 1.64/1.83 tff(3540,plain,
% 1.64/1.83 (~r(s(s(s(z))), s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[3017, 217, 634])).
% 1.64/1.83 tff(3541,plain,
% 1.64/1.83 (b(s(s(s(z))), s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[52, 3540])).
% 1.64/1.83 tff(3542,plain,
% 1.64/1.83 (~r(s(z), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[2937, 333, 634, 3541, 217])).
% 1.64/1.83 tff(3543,plain,
% 1.64/1.83 (~b(s(z), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[2336, 333, 217, 634, 3541])).
% 1.64/1.83 tff(3544,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1069, 3543, 3542])).
% 1.64/1.83 tff(3545,plain,((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(3546,plain,
% 1.64/1.83 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[3545, 3539, 3532])).
% 1.64/1.83 tff(3547,plain,
% 1.64/1.83 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[86, 3546, 69])).
% 1.64/1.83 tff(3548,plain,
% 1.64/1.83 (~b(s(s(elem!1)), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[2388, 3547, 3531, 1555, 3516])).
% 1.64/1.83 tff(3549,plain,
% 1.64/1.83 (r(s(s(elem!1)), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[156, 3548, 3511])).
% 1.64/1.83 tff(3550,plain,
% 1.64/1.83 (r(s(s(s(s(z)))), s(s(z)))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[3549, 3505])).
% 1.64/1.83 tff(3551,plain,
% 1.64/1.83 (r(s(z), s(s(z))) <=> r(s(z), elem!1)),
% 1.64/1.83 inference(monotonicity,[status(thm)],[3501])).
% 1.64/1.83 tff(3552,plain,
% 1.64/1.83 (r(s(z), elem!1) <=> r(s(z), s(s(z)))),
% 1.64/1.83 inference(symmetry,[status(thm)],[3551])).
% 1.64/1.83 tff(3553,plain,
% 1.64/1.83 (r(s(z), s(s(z)))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[3539, 3552])).
% 1.64/1.83 tff(3554,plain,
% 1.64/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(3555,plain,
% 1.64/1.83 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(3556,plain,
% 1.64/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[3555])).
% 1.64/1.83 tff(3557,plain,
% 1.64/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[3556, 3554])).
% 1.64/1.84 tff(3558,plain,
% 1.64/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(3559,plain,
% 1.64/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[3558, 3557])).
% 1.64/1.84 tff(3560,plain,
% 1.64/1.84 ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[3559, 183, 3553])).
% 1.64/1.84 tff(3561,plain,
% 1.64/1.84 (~r(s(s(s(s(z)))), s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[3560, 3550])).
% 1.64/1.84 tff(3562,plain,
% 1.64/1.84 (b(s(s(s(s(z)))), s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[2411, 47, 1713, 3561])).
% 1.64/1.84 tff(3563,plain,
% 1.64/1.84 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(z))), elem!1)),
% 1.64/1.84 inference(monotonicity,[status(thm)],[3501])).
% 1.64/1.84 tff(3564,plain,
% 1.64/1.84 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(z)))),
% 1.64/1.84 inference(symmetry,[status(thm)],[3563])).
% 1.64/1.84 tff(3565,plain,
% 1.64/1.84 (r(s(s(s(z))), s(s(z)))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[3532, 3564])).
% 1.64/1.84 tff(3566,plain,
% 1.64/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(3567,plain,
% 1.64/1.84 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(3568,plain,
% 1.64/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[3567])).
% 1.64/1.84 tff(3569,plain,
% 1.64/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[3568, 3566])).
% 1.64/1.84 tff(3570,plain,
% 1.64/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(3571,plain,
% 1.64/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[3570, 3569])).
% 1.64/1.84 tff(3572,plain,
% 1.64/1.84 ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[3571, 183, 3565])).
% 1.64/1.84 tff(3573,plain,
% 1.64/1.84 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[3572, 3550])).
% 1.64/1.84 tff(3574,plain,
% 1.64/1.84 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1702, 3573])).
% 1.64/1.84 tff(3575,plain,
% 1.64/1.84 (~r(s(s(s(z))), s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[3017, 3539, 3532])).
% 1.64/1.84 tff(3576,plain,
% 1.64/1.84 (b(s(s(s(z))), s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[52, 3575])).
% 1.64/1.84 tff(3577,plain,
% 1.64/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(3578,plain,
% 1.64/1.84 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(3579,plain,
% 1.64/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[3578])).
% 1.64/1.84 tff(3580,plain,
% 1.64/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[3579, 3577])).
% 1.64/1.84 tff(3581,plain,
% 1.64/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(3582,plain,
% 1.64/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[3581, 3580])).
% 1.64/1.84 tff(3583,plain,
% 1.64/1.84 ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[3582, 183])).
% 1.64/1.84 tff(3584,plain,
% 1.64/1.84 (~r(s(z), s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[3583, 3553, 3565])).
% 1.64/1.84 tff(3585,plain,
% 1.64/1.84 (b(s(z), s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1291, 3584])).
% 1.64/1.84 tff(3586,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(3587,plain,
% 1.64/1.84 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(3588,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[3587])).
% 1.64/1.84 tff(3589,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[3588, 3586])).
% 1.64/1.84 tff(3590,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(3591,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[3590, 3589])).
% 1.64/1.84 tff(3592,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[3591, 246, 3585, 3576, 3574, 3562])).
% 1.64/1.84 tff(3593,plain,(b(z, s(s(s(z)))) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | (s(s(s(s(s(elem!1))))) = elem!1) | b(elem!1, s(s(s(z)))) | b(s(s(s(z))), elem!1) | b(s(z), elem!1) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(3594,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[3593, 2212, 2210, 358, 56, 568, 1445, 2201])).
% 1.64/1.84 tff(3595,plain,((~b(s(s(s(elem!1))), s(elem!1))) | r(z, elem!1) | b(s(z), elem!1) | (~(z = elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(3596,plain,
% 1.64/1.84 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[3595, 2121, 56, 61, 2159, 2143, 1426])).
% 1.64/1.84 tff(3597,plain,
% 1.64/1.84 (~b(s(s(s(z))), s(elem!1))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[3596, 2189])).
% 1.64/1.84 tff(3598,plain,
% 1.64/1.84 (r(s(s(s(z))), s(elem!1))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[2675, 3597, 2186])).
% 1.64/1.84 tff(3599,plain,
% 1.64/1.84 (r(s(s(s(elem!1))), s(elem!1))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[3598, 2180])).
% 1.64/1.84 tff(3600,plain,
% 1.64/1.84 ((s(s(s(s(s(elem!1))))) = s(z)) <=> (s(s(s(s(s(elem!1))))) = s(elem!1))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[141])).
% 1.64/1.84 tff(3601,plain,
% 1.64/1.84 ((~(s(s(s(s(s(elem!1))))) = s(z))) <=> (~(s(s(s(s(s(elem!1))))) = s(elem!1)))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[3600])).
% 1.64/1.84 tff(3602,plain,
% 1.64/1.84 (~(s(s(s(s(s(elem!1))))) = s(elem!1))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[331, 3601])).
% 1.64/1.84 tff(3603,plain,
% 1.64/1.84 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[398, 2143, 2155, 61, 2152])).
% 1.64/1.84 tff(3604,plain,
% 1.64/1.84 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[86, 3603, 66])).
% 1.64/1.84 tff(3605,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(3606,plain,
% 1.64/1.84 (((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(3607,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[3606])).
% 1.64/1.84 tff(3608,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[3607, 3605])).
% 1.64/1.84 tff(3609,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(3610,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[3609, 3608])).
% 1.64/1.84 tff(3611,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[3610, 246, 442, 363, 714, 2866, 1574])).
% 1.64/1.84 tff(3612,plain,((~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(3613,plain,
% 1.64/1.84 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[3612, 2159, 2143, 3604, 1426])).
% 1.64/1.84 tff(3614,plain,
% 1.64/1.84 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1795, 3613, 3602])).
% 1.64/1.84 tff(3615,plain,
% 1.64/1.84 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1862, 183, 3614, 3599])).
% 1.64/1.84 tff(3616,plain,
% 1.64/1.84 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[770, 61])).
% 1.64/1.84 tff(3617,plain,
% 1.64/1.84 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[811, 47, 3616, 3615])).
% 1.64/1.84 tff(3618,plain,
% 1.64/1.84 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.64/1.84 inference(monotonicity,[status(thm)],[2172])).
% 1.64/1.84 tff(3619,plain,
% 1.64/1.84 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.64/1.84 inference(symmetry,[status(thm)],[3618])).
% 1.64/1.84 tff(3620,plain,
% 1.64/1.84 (b(s(s(s(z))), s(z)) <=> b(s(s(s(z))), s(elem!1))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[141])).
% 1.64/1.84 tff(3621,plain,
% 1.64/1.84 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(z))),
% 1.64/1.84 inference(symmetry,[status(thm)],[3620])).
% 1.64/1.84 tff(3622,plain,
% 1.64/1.84 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(z))), s(z))),
% 1.64/1.84 inference(transitivity,[status(thm)],[2188, 3621])).
% 1.64/1.84 tff(3623,plain,
% 1.64/1.84 ((~b(s(s(s(elem!1))), s(elem!1))) <=> (~b(s(s(s(z))), s(z)))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[3622])).
% 1.64/1.84 tff(3624,plain,
% 1.64/1.84 (~b(s(s(s(z))), s(z))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[3596, 3623])).
% 1.64/1.84 tff(3625,plain,
% 1.64/1.84 (r(s(s(s(z))), s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[52, 3624])).
% 1.64/1.84 tff(3626,plain,
% 1.64/1.84 (~r(s(s(s(z))), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[3017, 3625, 2122])).
% 1.64/1.84 tff(3627,plain,
% 1.64/1.84 (b(s(s(s(z))), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[647, 3626, 81])).
% 1.64/1.84 tff(3628,plain,
% 1.64/1.84 (b(s(s(s(elem!1))), elem!1)),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[3627, 3619])).
% 1.64/1.84 tff(3629,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(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(elem!1))))), s(s(s(elem!1))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(3630,plain,
% 1.64/1.84 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(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(elem!1))))), s(s(s(elem!1))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(3631,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(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(elem!1))))), s(s(s(elem!1)))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[3630])).
% 1.64/1.84 tff(3632,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(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(elem!1))))), s(s(s(elem!1))))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[3631, 3629])).
% 1.64/1.84 tff(3633,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(3634,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[3633, 3632])).
% 1.64/1.84 tff(3635,plain,
% 1.64/1.84 (~b(elem!1, s(s(s(elem!1))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[3634, 246, 3604, 3628, 1426, 3617])).
% 1.64/1.84 tff(3636,plain,
% 1.64/1.84 (~b(elem!1, s(s(s(z))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[3635, 2178])).
% 1.64/1.84 tff(3637,plain,
% 1.64/1.84 (r(elem!1, s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[470, 3636, 2176])).
% 1.64/1.84 tff(3638,plain,
% 1.64/1.84 (r(elem!1, s(s(s(elem!1))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[3637, 2174])).
% 1.64/1.84 tff(3639,plain,
% 1.64/1.84 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[2172])).
% 1.64/1.84 tff(3640,plain,
% 1.64/1.84 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 1.64/1.84 inference(transitivity,[status(thm)],[3639, 417])).
% 1.64/1.84 tff(3641,plain,
% 1.64/1.84 ((s(s(s(z))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 1.64/1.84 inference(symmetry,[status(thm)],[3640])).
% 1.64/1.84 tff(3642,plain,
% 1.64/1.84 ((~(s(s(s(z))) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[3641])).
% 1.64/1.84 tff(3643,plain,
% 1.64/1.84 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[116, 3642])).
% 1.64/1.84 tff(3644,assumption,(~b(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 1.64/1.84 tff(3645,plain,
% 1.64/1.84 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1820, 47, 3644, 3643])).
% 1.64/1.84 tff(3646,plain,
% 1.64/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(3647,plain,
% 1.64/1.84 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(3648,plain,
% 1.64/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[3647])).
% 1.64/1.84 tff(3649,plain,
% 1.64/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[3648, 3646])).
% 1.64/1.84 tff(3650,plain,
% 1.64/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(3651,plain,
% 1.64/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[3650, 3649])).
% 1.64/1.84 tff(3652,plain,
% 1.64/1.84 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[3651, 183, 2167, 3645, 3638])).
% 1.64/1.85 tff(3653,plain,(b(s(s(elem!1)), elem!1) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(z, elem!1) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(3654,plain,
% 1.64/1.85 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[3653, 145, 56, 55])).
% 1.64/1.85 tff(3655,plain,
% 1.64/1.85 (r(s(s(s(z))), s(z)) <=> r(s(s(s(z))), s(elem!1))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[141])).
% 1.64/1.85 tff(3656,plain,
% 1.64/1.85 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.64/1.85 inference(transitivity,[status(thm)],[3655, 2180])).
% 1.64/1.85 tff(3657,plain,
% 1.64/1.85 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[3595, 2159, 56, 61, 2143, 2121, 1426])).
% 1.64/1.85 tff(3658,plain,
% 1.64/1.85 (b(s(s(s(elem!1))), s(elem!1))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[2003, 1849])).
% 1.64/1.85 tff(3659,assumption,(~b(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 1.64/1.85 tff(3660,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[3659, 3658])).
% 1.64/1.85 tff(3661,plain,((~b(s(s(s(z))), s(z))) | b(s(s(s(elem!1))), s(elem!1)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(3662,plain,
% 1.64/1.85 (~b(s(s(s(z))), s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[3661, 3657, 61])).
% 1.64/1.85 tff(3663,plain,
% 1.64/1.85 (r(s(s(s(z))), s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[52, 3662])).
% 1.64/1.85 tff(3664,plain,
% 1.64/1.85 (r(s(s(s(elem!1))), s(elem!1))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[3663, 3656])).
% 1.64/1.85 tff(3665,plain,
% 1.64/1.85 (r(s(z), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[89])).
% 1.64/1.85 tff(3666,plain,
% 1.64/1.85 (r(s(elem!1), s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 1.64/1.85 inference(symmetry,[status(thm)],[3665])).
% 1.64/1.85 tff(3667,plain,
% 1.64/1.85 ((~r(s(elem!1), s(s(elem!1)))) <=> (~r(s(z), s(s(elem!1))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[3666])).
% 1.64/1.85 tff(3668,plain,
% 1.64/1.85 (r(s(z), z) <=> r(s(z), elem!1)),
% 1.64/1.85 inference(monotonicity,[status(thm)],[88])).
% 1.64/1.85 tff(3669,plain,
% 1.64/1.85 (r(s(z), z) <=> r(s(elem!1), elem!1)),
% 1.64/1.85 inference(transitivity,[status(thm)],[3668, 2733])).
% 1.64/1.85 tff(3670,plain,
% 1.64/1.85 (~b(s(z), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2114, 145, 88, 55])).
% 1.64/1.85 tff(3671,plain,
% 1.64/1.85 (r(s(z), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1069, 3670])).
% 1.64/1.85 tff(3672,plain,
% 1.64/1.85 (r(s(elem!1), elem!1)),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[3671, 3669])).
% 1.64/1.85 tff(3673,plain,
% 1.64/1.85 (~r(s(elem!1), s(s(elem!1)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[373, 183, 157, 3672])).
% 1.64/1.85 tff(3674,plain,
% 1.64/1.85 (~r(s(z), s(s(elem!1)))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[3673, 3667])).
% 1.64/1.85 tff(3675,plain,
% 1.64/1.85 (b(s(z), s(s(elem!1)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[233, 3674])).
% 1.64/1.85 tff(3676,plain,
% 1.64/1.85 (b(s(elem!1), s(s(elem!1)))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[3675, 364])).
% 1.64/1.85 tff(3677,plain,
% 1.64/1.85 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[89])).
% 1.64/1.85 tff(3678,plain,
% 1.64/1.85 (~(s(z) = elem!1)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[121, 416])).
% 1.64/1.85 tff(3679,plain,
% 1.64/1.85 (~b(s(z), elem!1)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2120, 3670, 88])).
% 1.64/1.85 tff(3680,plain,
% 1.64/1.85 (r(s(z), elem!1)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1034, 3679, 3678])).
% 1.64/1.85 tff(3681,plain,
% 1.64/1.85 (b(s(s(elem!1)), s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2141, 1435, 145, 3680])).
% 1.64/1.85 tff(3682,plain,
% 1.64/1.85 (b(s(s(elem!1)), s(elem!1))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[3681, 3677])).
% 1.64/1.85 tff(3683,plain,
% 1.64/1.85 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[398, 3682, 157, 88, 3672])).
% 1.64/1.85 tff(3684,plain,
% 1.64/1.85 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[86, 3683, 568])).
% 1.64/1.85 tff(3685,plain,
% 1.64/1.85 (~b(s(elem!1), s(s(elem!1)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[3612, 3684, 2866, 3682, 1451])).
% 1.64/1.85 tff(3686,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[3685, 3676])).
% 1.64/1.85 tff(3687,plain,(b(s(s(elem!1)), elem!1) | (~(z = elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(3688,plain,
% 1.64/1.85 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[3687, 145, 61, 55])).
% 1.64/1.85 tff(3689,plain,
% 1.64/1.85 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1795, 3688, 3602])).
% 1.64/1.85 tff(3690,plain,
% 1.64/1.85 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1862, 183, 3689, 3664])).
% 1.64/1.85 tff(3691,assumption,(~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))), introduced(assumption)).
% 1.64/1.85 tff(3692,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[811, 47, 775, 3691, 3379])).
% 1.64/1.85 tff(3693,plain,(b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(3694,plain,
% 1.64/1.85 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[3693, 3690, 3616])).
% 1.64/1.85 tff(3695,plain,
% 1.64/1.85 (~r(s(s(s(z))), elem!1)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[3017, 3663, 2122])).
% 1.64/1.85 tff(3696,plain,
% 1.64/1.85 (b(s(s(s(z))), elem!1)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[647, 3695, 81])).
% 1.64/1.85 tff(3697,assumption,(b(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.64/1.85 tff(3698,plain,
% 1.64/1.85 (b(s(s(s(elem!1))), elem!1)),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[3697, 549])).
% 1.64/1.85 tff(3699,assumption,(~b(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.64/1.85 tff(3700,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[3699, 3698])).
% 1.64/1.85 tff(3701,plain,((~b(s(s(s(z))), elem!1)) | b(s(s(s(elem!1))), elem!1) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(3702,plain,
% 1.64/1.85 (b(s(s(s(elem!1))), elem!1)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[3701, 3696, 61])).
% 1.64/1.85 tff(3703,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(3704,plain,
% 1.64/1.85 (((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(3705,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[3704])).
% 1.64/1.85 tff(3706,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[3705, 3703])).
% 1.64/1.85 tff(3707,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(3708,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[3707, 3706])).
% 1.64/1.85 tff(3709,plain,
% 1.64/1.85 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[3708, 246, 2143, 3702, 1426, 3694, 3654])).
% 1.64/1.85 tff(3710,plain,
% 1.64/1.85 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1557, 3709, 2169])).
% 1.64/1.85 tff(3711,plain,
% 1.64/1.85 (~r(z, s(s(s(s(s(elem!1))))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[3325, 3710, 2168])).
% 1.64/1.85 tff(3712,plain,
% 1.64/1.85 (~r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[3711, 130])).
% 1.64/1.85 tff(3713,plain,
% 1.64/1.85 (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1879, 183, 3689, 3664])).
% 1.64/1.85 tff(3714,plain,
% 1.64/1.85 (~(s(s(s(elem!1))) = s(s(s(s(s(elem!1))))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[777, 3616])).
% 1.64/1.85 tff(3715,plain,
% 1.64/1.85 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[913, 47, 3714, 3713])).
% 1.64/1.85 tff(3716,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(3717,plain,
% 1.64/1.85 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(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(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(3718,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1)))))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[3717])).
% 1.64/1.85 tff(3719,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[3718, 3716])).
% 1.64/1.85 tff(3720,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(3721,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1)))))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[3720, 3719])).
% 1.64/1.85 tff(3722,plain,
% 1.64/1.85 (~b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[3721, 246, 3604, 3702, 1426, 3715])).
% 1.64/1.85 tff(3723,plain,
% 1.64/1.85 ((elem!1 = s(s(s(s(s(elem!1)))))) | r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[3407, 47, 3722])).
% 1.64/1.85 tff(3724,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[3723, 3712, 126])).
% 1.64/1.85 tff(3725,plain,(b(s(s(elem!1)), elem!1) | r(z, elem!1) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(3726,plain,
% 1.64/1.85 (b(s(s(elem!1)), elem!1)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[3725, 56, 55])).
% 1.64/1.85 tff(3727,plain,
% 1.64/1.85 (r(z, s(z)) <=> r(elem!1, s(z))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[88])).
% 1.64/1.85 tff(3728,plain,
% 1.64/1.85 (r(elem!1, s(z)) <=> r(z, s(z))),
% 1.64/1.85 inference(symmetry,[status(thm)],[3727])).
% 1.64/1.85 tff(3729,plain,
% 1.64/1.85 (~(elem!1 = s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2279, 3678])).
% 1.64/1.85 tff(3730,plain,
% 1.64/1.85 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1820, 47, 3644, 1817])).
% 1.64/1.85 tff(3731,plain,
% 1.64/1.85 (b(s(elem!1), elem!1)),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[1044, 1452])).
% 1.64/1.85 tff(3732,plain,
% 1.64/1.85 (b(s(z), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2120, 1044, 88])).
% 1.64/1.85 tff(3733,plain,
% 1.64/1.85 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[3644, 424])).
% 1.64/1.85 tff(3734,plain,
% 1.64/1.85 (r(s(s(elem!1)), s(s(s(z))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[454, 3733, 422])).
% 1.64/1.85 tff(3735,plain,
% 1.64/1.85 (b(s(s(s(elem!1))), elem!1)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[3701, 3697, 88])).
% 1.64/1.85 tff(3736,plain,
% 1.64/1.85 (b(s(s(s(elem!1))), s(elem!1))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[3661, 2003, 88])).
% 1.64/1.85 tff(3737,plain,
% 1.64/1.85 ((s(s(elem!1)) = z) <=> (elem!1 = s(s(elem!1)))),
% 1.64/1.85 inference(transitivity,[status(thm)],[148, 134])).
% 1.64/1.85 tff(3738,plain,
% 1.64/1.85 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = s(s(elem!1))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[3737])).
% 1.64/1.85 tff(3739,plain,
% 1.64/1.85 (~(elem!1 = s(s(elem!1)))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[139, 3738])).
% 1.64/1.85 tff(3740,plain,
% 1.64/1.85 (r(elem!1, s(z)) <=> r(elem!1, s(elem!1))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[89])).
% 1.64/1.85 tff(3741,plain,
% 1.64/1.85 (r(z, s(z)) <=> r(elem!1, s(elem!1))),
% 1.64/1.85 inference(transitivity,[status(thm)],[3727, 3740])).
% 1.64/1.85 tff(3742,plain,
% 1.64/1.85 (b(s(s(s(z))), z)),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[3697, 1434])).
% 1.64/1.85 tff(3743,plain,
% 1.64/1.85 (~b(z, s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2098, 3742, 1056, 2003])).
% 1.64/1.85 tff(3744,plain,
% 1.64/1.85 (r(z, s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[169, 3743])).
% 1.64/1.85 tff(3745,plain,
% 1.64/1.85 (r(elem!1, s(elem!1))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[3744, 3741])).
% 1.64/1.85 tff(3746,plain,
% 1.64/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(3747,plain,
% 1.64/1.85 (((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(3748,plain,
% 1.64/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[3747])).
% 1.64/1.85 tff(3749,plain,
% 1.64/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[3748, 3746])).
% 1.64/1.85 tff(3750,plain,
% 1.64/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(3751,plain,
% 1.64/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[3750, 3749])).
% 1.64/1.85 tff(3752,plain,
% 1.64/1.85 (~r(elem!1, s(s(elem!1)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[3751, 183, 3745, 1951])).
% 1.64/1.85 tff(3753,plain,
% 1.64/1.85 (b(elem!1, s(s(elem!1)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1268, 3752, 3739])).
% 1.64/1.85 tff(3754,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(3755,plain,
% 1.64/1.85 (((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(3756,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[3755])).
% 1.64/1.85 tff(3757,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.64/1.85 inference(transitivity,[status(thm)],[3756, 3754])).
% 1.64/1.85 tff(3758,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(3759,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[3758, 3757])).
% 1.64/1.85 tff(3760,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[3759, 246, 2362, 3753, 3736, 1200, 3735])).
% 1.64/1.85 tff(3761,plain,((~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~(z = elem!1)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(3762,plain,
% 1.64/1.85 (~b(s(s(s(z))), elem!1)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[3761, 1951, 1200, 2362, 88, 1056, 2003])).
% 1.64/1.85 tff(3763,plain,
% 1.64/1.85 (r(s(s(s(z))), elem!1)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[647, 3762, 554])).
% 1.64/1.85 tff(3764,plain,
% 1.64/1.85 (r(s(s(s(elem!1))), z)),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[3763, 1777])).
% 1.64/1.85 tff(3765,plain,
% 1.64/1.85 (r(s(s(s(elem!1))), elem!1)),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[3764, 1775])).
% 1.64/1.85 tff(3766,plain,
% 1.64/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(3767,plain,
% 1.64/1.85 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(3768,plain,
% 1.64/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[3767])).
% 1.64/1.85 tff(3769,plain,
% 1.64/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.64/1.85 inference(transitivity,[status(thm)],[3768, 3766])).
% 1.64/1.85 tff(3770,plain,
% 1.64/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(3771,plain,
% 1.64/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[3770, 3769])).
% 1.64/1.85 tff(3772,plain,
% 1.64/1.85 ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[3771, 183, 333])).
% 1.64/1.85 tff(3773,plain,
% 1.64/1.85 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[3772, 3765])).
% 1.64/1.85 tff(3774,plain,
% 1.64/1.85 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[3693, 3773, 771])).
% 1.64/1.85 tff(3775,plain,
% 1.64/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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)))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(3776,plain,
% 1.64/1.85 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(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))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(3777,plain,
% 1.64/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[3776])).
% 1.64/1.85 tff(3778,plain,
% 1.64/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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)))),
% 1.64/1.85 inference(transitivity,[status(thm)],[3777, 3775])).
% 1.64/1.85 tff(3779,plain,
% 1.64/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(3780,plain,
% 1.64/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[3779, 3778])).
% 1.64/1.85 tff(3781,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[3780, 183, 333, 1853, 601])).
% 1.64/1.85 tff(3782,plain,((~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)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(3783,plain,
% 1.64/1.86 (~r(elem!1, s(elem!1))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[3782, 1853, 333])).
% 1.64/1.86 tff(3784,plain,
% 1.64/1.86 (b(elem!1, s(elem!1))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2864, 3783, 2829])).
% 1.64/1.86 tff(3785,plain,
% 1.64/1.86 (r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))) <=> r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.64/1.86 inference(symmetry,[status(thm)],[1472])).
% 1.64/1.86 tff(3786,plain,
% 1.64/1.86 ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) <=> (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[1470])).
% 1.64/1.86 tff(3787,plain,
% 1.64/1.86 ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[1458])).
% 1.64/1.86 tff(3788,plain,
% 1.64/1.86 (~r(s(z), elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[3545, 634, 333])).
% 1.64/1.86 tff(3789,plain,
% 1.64/1.86 (b(s(z), elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1034, 3788, 3678])).
% 1.64/1.86 tff(3790,plain,
% 1.64/1.86 (b(elem!1, s(elem!1)) <=> b(elem!1, s(z))),
% 1.64/1.86 inference(symmetry,[status(thm)],[1449])).
% 1.64/1.86 tff(3791,plain,
% 1.64/1.86 (b(elem!1, s(z))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[3784, 3790])).
% 1.64/1.86 tff(3792,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(3793,plain,
% 1.64/1.86 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(3794,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z)))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[3793])).
% 1.64/1.86 tff(3795,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[3794, 3792])).
% 1.64/1.86 tff(3796,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(3797,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z)))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[3796, 3795])).
% 1.64/1.86 tff(3798,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[3797, 246, 201, 1044, 2362, 2001])).
% 1.64/1.86 tff(3799,plain,((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(3800,plain,
% 1.64/1.86 (~b(s(s(elem!1)), s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[3799, 3789, 2362, 3791])).
% 1.64/1.86 tff(3801,plain,
% 1.64/1.86 (r(s(s(elem!1)), s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[197, 3800])).
% 1.64/1.86 tff(3802,plain,
% 1.64/1.86 (r(s(s(elem!1)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[89])).
% 1.64/1.86 tff(3803,plain,
% 1.64/1.86 (r(s(s(elem!1)), s(elem!1))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[173, 3802])).
% 1.64/1.86 tff(3804,assumption,(~r(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 1.64/1.86 tff(3805,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[3804, 3803])).
% 1.64/1.86 tff(3806,plain,((~r(s(s(elem!1)), s(z))) | r(s(s(elem!1)), s(elem!1)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(3807,plain,
% 1.64/1.86 (r(s(s(elem!1)), s(elem!1))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[3806, 3801, 88])).
% 1.64/1.86 tff(3808,plain,
% 1.64/1.86 (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2767, 1779])).
% 1.64/1.86 tff(3809,plain,
% 1.64/1.86 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[913, 47, 778, 3808])).
% 1.64/1.86 tff(3810,plain,
% 1.64/1.86 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[3772, 1779])).
% 1.64/1.86 tff(3811,plain,
% 1.64/1.86 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[3693, 3810, 771])).
% 1.64/1.86 tff(3812,assumption,(s(s(elem!1)) = s(s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.64/1.86 tff(3813,plain,
% 1.64/1.86 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 1.64/1.86 inference(symmetry,[status(thm)],[3812])).
% 1.64/1.86 tff(3814,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1555, 3813])).
% 1.64/1.86 tff(3815,plain,((~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))) | (s(s(s(s(s(elem!1))))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(3816,plain,
% 1.64/1.86 (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[3815, 358])).
% 1.64/1.86 tff(3817,plain,
% 1.64/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(3818,plain,
% 1.64/1.86 (((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(3819,plain,
% 1.64/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[3818])).
% 1.64/1.86 tff(3820,plain,
% 1.64/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.64/1.86 inference(transitivity,[status(thm)],[3819, 3817])).
% 1.64/1.86 tff(3821,plain,
% 1.64/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(3822,plain,
% 1.64/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[3821, 3820])).
% 1.64/1.86 tff(3823,plain,
% 1.64/1.86 (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[3822, 183, 333, 1853, 3807])).
% 1.64/1.86 tff(3824,plain,
% 1.64/1.86 (b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1547, 47, 3823, 3816])).
% 1.64/1.86 tff(3825,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), 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(elem!1))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(3826,plain,
% 1.64/1.86 (((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(3827,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), 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(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[3826])).
% 1.64/1.86 tff(3828,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), 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(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[3827, 3825])).
% 1.64/1.86 tff(3829,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), 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(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(3830,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[3829, 3828])).
% 1.64/1.86 tff(3831,plain,
% 1.64/1.86 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[3830, 246, 3824, 3811, 3809])).
% 1.64/1.86 tff(3832,plain,
% 1.64/1.86 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1820, 47, 3831, 1817])).
% 1.64/1.86 tff(3833,assumption,(r(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 1.64/1.86 tff(3834,plain,
% 1.64/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(3835,plain,
% 1.64/1.86 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(3836,plain,
% 1.64/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1)))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[3835])).
% 1.64/1.86 tff(3837,plain,
% 1.64/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[3836, 3834])).
% 1.64/1.86 tff(3838,plain,
% 1.64/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(3839,plain,
% 1.64/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[3838, 3837])).
% 1.64/1.86 tff(3840,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[3839, 183, 3833, 820, 1951])).
% 1.64/1.86 tff(3841,plain,((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(3842,plain,
% 1.64/1.86 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[3841, 3832, 3807])).
% 1.64/1.86 tff(3843,plain,
% 1.64/1.86 (~r(s(s(s(z))), s(z))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[3842, 1852])).
% 1.64/1.86 tff(3844,plain,
% 1.64/1.86 (b(s(s(s(z))), s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[52, 3843])).
% 1.64/1.86 tff(3845,plain,
% 1.64/1.86 (~b(elem!1, s(s(s(z))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2011, 3844, 3791, 3789])).
% 1.64/1.86 tff(3846,plain,
% 1.64/1.86 (r(elem!1, s(s(s(z))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[470, 3845, 718])).
% 1.64/1.86 tff(3847,plain,
% 1.64/1.86 (r(elem!1, s(s(s(elem!1))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[3846, 412])).
% 1.64/1.86 tff(3848,assumption,(s(s(s(s(elem!1)))) = elem!1), introduced(assumption)).
% 1.64/1.86 tff(3849,plain,
% 1.64/1.86 (s(s(s(s(elem!1)))) = z),
% 1.64/1.86 inference(transitivity,[status(thm)],[3848, 341])).
% 1.64/1.86 tff(3850,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[329, 3849])).
% 1.64/1.86 tff(3851,plain,((~(s(s(s(s(elem!1)))) = elem!1)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(3852,plain,
% 1.64/1.86 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[3851, 88])).
% 1.64/1.86 tff(3853,assumption,(r(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 1.64/1.86 tff(3854,plain,
% 1.64/1.86 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2034, 183, 3427, 3853])).
% 1.64/1.86 tff(3855,plain,
% 1.64/1.86 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1571, 47, 3854, 3852])).
% 1.64/1.86 tff(3856,plain,
% 1.64/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(3857,plain,
% 1.64/1.86 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(3858,plain,
% 1.64/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[3857])).
% 1.64/1.86 tff(3859,plain,
% 1.64/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[3858, 3856])).
% 1.64/1.86 tff(3860,plain,
% 1.64/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(3861,plain,
% 1.64/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[3860, 3859])).
% 1.64/1.86 tff(3862,plain,
% 1.64/1.86 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[3861, 183, 3730, 3853])).
% 1.64/1.86 tff(3863,assumption,(~b(s(s(s(s(elem!1)))), s(s(elem!1)))), introduced(assumption)).
% 1.64/1.86 tff(3864,plain,
% 1.64/1.86 ((s(s(s(s(elem!1)))) = s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1844, 47, 3863])).
% 1.64/1.86 tff(3865,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[3864, 3862, 1830])).
% 1.64/1.86 tff(3866,plain,(b(s(s(s(s(elem!1)))), s(s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~(z = elem!1)) | b(s(s(elem!1)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(3867,plain,
% 1.64/1.86 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[3866, 3853, 88, 3644])).
% 1.64/1.86 tff(3868,plain,
% 1.64/1.86 (~r(elem!1, s(s(elem!1)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[3651, 183, 3730, 3427])).
% 1.64/1.86 tff(3869,plain,
% 1.64/1.86 (b(elem!1, s(s(elem!1)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1268, 3868, 3739])).
% 1.64/1.86 tff(3870,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(3871,plain,
% 1.64/1.86 (((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(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)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(3872,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[3871])).
% 1.64/1.86 tff(3873,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[3872, 3870])).
% 1.64/1.86 tff(3874,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(3875,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[3874, 3873])).
% 1.64/1.86 tff(3876,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[3875, 246, 2362, 3869, 3867, 3855])).
% 1.64/1.86 tff(3877,plain,((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~(z = elem!1)) | b(s(s(elem!1)), s(s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(3878,plain,
% 1.64/1.86 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[3877, 3831, 88, 2362, 3847])).
% 1.64/1.87 tff(3879,plain,
% 1.64/1.87 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[3878, 3787])).
% 1.64/1.87 tff(3880,plain,
% 1.64/1.87 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1702, 3879])).
% 1.64/1.87 tff(3881,plain,
% 1.64/1.87 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[3880, 1832])).
% 1.64/1.87 tff(3882,plain,
% 1.64/1.87 (b(s(s(s(elem!1))), s(elem!1))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[3661, 3844, 88])).
% 1.64/1.87 tff(3883,plain,
% 1.64/1.87 ((~r(s(elem!1), s(s(s(z))))) <=> (~r(s(z), s(s(s(z)))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[1929])).
% 1.64/1.87 tff(3884,plain,
% 1.64/1.87 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[3831, 424])).
% 1.64/1.87 tff(3885,plain,
% 1.64/1.87 (r(s(s(elem!1)), s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[454, 3884, 422])).
% 1.64/1.87 tff(3886,assumption,(r(s(s(elem!1)), s(s(s(z))))), introduced(assumption)).
% 1.64/1.87 tff(3887,plain,
% 1.64/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(3888,plain,
% 1.64/1.87 (((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(3889,plain,
% 1.64/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(z)))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[3888])).
% 1.64/1.87 tff(3890,plain,
% 1.64/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[3889, 3887])).
% 1.64/1.87 tff(3891,plain,
% 1.64/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(3892,plain,
% 1.64/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(z)))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[3891, 3890])).
% 1.64/1.87 tff(3893,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[3892, 183, 3886, 1951, 3171])).
% 1.64/1.87 tff(3894,plain,((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(3895,plain,
% 1.64/1.87 (~r(s(elem!1), s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[3894, 3885, 3807])).
% 1.64/1.87 tff(3896,plain,
% 1.64/1.87 (~r(s(z), s(s(s(z))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[3895, 3883])).
% 1.64/1.87 tff(3897,plain,
% 1.64/1.87 (b(s(z), s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1291, 3896])).
% 1.64/1.87 tff(3898,plain,
% 1.64/1.87 (b(s(elem!1), s(s(s(elem!1))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[3897, 1927])).
% 1.64/1.87 tff(3899,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(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))))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(3900,plain,
% 1.64/1.87 (((~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(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(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(3901,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(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)))))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[3900])).
% 1.64/1.87 tff(3902,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(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))))))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[3901, 3899])).
% 1.64/1.87 tff(3903,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), 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(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))))))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(3904,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[3903, 3902])).
% 1.64/1.87 tff(3905,plain,
% 1.64/1.87 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[3904, 246, 3898, 3882, 3811, 3881])).
% 1.64/1.87 tff(3906,plain,
% 1.64/1.87 (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[3905, 3786])).
% 1.64/1.87 tff(3907,plain,
% 1.64/1.87 (r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1506, 3906])).
% 1.64/1.87 tff(3908,plain,
% 1.64/1.87 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[3907, 3785])).
% 1.64/1.87 tff(3909,plain,
% 1.64/1.87 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2902, 246, 3898, 3882, 3881])).
% 1.64/1.87 tff(3910,assumption,(s(elem!1) = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.64/1.87 tff(3911,plain,
% 1.64/1.87 (s(s(s(s(elem!1)))) = s(elem!1)),
% 1.64/1.87 inference(symmetry,[status(thm)],[3910])).
% 1.64/1.87 tff(3912,plain,
% 1.64/1.87 (s(s(s(s(z)))) = s(elem!1)),
% 1.64/1.87 inference(transitivity,[status(thm)],[1456, 3911])).
% 1.64/1.87 tff(3913,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1714, 3912])).
% 1.64/1.87 tff(3914,plain,((~(s(elem!1) = s(s(s(s(elem!1)))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(3915,plain,
% 1.64/1.87 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[3914, 88])).
% 1.64/1.87 tff(3916,plain,
% 1.64/1.87 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2907, 47, 3915, 3909])).
% 1.64/1.87 tff(3917,assumption,(s(elem!1) = s(s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.64/1.87 tff(3918,plain,
% 1.64/1.87 (s(s(s(s(s(elem!1))))) = s(elem!1)),
% 1.64/1.87 inference(symmetry,[status(thm)],[3917])).
% 1.64/1.87 tff(3919,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[3410, 3918])).
% 1.64/1.87 tff(3920,plain,((~(s(elem!1) = s(s(s(s(s(elem!1))))))) | (s(s(s(s(s(elem!1))))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(3921,plain,
% 1.64/1.87 (~(s(elem!1) = s(s(s(s(s(elem!1))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[3920, 1787])).
% 1.64/1.87 tff(3922,plain,
% 1.64/1.87 (b(s(elem!1), elem!1)),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[3789, 1452])).
% 1.64/1.87 tff(3923,plain,
% 1.64/1.87 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1959, 3807, 1853])).
% 1.64/1.87 tff(3924,plain,
% 1.64/1.87 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1557, 3923, 358])).
% 1.64/1.87 tff(3925,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(3926,plain,
% 1.64/1.87 (((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(s(elem!1)), 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(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))))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(3927,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1)))))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[3926])).
% 1.64/1.87 tff(3928,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[3927, 3925])).
% 1.64/1.87 tff(3929,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(3930,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), 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(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)))))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[3929, 3928])).
% 1.64/1.87 tff(3931,plain,
% 1.64/1.87 ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(elem!1)))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[3930, 246, 2362, 3924, 3922, 3809])).
% 1.64/1.87 tff(3932,plain,
% 1.64/1.87 (~b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[3931, 3882])).
% 1.64/1.87 tff(3933,plain,
% 1.64/1.87 (r(s(elem!1), s(s(s(s(s(elem!1))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[395, 47, 3932, 3921])).
% 1.64/1.87 tff(3934,plain,
% 1.64/1.87 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1985, 246, 3898, 3882, 3881])).
% 1.64/1.87 tff(3935,plain,
% 1.64/1.87 (~b(s(s(s(s(z)))), s(elem!1))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[3934, 1716])).
% 1.64/1.87 tff(3936,plain,
% 1.64/1.87 (r(s(s(s(s(z)))), s(elem!1))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1728, 3935, 1714])).
% 1.64/1.87 tff(3937,plain,
% 1.64/1.87 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[3936, 1706])).
% 1.64/1.87 tff(3938,plain,
% 1.64/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(3939,plain,
% 1.64/1.87 (((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), 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(elem!1)))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(3940,plain,
% 1.64/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[3939])).
% 1.64/1.87 tff(3941,plain,
% 1.64/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[3940, 3938])).
% 1.64/1.87 tff(3942,plain,
% 1.64/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(3943,plain,
% 1.64/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(elem!1))))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[3942, 3941])).
% 1.64/1.87 tff(3944,plain,
% 1.64/1.87 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[3943, 183, 3937, 3933, 3916])).
% 1.64/1.87 tff(3945,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[3944, 3908])).
% 1.64/1.87 tff(3946,plain,((~r(s(s(s(z))), elem!1)) | (~(z = elem!1)) | (~b(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(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(3947,plain,
% 1.64/1.87 (~r(s(s(s(z))), elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[3946, 1853, 2362, 333, 88])).
% 1.64/1.87 tff(3948,plain,
% 1.64/1.87 (b(s(s(s(z))), elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[647, 3947, 554])).
% 1.64/1.87 tff(3949,plain,
% 1.64/1.87 (b(s(s(s(elem!1))), elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[3701, 3948, 88])).
% 1.64/1.87 tff(3950,assumption,(s(elem!1) = elem!1), introduced(assumption)).
% 1.64/1.87 tff(3951,plain,
% 1.64/1.87 (elem!1 = s(elem!1)),
% 1.64/1.87 inference(symmetry,[status(thm)],[3950])).
% 1.64/1.87 tff(3952,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[3425, 3951])).
% 1.64/1.87 tff(3953,plain,((~(s(elem!1) = elem!1)) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(3954,plain,
% 1.64/1.87 (~(s(elem!1) = elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[3953, 2829])).
% 1.64/1.87 tff(3955,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2748, 183, 333, 367, 1853])).
% 1.64/1.87 tff(3956,plain,((~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)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(3957,plain,
% 1.64/1.87 (~r(s(elem!1), elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[3956, 1853, 333])).
% 1.64/1.87 tff(3958,plain,
% 1.64/1.87 (b(s(elem!1), elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[3437, 47, 3957, 3954])).
% 1.64/1.87 tff(3959,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(3960,plain,
% 1.64/1.87 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(3961,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[3960])).
% 1.64/1.87 tff(3962,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.64/1.87 inference(transitivity,[status(thm)],[3961, 3959])).
% 1.64/1.87 tff(3963,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(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))))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(3964,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[3963, 3962])).
% 1.64/1.87 tff(3965,plain,
% 1.64/1.87 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[3964, 246, 2362, 3958, 3949, 3784])).
% 1.64/1.87 tff(3966,plain,
% 1.64/1.87 (r(s(elem!1), elem!1) <=> r(s(z), elem!1)),
% 1.64/1.87 inference(symmetry,[status(thm)],[2733])).
% 1.64/1.87 tff(3967,plain,
% 1.64/1.87 ((~r(s(elem!1), elem!1)) <=> (~r(s(z), elem!1))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[3966])).
% 1.64/1.87 tff(3968,plain,
% 1.64/1.87 (~r(s(z), elem!1)),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[3957, 3967])).
% 1.64/1.87 tff(3969,plain,
% 1.64/1.87 (b(s(z), elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1034, 3968, 3678])).
% 1.64/1.87 tff(3970,plain,
% 1.64/1.87 (~b(s(s(elem!1)), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[3799, 3969, 2362, 3791])).
% 1.64/1.87 tff(3971,plain,
% 1.64/1.87 (r(s(s(elem!1)), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[197, 3970])).
% 1.64/1.87 tff(3972,plain,
% 1.64/1.87 (r(s(s(elem!1)), s(elem!1))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[3806, 3971, 88])).
% 1.64/1.87 tff(3973,plain,
% 1.64/1.87 (b(s(s(s(z))), z)),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[3948, 1434])).
% 1.64/1.87 tff(3974,plain,
% 1.64/1.87 (b(elem!1, s(elem!1)) <=> b(z, s(z))),
% 1.64/1.87 inference(transitivity,[status(thm)],[3790, 147])).
% 1.64/1.87 tff(3975,plain,
% 1.64/1.87 (b(z, s(z))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[3784, 3974])).
% 1.64/1.87 tff(3976,plain,
% 1.64/1.87 (r(s(z), elem!1) <=> r(s(z), z)),
% 1.64/1.87 inference(symmetry,[status(thm)],[3668])).
% 1.64/1.87 tff(3977,plain,
% 1.64/1.87 (r(s(elem!1), elem!1) <=> r(s(z), z)),
% 1.64/1.87 inference(transitivity,[status(thm)],[3966, 3976])).
% 1.64/1.87 tff(3978,plain,
% 1.64/1.87 ((~r(s(elem!1), elem!1)) <=> (~r(s(z), z))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[3977])).
% 1.64/1.87 tff(3979,plain,
% 1.64/1.87 (~r(s(z), z)),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[3957, 3978])).
% 1.64/1.87 tff(3980,plain,
% 1.64/1.87 (b(s(z), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1069, 3979])).
% 1.64/1.87 tff(3981,plain,
% 1.64/1.87 (~b(s(s(s(z))), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2098, 3980, 3975, 3973])).
% 1.64/1.87 tff(3982,plain,
% 1.64/1.87 (r(s(s(s(z))), s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[52, 3981])).
% 1.64/1.88 tff(3983,plain,
% 1.64/1.88 (r(s(s(s(elem!1))), s(elem!1))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[3982, 1431])).
% 1.64/1.88 tff(3984,plain,
% 1.64/1.88 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[3839, 183, 3983, 3972])).
% 1.64/1.88 tff(3985,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1820, 47, 3984, 3965, 1817])).
% 1.64/1.88 tff(3986,plain,((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~(z = elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(3987,plain,
% 1.64/1.88 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[3986, 333, 88, 2362])).
% 1.64/1.88 tff(3988,plain,
% 1.64/1.88 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1795, 3987, 1787])).
% 1.64/1.88 tff(3989,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(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(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), 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))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(3990,plain,
% 1.64/1.88 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(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(elem!1), 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))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(3991,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), 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)))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[3990])).
% 1.64/1.88 tff(3992,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), 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))))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[3991, 3989])).
% 1.64/1.88 tff(3993,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(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))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(3994,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[3993, 3992])).
% 1.64/1.88 tff(3995,plain,
% 1.64/1.88 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[3994, 246, 3736, 1200, 3988, 3774])).
% 1.64/1.88 tff(3996,plain,
% 1.64/1.88 (~b(s(elem!1), s(s(s(z))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[3995, 1738])).
% 1.64/1.88 tff(3997,plain,
% 1.64/1.88 (r(s(elem!1), s(s(s(z))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1754, 3996, 1735])).
% 1.64/1.88 tff(3998,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[3894, 3997, 3734, 1951])).
% 1.64/1.88 tff(3999,plain,((~r(s(s(elem!1)), s(elem!1))) | (~(z = elem!1)) | b(s(s(elem!1)), s(s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(4000,plain,
% 1.64/1.88 (~r(s(s(elem!1)), s(elem!1))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[3999, 2003, 3644, 3731, 333, 2362, 3732, 88])).
% 1.64/1.88 tff(4001,plain,
% 1.64/1.88 (~r(s(s(elem!1)), s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[3806, 4000, 88])).
% 1.64/1.88 tff(4002,plain,
% 1.64/1.88 (b(s(s(elem!1)), s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[197, 4001])).
% 1.64/1.88 tff(4003,plain,
% 1.64/1.88 (b(s(s(elem!1)), s(elem!1))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[4002, 3677])).
% 1.64/1.88 tff(4004,plain,
% 1.64/1.88 (~b(elem!1, s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[3799, 4002, 2362, 1044])).
% 1.64/1.88 tff(4005,plain,
% 1.64/1.88 (r(elem!1, s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[214, 4004, 3729])).
% 1.64/1.88 tff(4006,plain,
% 1.64/1.88 (r(elem!1, s(elem!1))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[4005, 3740])).
% 1.64/1.88 tff(4007,plain,
% 1.64/1.88 (~r(elem!1, s(s(elem!1)))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[3651, 183, 3730, 414])).
% 1.64/1.88 tff(4008,plain,
% 1.64/1.88 (b(elem!1, s(s(elem!1)))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1268, 4007, 3739])).
% 1.64/1.88 tff(4009,plain,
% 1.64/1.88 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[88])).
% 1.64/1.88 tff(4010,plain,
% 1.64/1.88 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(elem!1)))),
% 1.64/1.88 inference(symmetry,[status(thm)],[4009])).
% 1.64/1.88 tff(4011,plain,
% 1.64/1.88 (b(z, s(s(elem!1)))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[947, 4010])).
% 1.64/1.88 tff(4012,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[259, 4011])).
% 1.64/1.88 tff(4013,plain,((~b(elem!1, s(s(elem!1)))) | b(z, s(s(elem!1))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(4014,plain,
% 1.64/1.88 (b(z, s(s(elem!1)))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4013, 4008, 88])).
% 1.64/1.88 tff(4015,plain,
% 1.64/1.88 (r(elem!1, s(elem!1)) <=> r(elem!1, s(z))),
% 1.64/1.88 inference(symmetry,[status(thm)],[3740])).
% 1.64/1.88 tff(4016,plain,
% 1.64/1.88 (r(elem!1, s(elem!1)) <=> r(z, s(z))),
% 1.64/1.88 inference(transitivity,[status(thm)],[4015, 3728])).
% 1.64/1.88 tff(4017,plain,
% 1.64/1.88 (r(z, s(z))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[601, 4016])).
% 1.64/1.88 tff(4018,plain,
% 1.64/1.88 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(z))),
% 1.64/1.88 inference(symmetry,[status(thm)],[3677])).
% 1.64/1.88 tff(4019,plain,
% 1.64/1.88 ((~b(s(s(elem!1)), s(elem!1))) <=> (~b(s(s(elem!1)), s(z)))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[4018])).
% 1.64/1.88 tff(4020,plain,
% 1.64/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4021,plain,
% 1.64/1.88 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(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))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4022,plain,
% 1.64/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[4021])).
% 1.64/1.88 tff(4023,plain,
% 1.64/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.64/1.88 inference(transitivity,[status(thm)],[4022, 4020])).
% 1.64/1.88 tff(4024,plain,
% 1.64/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(4025,plain,
% 1.64/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[4024, 4023])).
% 1.64/1.88 tff(4026,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4025, 183, 333, 3412, 601, 3427])).
% 1.64/1.88 tff(4027,plain,((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(4028,plain,
% 1.64/1.88 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4027, 414, 601, 333])).
% 1.64/1.88 tff(4029,plain,
% 1.64/1.88 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[3693, 4028, 771])).
% 1.64/1.88 tff(4030,assumption,(~r(z, s(s(s(z))))), introduced(assumption)).
% 1.64/1.88 tff(4031,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4030, 428])).
% 1.64/1.88 tff(4032,plain,((~r(elem!1, s(s(s(z))))) | r(z, s(s(s(z)))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(4033,plain,
% 1.64/1.88 (r(z, s(s(s(z))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4032, 413, 88])).
% 1.64/1.88 tff(4034,plain,
% 1.64/1.88 (~r(s(s(s(z))), s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[438, 4033, 4017])).
% 1.64/1.88 tff(4035,plain,
% 1.64/1.88 (b(s(s(s(z))), s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[52, 4034])).
% 1.64/1.88 tff(4036,plain,
% 1.64/1.88 (b(s(s(s(elem!1))), s(elem!1))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[4035, 1849])).
% 1.64/1.88 tff(4037,plain,
% 1.64/1.88 (~(s(elem!1) = s(s(s(s(s(elem!1))))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[3920, 3410])).
% 1.64/1.88 tff(4038,plain,
% 1.64/1.88 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1795, 2749, 3410])).
% 1.64/1.88 tff(4039,assumption,(b(s(elem!1), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.64/1.88 tff(4040,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4041,plain,
% 1.64/1.88 (((~b(s(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(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(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4042,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[4041])).
% 1.64/1.88 tff(4043,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[4042, 4040])).
% 1.64/1.88 tff(4044,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(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))))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(4045,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[4044, 4043])).
% 1.64/1.88 tff(4046,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4045, 246, 1937, 2866, 1658, 4039])).
% 1.64/1.88 tff(4047,plain,((~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(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(4048,plain,
% 1.64/1.88 (~b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4047, 4038, 1937, 1658])).
% 1.64/1.88 tff(4049,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[395, 47, 392, 4048, 4037])).
% 1.64/1.88 tff(4050,plain,((~r(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (s(s(s(s(s(elem!1))))) = s(elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(4051,plain,
% 1.64/1.88 (~r(s(elem!1), elem!1)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4050, 4036, 4029, 1787, 333])).
% 1.64/1.88 tff(4052,plain,
% 1.64/1.88 (~r(s(z), z)),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[4051, 3978])).
% 1.64/1.88 tff(4053,plain,
% 1.64/1.88 (b(s(z), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1069, 4052])).
% 1.64/1.88 tff(4054,plain,
% 1.64/1.88 (b(s(elem!1), elem!1)),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[4053, 1454])).
% 1.64/1.88 tff(4055,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4056,plain,
% 1.64/1.88 (((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4057,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[4056])).
% 1.64/1.88 tff(4058,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.64/1.88 inference(transitivity,[status(thm)],[4057, 4055])).
% 1.64/1.88 tff(4059,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(4060,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[4059, 4058])).
% 1.64/1.88 tff(4061,plain,
% 1.64/1.88 (~b(s(s(elem!1)), s(elem!1))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4060, 246, 2362, 4008, 4054])).
% 1.64/1.88 tff(4062,plain,
% 1.64/1.88 (~b(s(s(elem!1)), s(z))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[4061, 4019])).
% 1.64/1.88 tff(4063,plain,
% 1.64/1.88 (r(s(s(elem!1)), s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[197, 4062])).
% 1.64/1.88 tff(4064,assumption,(r(s(s(s(s(s(elem!1))))), s(z))), introduced(assumption)).
% 1.64/1.88 tff(4065,plain,
% 1.64/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4066,plain,
% 1.64/1.88 (((~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4067,plain,
% 1.64/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z)))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[4066])).
% 1.64/1.88 tff(4068,plain,
% 1.64/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[4067, 4065])).
% 1.64/1.88 tff(4069,plain,
% 1.64/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(4070,plain,
% 1.64/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z)))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[4069, 4068])).
% 1.64/1.88 tff(4071,plain,
% 1.64/1.88 ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z)))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4070, 183, 171])).
% 1.64/1.88 tff(4072,plain,
% 1.64/1.88 (~r(s(s(s(s(s(elem!1))))), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4071, 4064])).
% 1.64/1.88 tff(4073,plain,
% 1.64/1.88 (b(s(s(s(s(s(elem!1))))), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1600, 47, 65, 4072])).
% 1.64/1.88 tff(4074,plain,
% 1.64/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4075,plain,
% 1.64/1.88 (((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4076,plain,
% 1.64/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[4075])).
% 1.64/1.88 tff(4077,plain,
% 1.64/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[4076, 4074])).
% 1.64/1.88 tff(4078,plain,
% 1.64/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(4079,plain,
% 1.64/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[4078, 4077])).
% 1.64/1.88 tff(4080,plain,
% 1.64/1.88 ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4079, 183, 173])).
% 1.64/1.88 tff(4081,plain,
% 1.64/1.88 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4080, 4064])).
% 1.64/1.88 tff(4082,plain,
% 1.64/1.88 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[361, 47, 1555, 4081])).
% 1.64/1.88 tff(4083,plain,
% 1.64/1.88 (~r(s(s(elem!1)), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[191, 171, 173])).
% 1.64/1.88 tff(4084,plain,
% 1.64/1.88 (b(s(s(elem!1)), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[523, 4083])).
% 1.64/1.88 tff(4085,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4086,plain,
% 1.64/1.88 (((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4087,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[4086])).
% 1.64/1.88 tff(4088,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[4087, 4085])).
% 1.64/1.88 tff(4089,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(4090,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[4089, 4088])).
% 1.64/1.88 tff(4091,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4090, 246, 4084, 1099, 4082, 4073])).
% 1.64/1.88 tff(4092,plain,((~r(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(s(elem!1)))) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(4093,plain,
% 1.64/1.88 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4092, 4063, 4017, 358, 4014])).
% 1.64/1.89 tff(4094,plain,
% 1.64/1.89 (r(s(s(s(s(s(elem!1))))), s(z)) <=> r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[89])).
% 1.64/1.89 tff(4095,plain,
% 1.64/1.89 (r(s(s(s(s(s(elem!1))))), s(elem!1)) <=> r(s(s(s(s(s(elem!1))))), s(z))),
% 1.64/1.89 inference(symmetry,[status(thm)],[4094])).
% 1.64/1.89 tff(4096,plain,
% 1.64/1.89 (r(s(s(s(s(s(elem!1))))), s(z))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[1853, 4095])).
% 1.64/1.89 tff(4097,assumption,(~r(s(s(s(s(s(elem!1))))), s(z))), introduced(assumption)).
% 1.64/1.89 tff(4098,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4097, 4096])).
% 1.64/1.89 tff(4099,plain,((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | r(s(s(s(s(s(elem!1))))), s(z)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(4100,plain,
% 1.64/1.89 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4099, 4093, 88])).
% 1.64/1.89 tff(4101,plain,
% 1.64/1.89 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1795, 4100, 1787])).
% 1.64/1.89 tff(4102,plain,
% 1.64/1.89 ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[3994, 246, 4036, 4054, 4029])).
% 1.64/1.89 tff(4103,plain,
% 1.64/1.89 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4102, 4101])).
% 1.64/1.89 tff(4104,plain,
% 1.64/1.89 (~b(s(elem!1), s(s(s(z))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4103, 1738])).
% 1.64/1.89 tff(4105,plain,
% 1.64/1.89 (r(s(s(elem!1)), s(elem!1))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1949, 47, 4061, 1936])).
% 1.64/1.89 tff(4106,plain,
% 1.64/1.89 (~r(s(elem!1), s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[3894, 4105, 3734])).
% 1.64/1.89 tff(4107,plain,
% 1.64/1.89 (b(s(elem!1), s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1754, 4106, 1735])).
% 1.64/1.89 tff(4108,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4107, 4104])).
% 1.64/1.89 tff(4109,plain,((~r(elem!1, s(s(s(z))))) | (~(z = elem!1)) | (~b(s(s(elem!1)), elem!1)) | b(s(s(elem!1)), s(s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(4110,plain,
% 1.64/1.89 (~r(elem!1, s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4109, 4006, 88, 3644, 2362, 333])).
% 1.64/1.89 tff(4111,plain,
% 1.64/1.89 (b(elem!1, s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[470, 4110, 718])).
% 1.64/1.89 tff(4112,assumption,(~b(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.64/1.89 tff(4113,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4112, 2017])).
% 1.64/1.89 tff(4114,plain,((~b(elem!1, s(s(s(z))))) | b(elem!1, s(s(s(elem!1)))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(4115,plain,
% 1.64/1.89 (b(elem!1, s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4114, 4111, 88])).
% 1.64/1.89 tff(4116,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(4117,plain,
% 1.64/1.89 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(4118,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[4117])).
% 1.64/1.89 tff(4119,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.64/1.89 inference(transitivity,[status(thm)],[4118, 4116])).
% 1.64/1.89 tff(4120,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(4121,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4120, 4119])).
% 1.64/1.89 tff(4122,plain,
% 1.64/1.89 (~b(s(elem!1), s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4121, 246, 2362, 4003, 4115, 3736, 3731])).
% 1.64/1.89 tff(4123,plain,
% 1.64/1.89 (~b(s(z), s(s(elem!1)))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4122, 1296])).
% 1.64/1.89 tff(4124,plain,
% 1.64/1.89 (r(s(z), s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[233, 4123])).
% 1.64/1.89 tff(4125,plain,
% 1.64/1.89 (r(s(elem!1), s(s(elem!1)))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4124, 3665])).
% 1.64/1.89 tff(4126,plain,
% 1.64/1.89 (~r(elem!1, s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1217, 4125, 4006])).
% 1.64/1.89 tff(4127,plain,
% 1.64/1.89 (b(elem!1, s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1268, 4126, 3739])).
% 1.64/1.89 tff(4128,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4060, 246, 2362, 4127, 4003, 3731])).
% 1.64/1.89 tff(4129,plain,((~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~(z = elem!1)) | b(s(s(elem!1)), s(s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(4130,plain,
% 1.64/1.89 (~b(s(s(s(z))), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4129, 3644, 88, 2362, 333, 1044])).
% 1.64/1.89 tff(4131,plain,
% 1.64/1.89 (r(s(s(s(z))), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[52, 4130])).
% 1.64/1.89 tff(4132,plain,
% 1.64/1.89 (r(s(s(s(elem!1))), s(elem!1))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4131, 1431])).
% 1.64/1.89 tff(4133,plain,
% 1.64/1.89 (~r(s(s(elem!1)), s(elem!1))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[3841, 4132, 3730])).
% 1.64/1.89 tff(4134,plain,
% 1.64/1.89 (~r(s(s(elem!1)), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[3806, 4133, 88])).
% 1.64/1.89 tff(4135,plain,
% 1.64/1.89 (b(s(s(elem!1)), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[197, 4134])).
% 1.64/1.89 tff(4136,plain,
% 1.64/1.89 (~b(elem!1, s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[3799, 4135, 2362, 1044])).
% 1.64/1.89 tff(4137,plain,
% 1.64/1.89 (r(elem!1, s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[214, 4136, 3729])).
% 1.64/1.89 tff(4138,plain,
% 1.64/1.89 (r(z, s(z))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4137, 3728])).
% 1.64/1.89 tff(4139,plain,
% 1.64/1.89 (r(s(s(s(elem!1))), s(elem!1))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[430, 1431])).
% 1.64/1.89 tff(4140,plain,
% 1.64/1.89 (~r(s(s(s(z))), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1023, 430, 474])).
% 1.64/1.89 tff(4141,plain,
% 1.64/1.89 (b(s(s(s(z))), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[647, 4140, 554])).
% 1.64/1.89 tff(4142,plain,
% 1.64/1.89 (b(s(s(s(elem!1))), elem!1)),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4141, 549])).
% 1.64/1.89 tff(4143,plain,
% 1.64/1.89 (~r(z, s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[438, 430, 171])).
% 1.64/1.89 tff(4144,plain,
% 1.64/1.89 (~r(elem!1, s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4032, 4143, 88])).
% 1.64/1.89 tff(4145,plain,
% 1.64/1.89 (b(elem!1, s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[470, 4144, 718])).
% 1.64/1.89 tff(4146,plain,
% 1.64/1.89 (b(elem!1, s(s(s(elem!1))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4145, 716])).
% 1.64/1.89 tff(4147,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(4148,plain,
% 1.64/1.89 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(4149,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[4148])).
% 1.64/1.89 tff(4150,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.64/1.89 inference(transitivity,[status(thm)],[4149, 4147])).
% 1.64/1.89 tff(4151,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(4152,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4151, 4150])).
% 1.64/1.89 tff(4153,plain,
% 1.64/1.89 (~b(s(s(elem!1)), s(elem!1))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4152, 246, 2362, 4146, 1200, 4142])).
% 1.64/1.89 tff(4154,plain,
% 1.64/1.89 (r(s(s(elem!1)), s(elem!1))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1949, 47, 4153, 1936])).
% 1.64/1.89 tff(4155,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[3841, 4154, 3730, 4139])).
% 1.64/1.89 tff(4156,plain,((~r(s(s(s(z))), s(z))) | b(s(s(elem!1)), s(s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~(z = elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(4157,plain,
% 1.64/1.89 (~r(z, s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4156, 4137, 3731, 2362, 88, 3644, 4131])).
% 1.64/1.89 tff(4158,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4157, 4138])).
% 1.64/1.89 tff(4159,plain,(b(s(s(elem!1)), s(s(s(elem!1)))) | (~(z = elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(4160,plain,
% 1.64/1.89 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4159, 1044, 2362, 88, 1469])).
% 1.64/1.89 tff(4161,plain,
% 1.64/1.89 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(z))), elem!1)),
% 1.64/1.89 inference(transitivity,[status(thm)],[1774, 1776])).
% 1.64/1.89 tff(4162,plain,
% 1.64/1.89 ((~r(s(s(s(elem!1))), elem!1)) <=> (~r(s(s(s(z))), elem!1))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[4161])).
% 1.64/1.89 tff(4163,plain,
% 1.64/1.89 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[3986, 1469, 88, 2362])).
% 1.64/1.89 tff(4164,plain,
% 1.64/1.89 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1795, 4163, 1787])).
% 1.64/1.89 tff(4165,plain,
% 1.64/1.89 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[88])).
% 1.64/1.89 tff(4166,plain,
% 1.64/1.89 (r(elem!1, s(s(elem!1))) <=> r(z, s(s(elem!1)))),
% 1.64/1.89 inference(symmetry,[status(thm)],[4165])).
% 1.64/1.89 tff(4167,plain,
% 1.64/1.89 (~r(s(s(elem!1)), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1670, 634, 1038, 82, 1555])).
% 1.64/1.89 tff(4168,plain,
% 1.64/1.89 (b(elem!1, s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[2282, 634, 430, 4167])).
% 1.64/1.89 tff(4169,plain,
% 1.64/1.89 (b(s(z), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[2713, 4167, 430, 634])).
% 1.64/1.89 tff(4170,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[3799, 4169, 4168, 2362, 201])).
% 1.64/1.89 tff(4171,plain,((~r(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~(elem!1 = z)) | b(s(s(s(s(s(elem!1))))), elem!1) | (s(s(s(s(s(elem!1))))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(4172,plain,
% 1.64/1.89 (~r(s(s(s(z))), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4171, 201, 2362, 430, 1441, 82, 358])).
% 1.64/1.89 tff(4173,plain,
% 1.64/1.89 (b(s(s(s(z))), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[647, 4172, 554])).
% 1.64/1.89 tff(4174,plain,
% 1.64/1.89 (b(s(s(s(elem!1))), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[3701, 4173, 88])).
% 1.64/1.89 tff(4175,plain,
% 1.64/1.89 (~b(elem!1, s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[3799, 201, 2362, 1044])).
% 1.64/1.89 tff(4176,plain,
% 1.64/1.89 (r(elem!1, s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[214, 4175, 3729])).
% 1.64/1.89 tff(4177,plain,
% 1.64/1.89 (r(z, s(z))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4176, 3728])).
% 1.64/1.89 tff(4178,plain,
% 1.64/1.89 (~r(z, s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[438, 4177, 430])).
% 1.64/1.89 tff(4179,plain,
% 1.64/1.89 (~r(elem!1, s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4032, 4178, 88])).
% 1.64/1.89 tff(4180,plain,
% 1.64/1.89 (b(elem!1, s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[470, 4179, 718])).
% 1.64/1.89 tff(4181,plain,
% 1.64/1.89 (b(elem!1, s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4114, 4180, 88])).
% 1.64/1.89 tff(4182,plain,
% 1.64/1.89 (b(s(s(elem!1)), s(elem!1))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[201, 3677])).
% 1.64/1.89 tff(4183,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4152, 246, 2362, 4182, 4181, 3731, 4174])).
% 1.64/1.89 tff(4184,plain,((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~(z = elem!1)) | (~r(s(s(s(z))), s(z))) | b(s(s(s(s(s(elem!1))))), elem!1) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(4185,plain,
% 1.64/1.89 (~b(s(s(elem!1)), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4184, 430, 88, 2362, 82, 1044])).
% 1.64/1.89 tff(4186,plain,
% 1.64/1.89 (r(s(s(elem!1)), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[197, 4185])).
% 1.64/1.89 tff(4187,plain,
% 1.64/1.89 (b(s(s(elem!1)), s(s(s(z))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4160, 423])).
% 1.64/1.89 tff(4188,plain,
% 1.64/1.89 (r(z, s(z))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[474, 3728])).
% 1.64/1.89 tff(4189,plain,
% 1.64/1.89 (~r(s(s(s(z))), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1023, 474, 430])).
% 1.64/1.89 tff(4190,plain,
% 1.64/1.89 (b(s(s(s(z))), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[647, 4189, 554])).
% 1.64/1.89 tff(4191,plain,
% 1.64/1.89 (b(s(s(s(elem!1))), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[3701, 4190, 88])).
% 1.64/1.89 tff(4192,plain,
% 1.64/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(4193,plain,
% 1.64/1.89 (((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(4194,plain,
% 1.64/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z)))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[4193])).
% 1.64/1.89 tff(4195,plain,
% 1.64/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[4194, 4192])).
% 1.64/1.89 tff(4196,plain,
% 1.64/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(4197,plain,
% 1.64/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z)))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4196, 4195])).
% 1.64/1.89 tff(4198,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4197, 183, 173, 474, 602])).
% 1.64/1.89 tff(4199,plain,((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(4200,plain,
% 1.64/1.89 (~r(elem!1, s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4199, 474, 173])).
% 1.64/1.89 tff(4201,plain,
% 1.64/1.89 (b(elem!1, s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1268, 4200, 3739])).
% 1.64/1.89 tff(4202,plain,
% 1.64/1.89 (~b(elem!1, s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[973, 4201, 963, 4191, 88])).
% 1.64/1.89 tff(4203,plain,
% 1.64/1.89 (~b(elem!1, s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4114, 4202, 88])).
% 1.64/1.89 tff(4204,plain,
% 1.64/1.89 (r(elem!1, s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[470, 4203, 718])).
% 1.64/1.89 tff(4205,plain,
% 1.64/1.89 (r(z, s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4032, 4204, 88])).
% 1.64/1.89 tff(4206,plain,
% 1.64/1.89 (~r(z, s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[438, 4205, 430])).
% 1.64/1.89 tff(4207,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4206, 4188])).
% 1.64/1.89 tff(4208,plain,((~r(elem!1, s(z))) | (~(z = elem!1)) | (~r(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(4209,plain,
% 1.64/1.89 (~r(elem!1, s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4208, 430, 88, 4187, 4186])).
% 1.64/1.89 tff(4210,plain,
% 1.64/1.89 (b(elem!1, s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[214, 4209, 3729])).
% 1.64/1.89 tff(4211,plain,
% 1.64/1.89 (b(z, s(z))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4210, 147])).
% 1.64/1.89 tff(4212,plain,
% 1.64/1.89 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 1.64/1.89 inference(symmetry,[status(thm)],[1309])).
% 1.64/1.89 tff(4213,plain,
% 1.64/1.89 ((~r(s(s(s(elem!1))), s(s(elem!1)))) <=> (~r(s(s(s(z))), s(s(elem!1))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[4212])).
% 1.64/1.89 tff(4214,plain,
% 1.64/1.89 (r(s(s(elem!1)), s(elem!1))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[3806, 4186, 88])).
% 1.64/1.89 tff(4215,plain,
% 1.64/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(4216,plain,
% 1.64/1.89 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(4217,plain,
% 1.64/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1)))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[4216])).
% 1.64/1.89 tff(4218,plain,
% 1.64/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[4217, 4215])).
% 1.64/1.89 tff(4219,plain,
% 1.64/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(4220,plain,
% 1.64/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4219, 4218])).
% 1.64/1.89 tff(4221,plain,
% 1.64/1.89 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4220, 183, 4139, 4214])).
% 1.64/1.89 tff(4222,plain,
% 1.64/1.89 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4221, 4213])).
% 1.64/1.89 tff(4223,plain,
% 1.64/1.89 (b(s(s(s(z))), s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[689, 4222, 416])).
% 1.64/1.89 tff(4224,plain,
% 1.64/1.89 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 1.64/1.89 inference(monotonicity,[status(thm)],[88])).
% 1.64/1.89 tff(4225,plain,
% 1.64/1.89 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), z)),
% 1.64/1.89 inference(symmetry,[status(thm)],[4224])).
% 1.64/1.89 tff(4226,plain,
% 1.64/1.89 (b(s(s(elem!1)), z)),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[2362, 4225])).
% 1.64/1.89 tff(4227,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1054, 4226])).
% 1.64/1.89 tff(4228,plain,((~(z = elem!1)) | b(s(s(elem!1)), z) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(4229,plain,
% 1.64/1.89 (b(s(s(elem!1)), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4228, 2362, 88])).
% 1.64/1.89 tff(4230,plain,
% 1.64/1.89 ((~r(s(s(s(elem!1))), z)) <=> (~r(s(s(s(z))), elem!1))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1776])).
% 1.64/1.89 tff(4231,plain,
% 1.64/1.89 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4223, 1797])).
% 1.64/1.89 tff(4232,plain,
% 1.64/1.89 (b(elem!1, s(elem!1))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4210, 1449])).
% 1.64/1.89 tff(4233,plain,
% 1.64/1.89 (~r(s(s(elem!1)), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1764, 4232, 82, 88, 3731, 55])).
% 1.64/1.89 tff(4234,plain,
% 1.64/1.89 (~(s(s(elem!1)) = s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[421, 119])).
% 1.64/1.89 tff(4235,plain,
% 1.64/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(4236,plain,
% 1.64/1.89 (((~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z)))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(4237,plain,
% 1.64/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[4236])).
% 1.64/1.89 tff(4238,plain,
% 1.64/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[4237, 4235])).
% 1.64/1.89 tff(4239,plain,
% 1.64/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(4240,plain,
% 1.64/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4239, 4238])).
% 1.64/1.89 tff(4241,plain,
% 1.64/1.89 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4240, 183, 2133, 430])).
% 1.64/1.89 tff(4242,plain,
% 1.64/1.89 (b(s(s(elem!1)), s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[454, 4241, 4234])).
% 1.64/1.89 tff(4243,plain,
% 1.64/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(4244,plain,
% 1.64/1.89 (((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(4245,plain,
% 1.64/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z)))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[4244])).
% 1.74/1.90 tff(4246,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[4245, 4243])).
% 1.74/1.90 tff(4247,plain,
% 1.74/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(4248,plain,
% 1.74/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z)))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[4247, 4246])).
% 1.74/1.90 tff(4249,plain,
% 1.74/1.90 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4248, 183, 2133, 430])).
% 1.74/1.90 tff(4250,plain,
% 1.74/1.90 (b(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[689, 4249, 119])).
% 1.74/1.90 tff(4251,plain,
% 1.74/1.90 (b(s(s(elem!1)), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[156, 2131, 2232])).
% 1.74/1.90 tff(4252,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(4253,plain,
% 1.74/1.90 (((~b(s(s(elem!1)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(4254,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[4253])).
% 1.74/1.90 tff(4255,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[4254, 4252])).
% 1.74/1.90 tff(4256,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(4257,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[4256, 4255])).
% 1.74/1.90 tff(4258,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4257, 246, 4251, 2002, 4250, 4242])).
% 1.74/1.90 tff(4259,plain,(b(s(s(elem!1)), s(z)) | (~b(elem!1, s(s(s(z))))) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(s(s(z))), s(z))) | r(s(s(elem!1)), elem!1) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(4260,plain,
% 1.74/1.90 (~b(elem!1, s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4259, 4233, 4185, 416, 430, 4210])).
% 1.74/1.90 tff(4261,plain,
% 1.74/1.90 (r(elem!1, s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[470, 4260, 718])).
% 1.74/1.90 tff(4262,plain,
% 1.74/1.90 (r(elem!1, s(s(s(elem!1))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[4261, 412])).
% 1.74/1.90 tff(4263,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(4264,plain,
% 1.74/1.90 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1))) <=> ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(4265,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[4264])).
% 1.74/1.90 tff(4266,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.74/1.90 inference(transitivity,[status(thm)],[4265, 4263])).
% 1.74/1.90 tff(4267,plain,
% 1.74/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(4268,plain,
% 1.74/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[4267, 4266])).
% 1.74/1.90 tff(4269,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4268, 183, 333, 3412, 3427])).
% 1.74/1.90 tff(4270,plain,((~r(elem!1, s(s(s(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)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(4271,plain,
% 1.74/1.90 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4270, 4262, 1469])).
% 1.74/1.90 tff(4272,plain,
% 1.74/1.90 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[3693, 4271, 771])).
% 1.74/1.90 tff(4273,plain,
% 1.74/1.90 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1667, 4272, 4160, 4231])).
% 1.74/1.90 tff(4274,plain,
% 1.74/1.90 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1557, 4273, 358])).
% 1.74/1.90 tff(4275,plain,
% 1.74/1.90 (r(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[4274, 1856])).
% 1.74/1.90 tff(4276,plain,
% 1.74/1.90 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(z))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[423, 1771])).
% 1.74/1.90 tff(4277,plain,
% 1.74/1.90 (b(s(s(z)), s(s(s(z))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[4160, 4276])).
% 1.74/1.90 tff(4278,plain,
% 1.74/1.90 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4270, 3427, 333])).
% 1.74/1.90 tff(4279,plain,
% 1.74/1.90 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[4278, 1870])).
% 1.74/1.90 tff(4280,plain,
% 1.74/1.90 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1626, 4279])).
% 1.74/1.90 tff(4281,assumption,(r(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.74/1.90 tff(4282,plain,
% 1.74/1.90 (r(s(s(s(elem!1))), elem!1)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[4281, 1775])).
% 1.74/1.90 tff(4283,plain,
% 1.74/1.90 (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2767, 4282])).
% 1.74/1.90 tff(4284,plain,
% 1.74/1.90 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[913, 47, 778, 4283])).
% 1.74/1.90 tff(4285,plain,
% 1.74/1.90 (b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[4284, 1873])).
% 1.74/1.90 tff(4286,plain,
% 1.74/1.90 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1918, 4285, 1854, 1883, 4280])).
% 1.74/1.90 tff(4287,plain,
% 1.74/1.90 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1702, 4286])).
% 1.74/1.90 tff(4288,plain,
% 1.74/1.90 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[4287, 1459])).
% 1.74/1.90 tff(4289,plain,
% 1.74/1.90 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2034, 183, 3427, 4288])).
% 1.74/1.90 tff(4290,plain,
% 1.74/1.90 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1571, 47, 4289, 3852])).
% 1.74/1.90 tff(4291,plain,
% 1.74/1.90 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[3693, 4278, 771])).
% 1.74/1.90 tff(4292,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), 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))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(4293,plain,
% 1.74/1.90 (((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), 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))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(4294,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), 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)))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[4293])).
% 1.74/1.90 tff(4295,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), 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))))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[4294, 4292])).
% 1.74/1.90 tff(4296,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(4297,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), 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)))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[4296, 4295])).
% 1.74/1.90 tff(4298,plain,
% 1.74/1.90 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4297, 246, 2362, 1200, 3988, 4291, 1659])).
% 1.74/1.90 tff(4299,plain,
% 1.74/1.90 (~b(s(elem!1), s(s(s(z))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[4298, 1738])).
% 1.74/1.90 tff(4300,plain,
% 1.74/1.90 (r(s(elem!1), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1754, 4299, 1735])).
% 1.74/1.90 tff(4301,plain,
% 1.74/1.90 (r(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[4300, 1732])).
% 1.74/1.90 tff(4302,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(4303,plain,
% 1.74/1.90 (((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(4304,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[4303])).
% 1.74/1.90 tff(4305,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[4304, 4302])).
% 1.74/1.90 tff(4306,plain,
% 1.74/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(4307,plain,
% 1.74/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1))))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[4306, 4305])).
% 1.74/1.90 tff(4308,plain,
% 1.74/1.90 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4307, 183, 4301, 4288])).
% 1.74/1.90 tff(4309,plain,
% 1.74/1.90 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2907, 47, 3915, 4308])).
% 1.74/1.90 tff(4310,plain,
% 1.74/1.90 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.74/1.90 inference(symmetry,[status(thm)],[1715])).
% 1.74/1.90 tff(4311,plain,
% 1.74/1.90 ((~r(s(s(s(s(elem!1)))), s(elem!1))) <=> (~r(s(s(s(s(z)))), s(elem!1)))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[1705])).
% 1.74/1.90 tff(4312,plain,
% 1.74/1.90 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1762, 183, 4301, 4288])).
% 1.74/1.90 tff(4313,plain,
% 1.74/1.90 (~r(s(s(s(s(z)))), s(elem!1))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[4312, 4311])).
% 1.74/1.90 tff(4314,plain,
% 1.74/1.90 (b(s(s(s(s(z)))), s(elem!1))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1728, 4313, 1714])).
% 1.74/1.90 tff(4315,plain,
% 1.74/1.90 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[4314, 4310])).
% 1.74/1.90 tff(4316,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(4317,plain,
% 1.74/1.90 (((~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(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)))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(4318,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(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(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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))))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[4317])).
% 1.74/1.90 tff(4319,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(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(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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)))))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[4318, 4316])).
% 1.74/1.90 tff(4320,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(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(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(4321,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[4320, 4319])).
% 1.74/1.90 tff(4322,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4321, 246, 1574, 4315, 4309, 4290])).
% 1.74/1.90 tff(4323,plain,((~r(s(s(s(elem!1))), z)) | (~b(elem!1, s(elem!1))) | (~(z = elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(4324,plain,
% 1.74/1.90 (~r(s(s(s(elem!1))), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4323, 4232, 88, 4262, 4277, 4275, 2362, 3731, 4231, 1469])).
% 1.74/1.90 tff(4325,plain,
% 1.74/1.90 (~r(s(s(s(z))), elem!1)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[4324, 4230])).
% 1.74/1.90 tff(4326,plain,
% 1.74/1.90 (b(s(s(s(z))), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[647, 4325, 554])).
% 1.74/1.90 tff(4327,assumption,(b(s(s(s(z))), s(s(elem!1)))), introduced(assumption)).
% 1.74/1.90 tff(4328,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(4329,plain,
% 1.74/1.90 (((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(4330,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[4329])).
% 1.74/1.90 tff(4331,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))),
% 1.74/1.91 inference(transitivity,[status(thm)],[4330, 4328])).
% 1.74/1.91 tff(4332,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(4333,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[4332, 4331])).
% 1.74/1.91 tff(4334,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4333, 246, 2001, 1100, 236, 947, 3697, 4327])).
% 1.74/1.91 tff(4335,plain,((~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(4336,plain,
% 1.74/1.91 (~b(elem!1, s(s(elem!1)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4335, 4326, 4229, 4223, 4210, 4211])).
% 1.74/1.91 tff(4337,plain,
% 1.74/1.91 (r(elem!1, s(s(elem!1)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1268, 4336, 3739])).
% 1.74/1.91 tff(4338,plain,
% 1.74/1.91 (r(z, s(s(elem!1)))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[4337, 4166])).
% 1.74/1.91 tff(4339,plain,
% 1.74/1.91 (r(elem!1, s(s(s(s(s(elem!1)))))) <=> r(z, s(s(s(s(s(elem!1))))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[341])).
% 1.74/1.91 tff(4340,plain,
% 1.74/1.91 (~(elem!1 = s(s(s(s(s(elem!1))))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[568, 125])).
% 1.74/1.91 tff(4341,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(4342,plain,
% 1.74/1.91 (((~b(elem!1, s(elem!1))) | (~b(s(s(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(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(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(s(s(s(s(elem!1))))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(4343,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(elem!1)))))))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[4342])).
% 1.74/1.91 tff(4344,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[4343, 4341])).
% 1.74/1.91 tff(4345,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(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(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(4346,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(elem!1)))))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[4345, 4344])).
% 1.74/1.91 tff(4347,plain,
% 1.74/1.91 (~b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4346, 246, 3731, 4164, 4232])).
% 1.74/1.91 tff(4348,plain,
% 1.74/1.91 ((elem!1 = s(s(s(s(s(elem!1)))))) | r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[3407, 47, 4347])).
% 1.74/1.91 tff(4349,plain,
% 1.74/1.91 (r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4348, 4340])).
% 1.74/1.91 tff(4350,plain,
% 1.74/1.91 (r(z, s(s(s(s(s(elem!1))))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[4349, 4339])).
% 1.74/1.91 tff(4351,plain,
% 1.74/1.91 (~r(z, s(s(elem!1)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[3325, 4350, 4274])).
% 1.74/1.91 tff(4352,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4351, 4338])).
% 1.74/1.91 tff(4353,plain,((~r(s(s(s(z))), s(z))) | (~(z = elem!1)) | (~b(s(s(elem!1)), elem!1)) | b(s(s(s(s(s(elem!1))))), elem!1) | b(z, elem!1) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(4354,plain,
% 1.74/1.91 (~r(s(s(s(z))), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4353, 1044, 2362, 82, 55, 88])).
% 1.74/1.91 tff(4355,plain,
% 1.74/1.91 (b(s(s(s(z))), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[52, 4354])).
% 1.74/1.91 tff(4356,plain,
% 1.74/1.91 (b(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[3661, 4355, 88])).
% 1.74/1.91 tff(4357,assumption,(r(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.74/1.91 tff(4358,plain,
% 1.74/1.91 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[3772, 4357])).
% 1.74/1.91 tff(4359,plain,
% 1.74/1.91 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[3693, 4358, 771])).
% 1.74/1.91 tff(4360,plain,
% 1.74/1.91 (~b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4047, 4359, 2866, 1937])).
% 1.74/1.91 tff(4361,plain,
% 1.74/1.91 (r(s(elem!1), s(s(s(s(s(elem!1))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[395, 47, 4360, 3921])).
% 1.74/1.91 tff(4362,plain,
% 1.74/1.91 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[3994, 246, 1937, 1200, 2866, 4359])).
% 1.74/1.91 tff(4363,plain,
% 1.74/1.91 (~b(s(elem!1), s(s(s(z))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[4362, 1738])).
% 1.74/1.91 tff(4364,plain,
% 1.74/1.91 (r(s(elem!1), s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1754, 4363, 1735])).
% 1.74/1.91 tff(4365,plain,
% 1.74/1.91 (r(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[4364, 1732])).
% 1.74/1.91 tff(4366,plain,
% 1.74/1.91 (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2767, 4357])).
% 1.74/1.91 tff(4367,plain,
% 1.74/1.91 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[913, 47, 778, 4366])).
% 1.74/1.91 tff(4368,plain,
% 1.74/1.91 (((~b(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(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(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(4369,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[4368])).
% 1.74/1.91 tff(4370,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[4369, 3825])).
% 1.74/1.91 tff(4371,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(4372,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[4371, 4370])).
% 1.74/1.91 tff(4373,plain,
% 1.74/1.91 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4372, 246, 4359, 1657, 4367])).
% 1.74/1.91 tff(4374,plain,
% 1.74/1.91 (r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1547, 47, 4373, 3816])).
% 1.74/1.91 tff(4375,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(4376,plain,
% 1.74/1.91 (((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(4377,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(elem!1)))))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[4376])).
% 1.74/1.91 tff(4378,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[4377, 4375])).
% 1.74/1.91 tff(4379,plain,
% 1.74/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(4380,plain,
% 1.74/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[4379, 4378])).
% 1.74/1.91 tff(4381,plain,
% 1.74/1.91 (~r(s(s(elem!1)), s(elem!1))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4380, 183, 4374, 4365, 4361])).
% 1.74/1.91 tff(4382,plain,
% 1.74/1.91 (~r(s(s(elem!1)), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[3806, 4381, 88])).
% 1.74/1.91 tff(4383,plain,
% 1.74/1.91 (b(s(s(elem!1)), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[197, 4382])).
% 1.74/1.91 tff(4384,plain,
% 1.74/1.91 (b(s(s(elem!1)), s(elem!1))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[4383, 3677])).
% 1.74/1.91 tff(4385,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(4386,plain,
% 1.74/1.91 (((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(4387,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1)))))))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[4386])).
% 1.74/1.91 tff(4388,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[4387, 4385])).
% 1.74/1.91 tff(4389,plain,
% 1.74/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(4390,plain,
% 1.74/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1)))))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[4389, 4388])).
% 1.74/1.91 tff(4391,plain,
% 1.74/1.91 (~r(s(elem!1), s(s(elem!1)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4390, 183, 4374, 4361])).
% 1.74/1.91 tff(4392,plain,
% 1.74/1.91 (~r(s(z), s(s(elem!1)))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[4391, 3667])).
% 1.74/1.91 tff(4393,plain,
% 1.74/1.91 (b(s(z), s(s(elem!1)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[233, 4392])).
% 1.74/1.91 tff(4394,plain,
% 1.74/1.91 (b(s(elem!1), s(s(elem!1)))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[4393, 364])).
% 1.74/1.91 tff(4395,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[448, 246, 4394, 4384, 1937, 1657])).
% 1.74/1.91 tff(4396,plain,((~r(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~(z = elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(4397,plain,
% 1.74/1.91 (~r(s(s(s(elem!1))), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4396, 4356, 4160, 88, 3731, 4164, 1469])).
% 1.74/1.91 tff(4398,plain,
% 1.74/1.91 (~r(s(s(s(z))), elem!1)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[4397, 4162])).
% 1.74/1.91 tff(4399,plain,
% 1.74/1.91 (b(s(s(s(z))), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[647, 4398, 554])).
% 1.74/1.91 tff(4400,plain,
% 1.74/1.91 (b(s(s(s(elem!1))), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[3701, 4399, 88])).
% 1.74/1.91 tff(4401,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(4402,plain,
% 1.74/1.91 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(4403,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1)))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[4402])).
% 1.74/1.91 tff(4404,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[4403, 4401])).
% 1.74/1.91 tff(4405,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(4406,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[4405, 4404])).
% 1.74/1.91 tff(4407,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4406, 246, 2362, 960, 1937, 961, 1657])).
% 1.74/1.91 tff(4408,plain,((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(4409,plain,
% 1.74/1.91 (~b(elem!1, s(s(s(elem!1))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4408, 4356, 2362, 4400, 4160])).
% 1.74/1.91 tff(4410,plain,
% 1.74/1.91 (~b(elem!1, s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4114, 4409, 88])).
% 1.74/1.91 tff(4411,plain,
% 1.74/1.91 (r(elem!1, s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[470, 4410, 718])).
% 1.74/1.91 tff(4412,assumption,(~r(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.74/1.91 tff(4413,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4412, 414])).
% 1.74/1.91 tff(4414,plain,((~r(elem!1, s(s(s(z))))) | r(elem!1, s(s(s(elem!1)))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(4415,plain,
% 1.74/1.91 (r(elem!1, s(s(s(elem!1))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4414, 4411, 88])).
% 1.74/1.91 tff(4416,plain,
% 1.74/1.91 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4270, 4415, 1469])).
% 1.74/1.91 tff(4417,plain,
% 1.74/1.91 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[3994, 246, 1937, 1200, 2866, 1658])).
% 1.74/1.91 tff(4418,plain,
% 1.74/1.91 (~b(s(elem!1), s(s(s(z))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[4417, 1738])).
% 1.74/1.91 tff(4419,plain,
% 1.74/1.91 (r(s(elem!1), s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1754, 4418, 1735])).
% 1.74/1.91 tff(4420,plain,
% 1.74/1.91 (r(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[4419, 1732])).
% 1.74/1.91 tff(4421,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(4422,plain,
% 1.74/1.91 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(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))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(4423,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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)))))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[4422])).
% 1.74/1.91 tff(4424,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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))))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[4423, 4421])).
% 1.74/1.92 tff(4425,plain,
% 1.74/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(4426,plain,
% 1.74/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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)))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[4425, 4424])).
% 1.74/1.92 tff(4427,plain,
% 1.74/1.92 (~r(elem!1, s(elem!1))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4426, 183, 4420, 3427])).
% 1.74/1.92 tff(4428,plain,
% 1.74/1.92 (b(elem!1, s(elem!1))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2864, 4427, 2829])).
% 1.74/1.92 tff(4429,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(4430,plain,
% 1.74/1.92 (((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(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(elem!1), 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))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(4431,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[4430])).
% 1.74/1.92 tff(4432,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[4431, 4429])).
% 1.74/1.92 tff(4433,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(4434,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[4433, 4432])).
% 1.74/1.92 tff(4435,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4434, 246, 1937, 1200, 2866, 4428, 1658])).
% 1.74/1.92 tff(4436,plain,((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(4437,plain,
% 1.74/1.92 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4436, 4415, 4164, 3731, 4356, 88])).
% 1.74/1.92 tff(4438,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[3693, 4437, 4416, 771])).
% 1.74/1.92 tff(4439,plain,((~b(s(z), elem!1)) | (~(z = elem!1)) | (~b(s(s(elem!1)), elem!1)) | b(s(s(s(s(s(elem!1))))), elem!1) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(4440,plain,
% 1.74/1.92 (~b(s(z), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4439, 82, 3726, 61, 55])).
% 1.74/1.92 tff(4441,plain,
% 1.74/1.92 (r(s(z), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1034, 4440, 122])).
% 1.74/1.92 tff(4442,plain,
% 1.74/1.92 (~r(s(s(s(z))), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[3545, 4441, 87])).
% 1.74/1.92 tff(4443,plain,
% 1.74/1.92 (b(s(s(s(z))), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[647, 4442, 81])).
% 1.74/1.92 tff(4444,plain,
% 1.74/1.92 (b(s(s(s(elem!1))), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[3701, 4443, 61])).
% 1.74/1.92 tff(4445,plain,
% 1.74/1.92 (b(s(s(s(z))), z) <=> b(s(s(s(z))), elem!1)),
% 1.74/1.92 inference(monotonicity,[status(thm)],[61])).
% 1.74/1.92 tff(4446,plain,
% 1.74/1.92 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), z)),
% 1.74/1.92 inference(symmetry,[status(thm)],[4445])).
% 1.74/1.92 tff(4447,plain,
% 1.74/1.92 (b(s(s(s(z))), z)),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[4443, 4446])).
% 1.74/1.92 tff(4448,assumption,(~r(s(elem!1), elem!1)), introduced(assumption)).
% 1.74/1.92 tff(4449,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4448, 2734])).
% 1.74/1.92 tff(4450,plain,((~r(s(z), elem!1)) | r(s(elem!1), elem!1) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(4451,plain,
% 1.74/1.92 (r(s(elem!1), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4450, 4441, 61])).
% 1.74/1.92 tff(4452,assumption,(~(s(s(elem!1)) = s(s(s(elem!1))))), introduced(assumption)).
% 1.74/1.92 tff(4453,assumption,(~r(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 1.74/1.92 tff(4454,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1820, 47, 4453, 3644, 4452])).
% 1.74/1.92 tff(4455,plain,(r(s(s(elem!1)), s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(4456,plain,
% 1.74/1.92 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4455, 3644, 3643])).
% 1.74/1.92 tff(4457,plain,
% 1.74/1.92 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[3986, 333, 61, 3726])).
% 1.74/1.92 tff(4458,plain,
% 1.74/1.92 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1795, 4457, 3602])).
% 1.74/1.92 tff(4459,plain,
% 1.74/1.92 (~(s(elem!1) = s(s(s(s(s(elem!1))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[3920, 3602])).
% 1.74/1.92 tff(4460,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[391, 183, 333, 367, 1932])).
% 1.74/1.92 tff(4461,plain,((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(4462,plain,
% 1.74/1.92 (~r(s(elem!1), s(s(s(s(s(elem!1))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4461, 367, 333])).
% 1.74/1.92 tff(4463,plain,
% 1.74/1.92 (b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[395, 47, 4462, 4459])).
% 1.74/1.92 tff(4464,plain,
% 1.74/1.92 (r(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[430, 3656])).
% 1.74/1.92 tff(4465,plain,
% 1.74/1.92 (~r(s(s(elem!1)), s(elem!1))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[3841, 4464, 4456])).
% 1.74/1.92 tff(4466,plain,
% 1.74/1.92 (~r(s(s(elem!1)), s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[3806, 4465, 61])).
% 1.74/1.92 tff(4467,plain,
% 1.74/1.92 (b(s(s(elem!1)), s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[197, 4466])).
% 1.74/1.92 tff(4468,plain,
% 1.74/1.92 (b(s(s(elem!1)), s(elem!1))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[4467, 1427])).
% 1.74/1.92 tff(4469,plain,
% 1.74/1.92 ((s(elem!1) = z) <=> (s(elem!1) = elem!1)),
% 1.74/1.92 inference(monotonicity,[status(thm)],[61])).
% 1.74/1.92 tff(4470,plain,
% 1.74/1.92 ((s(elem!1) = z) <=> (elem!1 = s(elem!1))),
% 1.74/1.92 inference(transitivity,[status(thm)],[4469, 2825])).
% 1.74/1.92 tff(4471,plain,
% 1.74/1.92 ((~(s(elem!1) = z)) <=> (~(elem!1 = s(elem!1)))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[4470])).
% 1.74/1.92 tff(4472,plain,
% 1.74/1.92 (~(elem!1 = s(elem!1))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[111, 4471])).
% 1.74/1.92 tff(4473,plain,
% 1.74/1.92 (b(s(s(elem!1)), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4228, 3726, 61])).
% 1.74/1.92 tff(4474,plain,
% 1.74/1.92 (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[3815, 2169])).
% 1.74/1.92 tff(4475,plain,
% 1.74/1.92 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1820, 47, 3644, 4452])).
% 1.74/1.92 tff(4476,assumption,(~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.74/1.92 tff(4477,assumption,(~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.74/1.92 tff(4478,plain,
% 1.74/1.92 (r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1547, 47, 4477, 4476])).
% 1.74/1.92 tff(4479,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(4480,plain,
% 1.74/1.92 (((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(4481,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[4480])).
% 1.74/1.92 tff(4482,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[4481, 4479])).
% 1.74/1.92 tff(4483,plain,
% 1.74/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(4484,plain,
% 1.74/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[4483, 4482])).
% 1.74/1.92 tff(4485,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4484, 183, 3412, 3833, 3306])).
% 1.74/1.92 tff(4486,plain,((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(4487,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4486, 4478, 4475, 3412])).
% 1.74/1.92 tff(4488,plain,(b(s(s(elem!1)), s(s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | b(s(s(elem!1)), s(s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(4489,plain,
% 1.74/1.92 (b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4488, 3644, 4474, 3412, 3643])).
% 1.74/1.92 tff(4490,plain,
% 1.74/1.92 (~r(s(s(elem!1)), s(elem!1))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[3841, 3645, 4464])).
% 1.74/1.92 tff(4491,plain,
% 1.74/1.92 (~r(s(s(elem!1)), s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[3806, 4490, 61])).
% 1.74/1.92 tff(4492,plain,
% 1.74/1.92 (b(s(s(elem!1)), s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[197, 4491])).
% 1.74/1.92 tff(4493,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(4494,plain,
% 1.74/1.92 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(4495,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[4494])).
% 1.74/1.92 tff(4496,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[4495, 4493])).
% 1.74/1.92 tff(4497,plain,
% 1.74/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(4498,plain,
% 1.74/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[4497, 4496])).
% 1.74/1.92 tff(4499,plain,
% 1.74/1.92 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4498, 183, 3412, 3645])).
% 1.74/1.92 tff(4500,plain,
% 1.74/1.92 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1557, 4499, 2169])).
% 1.74/1.92 tff(4501,plain,
% 1.74/1.92 (b(s(s(elem!1)), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[3653, 3644, 56, 55])).
% 1.74/1.92 tff(4502,plain,
% 1.74/1.92 (r(elem!1, s(z))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[601, 4015])).
% 1.74/1.92 tff(4503,plain,
% 1.74/1.92 (~r(s(s(s(z))), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1023, 4502, 430])).
% 1.74/1.92 tff(4504,plain,
% 1.74/1.92 (b(s(s(s(z))), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[647, 4503, 554])).
% 1.74/1.92 tff(4505,plain,
% 1.74/1.92 (b(s(s(s(elem!1))), elem!1)),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[4504, 549])).
% 1.74/1.92 tff(4506,plain,
% 1.74/1.92 (~r(z, s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[438, 4017, 430])).
% 1.74/1.92 tff(4507,plain,
% 1.74/1.92 (~r(elem!1, s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4032, 4506, 88])).
% 1.74/1.92 tff(4508,plain,
% 1.74/1.92 (b(elem!1, s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[470, 4507, 718])).
% 1.74/1.92 tff(4509,plain,
% 1.74/1.92 (b(elem!1, s(s(s(elem!1))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[4508, 716])).
% 1.74/1.92 tff(4510,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(4511,plain,
% 1.74/1.92 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(4512,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[4511])).
% 1.74/1.92 tff(4513,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.74/1.92 inference(transitivity,[status(thm)],[4512, 4510])).
% 1.74/1.92 tff(4514,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(4515,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[4514, 4513])).
% 1.74/1.92 tff(4516,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4515, 246, 2362, 4509, 714, 946, 4505])).
% 1.74/1.92 tff(4517,plain,((~r(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~(z = elem!1)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(4518,plain,
% 1.74/1.92 (~r(elem!1, s(elem!1))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4517, 714, 2362, 946, 88, 430])).
% 1.74/1.92 tff(4519,plain,
% 1.74/1.92 (b(elem!1, s(elem!1))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2864, 4518, 2829])).
% 1.74/1.92 tff(4520,assumption,(b(s(s(elem!1)), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.74/1.92 tff(4521,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(4522,plain,
% 1.74/1.92 (((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(4523,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1)))))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[4522])).
% 1.74/1.92 tff(4524,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[4523, 4521])).
% 1.74/1.92 tff(4525,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), elem!1)))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(4526,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1)))))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[4525, 4524])).
% 1.74/1.92 tff(4527,plain,
% 1.74/1.92 (~b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4526, 246, 2362, 4182, 946, 4520, 4519])).
% 1.74/1.92 tff(4528,plain,
% 1.74/1.92 ((elem!1 = s(s(s(s(s(elem!1)))))) | r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[3407, 47, 4527])).
% 1.74/1.92 tff(4529,plain,
% 1.74/1.92 (r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4528, 4340])).
% 1.74/1.92 tff(4530,plain,
% 1.74/1.92 (b(elem!1, s(z))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[4519, 3790])).
% 1.74/1.92 tff(4531,plain,
% 1.74/1.92 (~b(s(z), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[3799, 4530, 2362, 201])).
% 1.74/1.92 tff(4532,plain,
% 1.74/1.92 (r(s(z), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1034, 4531, 3678])).
% 1.74/1.92 tff(4533,plain,
% 1.74/1.92 (~r(s(s(s(z))), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[3017, 4532, 430])).
% 1.74/1.92 tff(4534,plain,
% 1.74/1.92 (b(s(s(s(z))), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[647, 4533, 554])).
% 1.74/1.92 tff(4535,plain,
% 1.74/1.92 (b(s(s(s(elem!1))), elem!1)),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[4534, 549])).
% 1.74/1.92 tff(4536,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4515, 246, 2362, 960, 714, 946, 961])).
% 1.74/1.92 tff(4537,plain,((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(4538,plain,
% 1.74/1.92 (~b(elem!1, s(s(s(elem!1))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4537, 714, 2362, 946, 4535])).
% 1.74/1.92 tff(4539,plain,
% 1.74/1.92 (~b(elem!1, s(s(s(z))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[4538, 2211])).
% 1.74/1.92 tff(4540,plain,
% 1.74/1.92 (r(elem!1, s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[470, 4539, 718])).
% 1.74/1.92 tff(4541,plain,
% 1.74/1.92 (r(elem!1, s(s(s(elem!1))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[4540, 412])).
% 1.74/1.92 tff(4542,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[3403, 183, 3412, 4541, 4529])).
% 1.74/1.92 tff(4543,plain,((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~(z = elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(4544,plain,
% 1.74/1.92 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4543, 4501, 61, 3412, 4500, 430, 4492, 4489])).
% 1.74/1.92 tff(4545,plain,
% 1.74/1.92 (elem!1 = z),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1440, 61])).
% 1.74/1.92 tff(4546,plain,
% 1.74/1.92 (~r(s(s(s(z))), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4171, 4501, 4492, 430, 4545, 4544, 2169])).
% 1.74/1.92 tff(4547,plain,
% 1.74/1.92 (b(s(s(s(z))), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[647, 4546, 81])).
% 1.74/1.92 tff(4548,plain,
% 1.74/1.92 (b(s(s(s(elem!1))), elem!1)),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[4547, 3619])).
% 1.74/1.92 tff(4549,plain,
% 1.74/1.92 (b(s(z), elem!1) <=> b(s(elem!1), elem!1)),
% 1.74/1.92 inference(monotonicity,[status(thm)],[141])).
% 1.74/1.92 tff(4550,plain,
% 1.74/1.92 (b(s(z), z) <=> b(s(z), elem!1)),
% 1.74/1.92 inference(monotonicity,[status(thm)],[61])).
% 1.74/1.92 tff(4551,plain,
% 1.74/1.92 (b(s(z), z) <=> b(s(elem!1), elem!1)),
% 1.74/1.92 inference(transitivity,[status(thm)],[4550, 4549])).
% 1.74/1.92 tff(4552,plain,
% 1.74/1.92 (r(s(z), elem!1) <=> r(s(z), z)),
% 1.74/1.92 inference(symmetry,[status(thm)],[2149])).
% 1.74/1.92 tff(4553,plain,
% 1.74/1.93 (r(s(elem!1), elem!1) <=> r(s(z), elem!1)),
% 1.74/1.93 inference(symmetry,[status(thm)],[2148])).
% 1.74/1.93 tff(4554,plain,
% 1.74/1.93 (r(s(elem!1), elem!1) <=> r(s(z), z)),
% 1.74/1.93 inference(transitivity,[status(thm)],[4553, 4552])).
% 1.74/1.93 tff(4555,plain,
% 1.74/1.93 ((~r(s(elem!1), elem!1)) <=> (~r(s(z), z))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[4554])).
% 1.74/1.93 tff(4556,plain,
% 1.74/1.93 (b(s(s(elem!1)), s(elem!1))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[4492, 1427])).
% 1.74/1.93 tff(4557,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(4558,plain,
% 1.74/1.93 (((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(4559,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[4558])).
% 1.74/1.93 tff(4560,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[4559, 4557])).
% 1.74/1.93 tff(4561,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(4562,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[4561, 4560])).
% 1.74/1.93 tff(4563,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[4562, 246, 363, 946, 4520, 2866, 4039])).
% 1.74/1.93 tff(4564,plain,((~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(4565,plain,
% 1.74/1.93 (~b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[4564, 4556, 4500, 4489, 2866])).
% 1.74/1.93 tff(4566,plain,
% 1.74/1.93 (r(s(elem!1), s(s(s(s(s(elem!1))))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[395, 47, 4565, 4459])).
% 1.74/1.93 tff(4567,plain,
% 1.74/1.93 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[86, 4544, 66])).
% 1.74/1.93 tff(4568,plain,
% 1.74/1.93 (~r(s(elem!1), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[4461, 4567, 4566])).
% 1.74/1.93 tff(4569,plain,
% 1.74/1.93 (~r(s(z), z)),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[4568, 4555])).
% 1.74/1.93 tff(4570,plain,
% 1.74/1.93 (b(s(z), z)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1069, 4569])).
% 1.74/1.93 tff(4571,plain,
% 1.74/1.93 (b(s(elem!1), elem!1)),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[4570, 4551])).
% 1.74/1.93 tff(4572,plain,
% 1.74/1.93 ((~r(elem!1, s(s(s(elem!1))))) <=> (~r(elem!1, s(s(s(z)))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[2173])).
% 1.74/1.93 tff(4573,plain,
% 1.74/1.93 (~r(elem!1, s(s(s(elem!1))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[4270, 4567, 3412])).
% 1.74/1.93 tff(4574,plain,
% 1.74/1.93 (~r(elem!1, s(s(s(z))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[4573, 4572])).
% 1.74/1.93 tff(4575,plain,
% 1.74/1.93 (b(elem!1, s(s(s(z))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[470, 4574, 2176])).
% 1.74/1.93 tff(4576,plain,
% 1.74/1.93 (b(elem!1, s(s(s(elem!1))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[4114, 4575, 61])).
% 1.74/1.93 tff(4577,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[4152, 246, 4501, 4556, 4576, 4571, 4548])).
% 1.74/1.93 tff(4578,plain,(b(s(s(elem!1)), s(s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | r(z, elem!1) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(4579,plain,
% 1.74/1.93 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[4578, 430, 2866, 3644, 56, 55])).
% 1.74/1.93 tff(4580,plain,
% 1.74/1.93 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[3693, 4579, 3616])).
% 1.74/1.93 tff(4581,plain,
% 1.74/1.93 ((s(s(s(s(s(s(s(elem!1))))))) = z) <=> (s(s(s(s(s(s(s(elem!1))))))) = elem!1)),
% 1.74/1.93 inference(monotonicity,[status(thm)],[88])).
% 1.74/1.93 tff(4582,plain,
% 1.74/1.93 ((~(s(s(s(s(s(s(s(elem!1))))))) = z)) <=> (~(s(s(s(s(s(s(s(elem!1))))))) = elem!1))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[4581])).
% 1.74/1.93 tff(4583,plain,
% 1.74/1.93 (~(s(s(s(s(s(s(s(elem!1))))))) = elem!1)),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[599, 4582])).
% 1.74/1.93 tff(4584,plain,
% 1.74/1.93 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(z))),
% 1.74/1.93 inference(symmetry,[status(thm)],[1848])).
% 1.74/1.93 tff(4585,plain,
% 1.74/1.93 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(z))), s(elem!1))),
% 1.74/1.93 inference(symmetry,[status(thm)],[1847])).
% 1.74/1.93 tff(4586,plain,
% 1.74/1.93 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(z))), s(z))),
% 1.74/1.93 inference(transitivity,[status(thm)],[4585, 4584])).
% 1.74/1.93 tff(4587,plain,
% 1.74/1.93 ((~b(s(s(s(elem!1))), s(elem!1))) <=> (~b(s(s(s(z))), s(z)))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[4586])).
% 1.74/1.93 tff(4588,plain,
% 1.74/1.93 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[4047, 1658, 2866, 4039])).
% 1.74/1.93 tff(4589,plain,
% 1.74/1.93 (~b(s(s(s(z))), s(z))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[4588, 4587])).
% 1.74/1.93 tff(4590,plain,
% 1.74/1.93 (r(s(s(s(z))), s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[52, 4589])).
% 1.74/1.93 tff(4591,plain,
% 1.74/1.93 (~r(z, s(s(s(z))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[438, 4017, 4590])).
% 1.74/1.93 tff(4592,plain,
% 1.74/1.93 (~r(elem!1, s(s(s(z))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[4032, 4591, 88])).
% 1.74/1.93 tff(4593,plain,
% 1.74/1.93 (b(elem!1, s(s(s(z))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[470, 4592, 718])).
% 1.74/1.93 tff(4594,plain,
% 1.74/1.93 (b(elem!1, s(s(s(elem!1))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[4593, 716])).
% 1.74/1.93 tff(4595,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(4596,plain,
% 1.74/1.93 (((~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(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(elem!1)))))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(4597,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(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(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(elem!1)))))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[4596])).
% 1.74/1.93 tff(4598,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(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(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[4597, 4595])).
% 1.74/1.93 tff(4599,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(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(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(4600,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(elem!1)))))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[4599, 4598])).
% 1.74/1.93 tff(4601,plain,
% 1.74/1.93 (~b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[4600, 246, 4594, 961, 1658])).
% 1.74/1.93 tff(4602,plain,
% 1.74/1.93 ((elem!1 = s(s(s(s(s(elem!1)))))) | r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[3407, 47, 4601])).
% 1.74/1.93 tff(4603,plain,
% 1.74/1.93 (r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[4602, 4340])).
% 1.74/1.93 tff(4604,plain,
% 1.74/1.93 ((s(z) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 1.74/1.93 inference(transitivity,[status(thm)],[1733, 2182])).
% 1.74/1.93 tff(4605,plain,
% 1.74/1.93 ((~(s(z) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[4604])).
% 1.74/1.93 tff(4606,plain,
% 1.74/1.93 (~(s(s(s(z))) = s(elem!1))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[767, 4605])).
% 1.74/1.93 tff(4607,plain,
% 1.74/1.93 ((~b(s(s(s(elem!1))), s(elem!1))) <=> (~b(s(s(s(z))), s(elem!1)))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[4585])).
% 1.74/1.93 tff(4608,plain,
% 1.74/1.93 (~b(s(s(s(z))), s(elem!1))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[4588, 4607])).
% 1.74/1.93 tff(4609,plain,
% 1.74/1.93 (r(s(s(s(z))), s(elem!1))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[2675, 4608, 4606])).
% 1.74/1.93 tff(4610,plain,
% 1.74/1.93 (r(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[4609, 1429])).
% 1.74/1.93 tff(4611,plain,
% 1.74/1.93 (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[860, 601, 88, 4610])).
% 1.74/1.93 tff(4612,plain,
% 1.74/1.93 (b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[818, 4611, 1222])).
% 1.74/1.93 tff(4613,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(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))))))) | (~b(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), 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(elem!1))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(4614,plain,
% 1.74/1.93 (((~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(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)))))))) <=> ((~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(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))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(4615,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(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))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(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))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[4614])).
% 1.74/1.93 tff(4616,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(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))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(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))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[4615, 4613])).
% 1.74/1.93 tff(4617,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(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))))))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(4618,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(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))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[4617, 4616])).
% 1.74/1.93 tff(4619,plain,
% 1.74/1.93 (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[4618, 246, 4612, 2866, 4039])).
% 1.74/1.93 tff(4620,plain,
% 1.74/1.93 (((~![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(elem!1)))))) | b(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(elem!1)))))))) <=> ((~![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(elem!1)))))) | b(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(elem!1)))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(4621,plain,
% 1.74/1.93 ((~![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(elem!1)))))) | b(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(elem!1)))))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(4622,plain,
% 1.74/1.93 ((~![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(elem!1)))))) | b(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(elem!1))))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[4621, 4620])).
% 1.74/1.93 tff(4623,plain,
% 1.74/1.93 (r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[4622, 47, 788, 4619])).
% 1.74/1.93 tff(4624,plain,
% 1.74/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(4625,plain,
% 1.74/1.93 (((~r(elem!1, 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(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1))) <=> ((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(4626,plain,
% 1.74/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, 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(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[4625])).
% 1.74/1.93 tff(4627,plain,
% 1.74/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, 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(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)))),
% 1.74/1.93 inference(transitivity,[status(thm)],[4626, 4624])).
% 1.74/1.93 tff(4628,plain,
% 1.74/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, 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(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(4629,plain,
% 1.74/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[4628, 4627])).
% 1.74/1.93 tff(4630,plain,
% 1.74/1.93 (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[4629, 183, 4623, 4603])).
% 1.74/1.93 tff(4631,plain,
% 1.74/1.93 ((s(s(s(s(s(s(s(elem!1))))))) = elem!1) | b(s(s(s(s(s(s(s(elem!1))))))), elem!1) | r(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[612, 47])).
% 1.74/1.93 tff(4632,plain,
% 1.74/1.93 (b(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[4631, 4630, 4583])).
% 1.74/1.93 tff(4633,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(4634,plain,
% 1.74/1.93 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(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(s(s(elem!1)))))))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(4635,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(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(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[4634])).
% 1.74/1.93 tff(4636,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(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(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)))),
% 1.74/1.93 inference(transitivity,[status(thm)],[4635, 4633])).
% 1.74/1.93 tff(4637,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(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(s(s(elem!1))))))))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(4638,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[4637, 4636])).
% 1.74/1.94 tff(4639,plain,
% 1.74/1.94 (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4638, 246, 4594, 4632, 961])).
% 1.74/1.94 tff(4640,plain,
% 1.74/1.94 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[672, 47, 669, 4639])).
% 1.74/1.94 tff(4641,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(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(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(4642,plain,
% 1.74/1.94 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(4643,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1))))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[4642])).
% 1.74/1.94 tff(4644,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[4643, 4641])).
% 1.74/1.94 tff(4645,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(4646,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(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(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[4645, 4644])).
% 1.74/1.94 tff(4647,plain,
% 1.74/1.94 (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4646, 246, 2362, 4594, 4632, 961])).
% 1.74/1.94 tff(4648,plain,
% 1.74/1.94 ((s(s(s(s(s(s(s(elem!1))))))) = s(s(elem!1))) | r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[592, 47, 4647])).
% 1.74/1.94 tff(4649,plain,
% 1.74/1.94 (r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4648, 581])).
% 1.74/1.94 tff(4650,plain,
% 1.74/1.94 (b(z, s(s(s(z))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[4593, 2191])).
% 1.74/1.94 tff(4651,assumption,(b(z, s(s(s(z))))), introduced(assumption)).
% 1.74/1.94 tff(4652,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), z)))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(4653,plain,
% 1.74/1.94 (((~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), z)))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(4654,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), z))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[4653])).
% 1.74/1.94 tff(4655,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), z)))),
% 1.74/1.94 inference(transitivity,[status(thm)],[4654, 4652])).
% 1.74/1.94 tff(4656,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(4657,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), z))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[4656, 4655])).
% 1.74/1.94 tff(4658,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4657, 246, 1100, 4327, 4651, 2090])).
% 1.74/1.94 tff(4659,plain,((~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(4660,plain,
% 1.74/1.94 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4659, 4650, 1100, 2090])).
% 1.74/1.94 tff(4661,plain,
% 1.74/1.94 (r(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[689, 4660, 416])).
% 1.74/1.94 tff(4662,plain,
% 1.74/1.94 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[4661, 1309])).
% 1.74/1.94 tff(4663,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[659, 183, 4662, 4649, 4640])).
% 1.74/1.94 tff(4664,plain,((~r(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~(z = elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~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(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(4665,plain,
% 1.74/1.94 (~r(elem!1, s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4664, 4580, 3726, 61, 4473, 2866, 4039, 2090, 961])).
% 1.74/1.94 tff(4666,plain,
% 1.74/1.94 (b(elem!1, s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2864, 4665, 4472])).
% 1.74/1.94 tff(4667,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(4668,plain,
% 1.74/1.94 (((~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(4669,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[4668])).
% 1.74/1.94 tff(4670,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[4669, 4667])).
% 1.74/1.94 tff(4671,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(4672,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[4671, 4670])).
% 1.74/1.94 tff(4673,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4672, 246, 2362, 363, 2866, 1574, 4039])).
% 1.74/1.94 tff(4674,plain,((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(4675,plain,
% 1.74/1.94 (~b(s(s(elem!1)), s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4674, 4666, 2866, 3726, 4039])).
% 1.74/1.94 tff(4676,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4675, 4468])).
% 1.74/1.94 tff(4677,plain,((~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), elem!1)) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(z, elem!1) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(4678,plain,
% 1.74/1.94 (~r(s(s(s(z))), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4677, 3644, 4463, 2090, 961, 4458, 56, 55])).
% 1.74/1.94 tff(4679,plain,
% 1.74/1.94 (b(s(s(s(z))), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[52, 4678])).
% 1.74/1.94 tff(4680,plain,
% 1.74/1.94 (b(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[3661, 4679, 61])).
% 1.74/1.94 tff(4681,plain,
% 1.74/1.94 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4050, 4680, 367, 3602, 333])).
% 1.74/1.94 tff(4682,plain,
% 1.74/1.94 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[3693, 4681, 3616])).
% 1.74/1.94 tff(4683,plain,
% 1.74/1.94 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[2171])).
% 1.74/1.94 tff(4684,plain,
% 1.74/1.94 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.94 inference(symmetry,[status(thm)],[4683])).
% 1.74/1.94 tff(4685,plain,
% 1.74/1.94 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[2171])).
% 1.74/1.94 tff(4686,plain,
% 1.74/1.94 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.74/1.94 inference(symmetry,[status(thm)],[4685])).
% 1.74/1.94 tff(4687,plain,
% 1.74/1.94 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[4686])).
% 1.74/1.94 tff(4688,plain,
% 1.74/1.94 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[4687, 4684])).
% 1.74/1.94 tff(4689,plain,
% 1.74/1.94 ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[4688])).
% 1.74/1.94 tff(4690,plain,
% 1.74/1.94 (~r(elem!1, s(s(s(elem!1))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4270, 4682, 333])).
% 1.74/1.94 tff(4691,plain,
% 1.74/1.94 (~r(elem!1, s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4414, 4690, 61])).
% 1.74/1.94 tff(4692,plain,
% 1.74/1.94 (b(elem!1, s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[470, 4691, 2176])).
% 1.74/1.94 tff(4693,plain,
% 1.74/1.94 (b(elem!1, s(s(s(elem!1))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4114, 4692, 61])).
% 1.74/1.94 tff(4694,plain,
% 1.74/1.94 (b(s(elem!1), s(s(s(z)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[2171])).
% 1.74/1.94 tff(4695,plain,
% 1.74/1.94 (b(s(z), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[141])).
% 1.74/1.94 tff(4696,plain,
% 1.74/1.94 (b(s(z), s(s(s(z)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[4695, 4694])).
% 1.74/1.94 tff(4697,plain,
% 1.74/1.94 (r(s(z), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[141])).
% 1.74/1.94 tff(4698,plain,
% 1.74/1.94 (r(s(elem!1), s(s(s(z)))) <=> r(s(z), s(s(s(z))))),
% 1.74/1.94 inference(symmetry,[status(thm)],[4697])).
% 1.74/1.94 tff(4699,plain,
% 1.74/1.94 ((~r(s(elem!1), s(s(s(z))))) <=> (~r(s(z), s(s(s(z)))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[4698])).
% 1.74/1.94 tff(4700,plain,
% 1.74/1.94 (r(s(s(elem!1)), s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[2171])).
% 1.74/1.94 tff(4701,plain,
% 1.74/1.94 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 1.74/1.94 inference(symmetry,[status(thm)],[4700])).
% 1.74/1.94 tff(4702,plain,
% 1.74/1.94 (r(s(s(elem!1)), s(s(s(z))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[4456, 4701])).
% 1.74/1.94 tff(4703,plain,
% 1.74/1.94 (s(elem!1) = s(z)),
% 1.74/1.94 inference(symmetry,[status(thm)],[141])).
% 1.74/1.94 tff(4704,plain,
% 1.74/1.94 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(elem!1)) = s(z))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[4703])).
% 1.74/1.94 tff(4705,plain,
% 1.74/1.94 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = s(elem!1))),
% 1.74/1.94 inference(symmetry,[status(thm)],[4704])).
% 1.74/1.94 tff(4706,plain,
% 1.74/1.94 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[4705])).
% 1.74/1.94 tff(4707,plain,
% 1.74/1.94 (~(s(s(elem!1)) = s(elem!1))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[113, 4706])).
% 1.74/1.94 tff(4708,plain,
% 1.74/1.94 (b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4488, 4682, 4474, 3644, 3643])).
% 1.74/1.94 tff(4709,plain,
% 1.74/1.94 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4498, 183, 4682, 4456])).
% 1.74/1.94 tff(4710,plain,
% 1.74/1.94 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1557, 4709, 2169])).
% 1.74/1.94 tff(4711,plain,
% 1.74/1.94 (~b(s(s(elem!1)), s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4564, 4710, 4463, 4708, 4458])).
% 1.74/1.94 tff(4712,plain,
% 1.74/1.94 (r(s(s(elem!1)), s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1949, 47, 4711, 4707])).
% 1.74/1.94 tff(4713,plain,
% 1.74/1.94 (~r(s(elem!1), s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[3894, 4712, 4702])).
% 1.74/1.94 tff(4714,plain,
% 1.74/1.94 (~r(s(z), s(s(s(z))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[4713, 4699])).
% 1.74/1.94 tff(4715,plain,
% 1.74/1.94 (b(s(z), s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1291, 4714])).
% 1.74/1.94 tff(4716,plain,
% 1.74/1.94 (b(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[4715, 4696])).
% 1.74/1.94 tff(4717,assumption,(b(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 1.74/1.94 tff(4718,plain,
% 1.74/1.94 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2902, 246, 2751, 1937, 4717])).
% 1.74/1.94 tff(4719,plain,
% 1.74/1.94 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2907, 47, 3915, 4718])).
% 1.74/1.94 tff(4720,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(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(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, 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(s(s(s(elem!1)))), elem!1)))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(4721,plain,
% 1.74/1.94 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~b(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(s(s(s(elem!1)))), elem!1)))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(4722,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(s(s(elem!1)))), elem!1))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[4721])).
% 1.74/1.94 tff(4723,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(s(s(s(elem!1)))), elem!1)))),
% 1.74/1.94 inference(transitivity,[status(thm)],[4722, 4720])).
% 1.74/1.94 tff(4724,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(4725,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(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(s(s(s(elem!1)))), elem!1))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[4724, 4723])).
% 1.74/1.94 tff(4726,plain,
% 1.74/1.94 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4725, 246, 2751, 960, 1937, 4717])).
% 1.74/1.94 tff(4727,plain,
% 1.74/1.94 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1571, 47, 3852, 4726])).
% 1.74/1.94 tff(4728,plain,
% 1.74/1.94 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1985, 246, 2751, 1937, 4717])).
% 1.74/1.94 tff(4729,plain,
% 1.74/1.94 (~b(s(s(s(s(z)))), s(elem!1))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[4728, 1716])).
% 1.74/1.94 tff(4730,plain,
% 1.74/1.94 (r(s(s(s(s(z)))), s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1728, 4729, 1714])).
% 1.74/1.94 tff(4731,plain,
% 1.74/1.94 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[4730, 1706])).
% 1.74/1.94 tff(4732,plain,
% 1.74/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(4733,plain,
% 1.74/1.94 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(4734,plain,
% 1.74/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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))) | (~r(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[4733])).
% 1.74/1.94 tff(4735,plain,
% 1.74/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[4734, 4732])).
% 1.74/1.95 tff(4736,plain,
% 1.74/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(4737,plain,
% 1.74/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1))))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[4736, 4735])).
% 1.74/1.95 tff(4738,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[4737, 183, 367, 4731, 4727, 4719])).
% 1.74/1.95 tff(4739,plain,((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~(z = elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(4740,plain,
% 1.74/1.95 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[4739, 4716, 61, 367, 4680, 4693])).
% 1.74/1.95 tff(4741,plain,
% 1.74/1.95 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[4740, 4689])).
% 1.74/1.95 tff(4742,plain,
% 1.74/1.95 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1702, 4741])).
% 1.74/1.95 tff(4743,assumption,(~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 1.74/1.95 tff(4744,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[4743, 2773])).
% 1.74/1.95 tff(4745,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(4746,plain,
% 1.74/1.95 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[4745, 4742, 61])).
% 1.74/1.95 tff(4747,plain,
% 1.74/1.95 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[3866, 4746, 61, 3644])).
% 1.74/1.95 tff(4748,plain,
% 1.74/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(4749,plain,
% 1.74/1.95 (((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(4750,plain,
% 1.74/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[4749])).
% 1.74/1.95 tff(4751,plain,
% 1.74/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[4750, 4748])).
% 1.74/1.95 tff(4752,plain,
% 1.74/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(4753,plain,
% 1.74/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[4752, 4751])).
% 1.74/1.95 tff(4754,plain,
% 1.74/1.95 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[4753, 183, 3412, 3853])).
% 1.74/1.95 tff(4755,plain,
% 1.74/1.95 (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[4754, 1473])).
% 1.74/1.95 tff(4756,plain,
% 1.74/1.95 (b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1506, 4755])).
% 1.74/1.95 tff(4757,plain,
% 1.74/1.95 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[4756, 1471])).
% 1.74/1.95 tff(4758,plain,
% 1.74/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(4759,plain,
% 1.74/1.95 (((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(4760,plain,
% 1.74/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[4759])).
% 1.74/1.95 tff(4761,plain,
% 1.74/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[4760, 4758])).
% 1.74/1.95 tff(4762,plain,
% 1.74/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(4763,plain,
% 1.74/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[4762, 4761])).
% 1.74/1.95 tff(4764,plain,
% 1.74/1.95 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[4763, 183, 3833, 3853])).
% 1.74/1.95 tff(4765,plain,
% 1.74/1.95 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[4764, 1512])).
% 1.74/1.95 tff(4766,plain,
% 1.74/1.95 (b(s(s(z)), s(s(s(s(z)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1531, 4765])).
% 1.74/1.95 tff(4767,plain,
% 1.74/1.95 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[4766, 1510])).
% 1.74/1.95 tff(4768,assumption,(b(s(s(s(s(elem!1)))), s(s(elem!1)))), introduced(assumption)).
% 1.74/1.95 tff(4769,plain,
% 1.74/1.95 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[4498, 183, 3412, 3833])).
% 1.74/1.95 tff(4770,plain,
% 1.74/1.95 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1557, 4769, 358])).
% 1.74/1.95 tff(4771,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(4772,plain,
% 1.74/1.95 (((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(4773,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[4772])).
% 1.74/1.95 tff(4774,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[4773, 4771])).
% 1.74/1.95 tff(4775,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(4776,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[4775, 4774])).
% 1.74/1.95 tff(4777,plain,
% 1.74/1.95 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[4776, 246, 4770, 4768, 4767])).
% 1.74/1.95 tff(4778,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[4777, 4757])).
% 1.74/1.95 tff(4779,plain,((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~(z = elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(4780,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[4779, 4747, 4746, 4682, 4456, 61])).
% 1.74/1.95 tff(4781,plain,(b(s(s(elem!1)), s(s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), elem!1)) | r(z, elem!1) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(4782,plain,
% 1.74/1.95 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[4781, 4451, 87, 4447, 4444, 56, 55])).
% 1.74/1.95 tff(4783,plain,
% 1.74/1.95 (~r(s(elem!1), s(s(s(s(s(elem!1))))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[4461, 4451, 87])).
% 1.74/1.95 tff(4784,plain,
% 1.74/1.95 (b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[395, 47, 4783, 4459])).
% 1.74/1.95 tff(4785,plain,
% 1.74/1.95 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[3986, 87, 61, 3726])).
% 1.74/1.95 tff(4786,plain,
% 1.74/1.95 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1795, 4785, 3602])).
% 1.74/1.95 tff(4787,plain,
% 1.74/1.95 (r(z, s(s(s(s(s(elem!1)))))) <=> r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.74/1.95 inference(symmetry,[status(thm)],[4339])).
% 1.74/1.95 tff(4788,plain,
% 1.74/1.95 ((~r(z, s(s(s(s(s(elem!1))))))) <=> (~r(elem!1, s(s(s(s(s(elem!1)))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[4787])).
% 1.74/1.95 tff(4789,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(4790,plain,
% 1.74/1.95 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(4791,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[4790])).
% 1.74/1.95 tff(4792,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[4791, 4789])).
% 1.74/1.95 tff(4793,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(4794,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[4793, 4792])).
% 1.74/1.95 tff(4795,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[4794, 246, 2362, 947, 961, 1657])).
% 1.74/1.95 tff(4796,plain,((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(4797,plain,
% 1.74/1.95 (~b(elem!1, s(s(elem!1)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[4796, 961, 2362, 1657])).
% 1.74/1.95 tff(4798,plain,
% 1.74/1.95 (r(elem!1, s(s(elem!1)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1268, 4797, 3739])).
% 1.74/1.95 tff(4799,plain,
% 1.74/1.95 (r(z, s(s(elem!1)))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[4798, 4166])).
% 1.74/1.95 tff(4800,plain,
% 1.74/1.95 (~r(elem!1, s(elem!1))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[4664, 1658, 2362, 88, 4229, 2866, 4039, 2090, 961])).
% 1.74/1.95 tff(4801,plain,
% 1.74/1.95 (b(elem!1, s(elem!1))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2864, 4800, 2829])).
% 1.74/1.95 tff(4802,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(4803,plain,
% 1.74/1.95 (((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(4804,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[4803])).
% 1.74/1.95 tff(4805,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[4804, 4802])).
% 1.74/1.95 tff(4806,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(4807,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[4806, 4805])).
% 1.74/1.95 tff(4808,plain,
% 1.74/1.95 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[4807, 246, 961, 2866, 4801, 1658, 1657])).
% 1.74/1.95 tff(4809,plain,
% 1.74/1.95 (r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1547, 47, 4808, 3816])).
% 1.74/1.95 tff(4810,plain,
% 1.74/1.95 (~r(z, s(s(s(s(s(elem!1))))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[3314, 4809, 4799])).
% 1.74/1.95 tff(4811,plain,
% 1.74/1.95 (~r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[4810, 4788])).
% 1.74/1.95 tff(4812,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(4813,plain,
% 1.74/1.95 (((~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(elem!1), s(s(s(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(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(4814,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(elem!1)))))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[4813])).
% 1.74/1.95 tff(4815,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[4814, 4812])).
% 1.74/1.96 tff(4816,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(4817,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(elem!1)))))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[4816, 4815])).
% 1.74/1.96 tff(4818,plain,
% 1.74/1.96 (~b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4817, 246, 2866, 4801, 4039])).
% 1.74/1.96 tff(4819,plain,
% 1.74/1.96 ((elem!1 = s(s(s(s(s(elem!1)))))) | r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[3407, 47, 4818])).
% 1.74/1.96 tff(4820,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4819, 4811, 4340])).
% 1.74/1.96 tff(4821,plain,((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~(z = elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(4822,plain,
% 1.74/1.96 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4821, 4444, 61, 4786, 4782, 4784, 3726, 4447])).
% 1.74/1.96 tff(4823,plain,
% 1.74/1.96 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[3693, 4822, 3616])).
% 1.74/1.96 tff(4824,plain,
% 1.74/1.96 (~r(elem!1, s(s(s(elem!1))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4270, 4823, 87])).
% 1.74/1.96 tff(4825,plain,
% 1.74/1.96 (~r(elem!1, s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4414, 4824, 61])).
% 1.74/1.96 tff(4826,plain,
% 1.74/1.96 (b(elem!1, s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[470, 4825, 2176])).
% 1.74/1.96 tff(4827,plain,
% 1.74/1.96 (b(elem!1, s(s(s(elem!1))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4114, 4826, 61])).
% 1.74/1.96 tff(4828,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(4829,plain,
% 1.74/1.96 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(4830,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[4829])).
% 1.74/1.96 tff(4831,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[4830, 4828])).
% 1.74/1.96 tff(4832,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(4833,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[4832, 4831])).
% 1.74/1.96 tff(4834,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4833, 246, 3726, 4827, 4444, 4782])).
% 1.74/1.96 tff(4835,plain,(b(s(s(s(s(s(elem!1))))), elem!1) | r(z, elem!1) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(4836,plain,
% 1.74/1.96 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4835, 56, 55])).
% 1.74/1.96 tff(4837,assumption,(r(elem!1, s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.74/1.96 tff(4838,plain,
% 1.74/1.96 (~(elem!1 = s(s(s(s(s(elem!1))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[71, 568])).
% 1.74/1.96 tff(4839,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(4840,plain,
% 1.74/1.96 (((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(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(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(4841,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(elem!1)))))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[4840])).
% 1.74/1.96 tff(4842,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[4841, 4839])).
% 1.74/1.96 tff(4843,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(4844,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(elem!1)))))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[4843, 4842])).
% 1.74/1.96 tff(4845,plain,
% 1.74/1.96 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4844, 246, 714, 961, 3422])).
% 1.74/1.96 tff(4846,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(4847,plain,
% 1.74/1.96 (((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(4848,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1)))))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[4847])).
% 1.74/1.96 tff(4849,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[4848, 4846])).
% 1.74/1.96 tff(4850,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(4851,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1)))))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[4850, 4849])).
% 1.74/1.96 tff(4852,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4851, 246, 2362, 714, 4520, 3422])).
% 1.74/1.96 tff(4853,plain,((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(4854,plain,
% 1.74/1.96 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4853, 3422, 714, 2362])).
% 1.74/1.96 tff(4855,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(4856,plain,
% 1.74/1.96 (((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(4857,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1)))))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[4856])).
% 1.74/1.96 tff(4858,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[4857, 4855])).
% 1.74/1.96 tff(4859,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(4860,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1)))))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[4859, 4858])).
% 1.74/1.96 tff(4861,plain,
% 1.74/1.96 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4860, 246, 2362, 714, 961, 3422])).
% 1.74/1.96 tff(4862,plain,
% 1.74/1.96 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4488, 4861, 4476, 4854, 4452])).
% 1.74/1.96 tff(4863,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[3693, 4862, 4845, 775])).
% 1.74/1.96 tff(4864,plain,((~b(elem!1, s(s(s(s(s(elem!1))))))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(4865,plain,
% 1.74/1.96 (~b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4864, 961, 3816, 1817, 714, 771, 2362])).
% 1.74/1.96 tff(4866,plain,
% 1.74/1.96 (r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[3407, 47, 4865, 4838])).
% 1.74/1.96 tff(4867,plain,
% 1.74/1.96 (r(z, s(s(s(s(s(elem!1))))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[4866, 4339])).
% 1.74/1.96 tff(4868,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[3403, 183, 3412, 3427, 4837])).
% 1.74/1.96 tff(4869,plain,((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(4870,plain,
% 1.74/1.96 (~r(elem!1, s(s(s(elem!1))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4869, 3412, 4866])).
% 1.74/1.96 tff(4871,plain,
% 1.74/1.96 (~r(elem!1, s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4414, 4870, 88])).
% 1.74/1.96 tff(4872,plain,
% 1.74/1.96 (b(elem!1, s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[470, 4871, 718])).
% 1.74/1.96 tff(4873,plain,
% 1.74/1.96 (b(elem!1, s(s(s(elem!1))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4114, 4872, 88])).
% 1.74/1.96 tff(4874,plain,
% 1.74/1.96 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4537, 4873, 2362, 714, 961])).
% 1.74/1.96 tff(4875,plain,
% 1.74/1.96 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1557, 4874, 358])).
% 1.74/1.96 tff(4876,plain,
% 1.74/1.96 (~r(z, s(s(elem!1)))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[3325, 4875, 4867])).
% 1.74/1.96 tff(4877,plain,
% 1.74/1.96 (r(z, s(s(elem!1)))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[602, 4166])).
% 1.74/1.96 tff(4878,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[258, 4877])).
% 1.74/1.96 tff(4879,plain,((~r(elem!1, s(s(elem!1)))) | r(z, s(s(elem!1))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(4880,plain,
% 1.74/1.96 (~r(elem!1, s(s(elem!1)))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4879, 4876, 88])).
% 1.74/1.96 tff(4881,plain,
% 1.74/1.96 (b(elem!1, s(s(elem!1)))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1268, 4880, 3739])).
% 1.74/1.96 tff(4882,plain,
% 1.74/1.96 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4796, 4881, 2362, 961])).
% 1.74/1.96 tff(4883,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(4884,plain,
% 1.74/1.96 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(4885,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[4884])).
% 1.74/1.96 tff(4886,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.74/1.96 inference(transitivity,[status(thm)],[4885, 4883])).
% 1.74/1.96 tff(4887,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(4888,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[4887, 4886])).
% 1.74/1.96 tff(4889,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4888, 246, 2362, 947, 714, 4520])).
% 1.74/1.96 tff(4890,plain,((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(4891,plain,
% 1.74/1.96 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4890, 4881, 714, 2362])).
% 1.74/1.96 tff(4892,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4488, 4891, 4882, 3816, 3412, 1817])).
% 1.74/1.96 tff(4893,plain,((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(4894,plain,
% 1.74/1.96 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4893, 961, 2362, 714, 88])).
% 1.74/1.96 tff(4895,plain,
% 1.74/1.96 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[3693, 4894, 771])).
% 1.74/1.96 tff(4896,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(4897,plain,
% 1.74/1.97 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(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))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(4898,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[4897])).
% 1.74/1.97 tff(4899,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[4898, 4896])).
% 1.74/1.97 tff(4900,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(4901,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[4900, 4899])).
% 1.74/1.97 tff(4902,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[4901, 246, 2362, 947, 714, 961, 1658])).
% 1.74/1.97 tff(4903,plain,((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(4904,plain,
% 1.74/1.97 (~b(elem!1, s(s(elem!1)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[4903, 961, 714, 2362, 4895])).
% 1.74/1.97 tff(4905,plain,
% 1.74/1.97 (r(elem!1, s(s(elem!1)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1268, 4904, 3739])).
% 1.74/1.97 tff(4906,plain,
% 1.74/1.97 (r(z, s(s(elem!1)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[4879, 4905, 88])).
% 1.74/1.97 tff(4907,plain,
% 1.74/1.97 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[3325, 4906, 4867])).
% 1.74/1.97 tff(4908,plain,
% 1.74/1.97 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1557, 4907, 358])).
% 1.74/1.97 tff(4909,plain,
% 1.74/1.97 (~b(elem!1, s(s(s(elem!1))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[4537, 4908, 2362, 714, 961])).
% 1.74/1.97 tff(4910,plain,
% 1.74/1.97 (~b(elem!1, s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[4114, 4909, 88])).
% 1.74/1.97 tff(4911,plain,
% 1.74/1.97 (r(elem!1, s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[470, 4910, 718])).
% 1.74/1.97 tff(4912,plain,
% 1.74/1.97 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2816, 4911, 358, 2362, 88, 714])).
% 1.74/1.97 tff(4913,plain,
% 1.74/1.97 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1702, 4912])).
% 1.74/1.97 tff(4914,plain,
% 1.74/1.97 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[4913, 1832])).
% 1.74/1.97 tff(4915,plain,
% 1.74/1.97 (r(elem!1, s(s(s(elem!1))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[4414, 4911, 88])).
% 1.74/1.97 tff(4916,assumption,(~b(elem!1, s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.74/1.97 tff(4917,plain,
% 1.74/1.97 (r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[3407, 47, 4916, 4838])).
% 1.74/1.97 tff(4918,plain,
% 1.74/1.97 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[4869, 4917, 3427])).
% 1.74/1.97 tff(4919,plain,
% 1.74/1.97 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[3693, 4918, 771])).
% 1.74/1.97 tff(4920,plain,
% 1.74/1.97 (r(z, s(s(s(s(s(elem!1))))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[4917, 4339])).
% 1.74/1.97 tff(4921,plain,
% 1.74/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(4922,plain,
% 1.74/1.97 (((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(elem!1)))))))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(4923,plain,
% 1.74/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(elem!1)))))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[4922])).
% 1.74/1.97 tff(4924,plain,
% 1.74/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[4923, 4921])).
% 1.74/1.97 tff(4925,plain,
% 1.74/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(4926,plain,
% 1.74/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(elem!1)))))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[4925, 4924])).
% 1.74/1.97 tff(4927,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[4926, 183, 1853, 601, 4837])).
% 1.74/1.97 tff(4928,plain,((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(4929,plain,
% 1.74/1.97 (~r(elem!1, s(elem!1))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[4928, 4917, 1853])).
% 1.74/1.97 tff(4930,plain,
% 1.74/1.97 (b(elem!1, s(elem!1))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2864, 4929, 2829])).
% 1.74/1.97 tff(4931,plain,
% 1.74/1.97 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[3693, 1863, 771])).
% 1.74/1.97 tff(4932,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(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))))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(4933,plain,
% 1.74/1.97 (((~b(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(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(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(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))))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(4934,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(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)))))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[4933])).
% 1.74/1.97 tff(4935,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(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))))))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[4934, 4932])).
% 1.74/1.97 tff(4936,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(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(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))))))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(4937,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[4936, 4935])).
% 1.74/1.97 tff(4938,plain,
% 1.74/1.97 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[4937, 246, 4931, 4717, 1881])).
% 1.74/1.97 tff(4939,plain,
% 1.74/1.97 (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[4938, 3786])).
% 1.74/1.97 tff(4940,plain,
% 1.74/1.97 (r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1506, 4939])).
% 1.74/1.97 tff(4941,plain,
% 1.74/1.97 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[4940, 3785])).
% 1.74/1.97 tff(4942,plain,
% 1.74/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(4943,plain,
% 1.74/1.97 (((~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(elem!1))))))) <=> ((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(4944,plain,
% 1.74/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[4943])).
% 1.74/1.97 tff(4945,plain,
% 1.74/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[4944, 4942])).
% 1.74/1.97 tff(4946,plain,
% 1.74/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(4947,plain,
% 1.74/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[4946, 4945])).
% 1.74/1.97 tff(4948,plain,
% 1.74/1.97 ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[4947, 183, 4917])).
% 1.74/1.97 tff(4949,plain,
% 1.74/1.97 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[4948, 4941])).
% 1.74/1.97 tff(4950,plain,
% 1.74/1.97 ((elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1)))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2055, 47, 4949])).
% 1.74/1.97 tff(4951,plain,
% 1.74/1.97 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[4950, 2044])).
% 1.74/1.97 tff(4952,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), 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(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(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(elem!1, s(s(s(s(elem!1)))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(4953,plain,
% 1.74/1.97 (((~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(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(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(elem!1, s(s(s(s(elem!1)))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(4954,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[4953])).
% 1.74/1.97 tff(4955,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[4954, 4952])).
% 1.74/1.97 tff(4956,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~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))))))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(4957,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[4956, 4955])).
% 1.74/1.97 tff(4958,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[4957, 246, 714, 961, 4931, 4717, 1881, 4951])).
% 1.74/1.97 tff(4959,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~(z = elem!1)) | b(elem!1, s(s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(4960,plain,
% 1.74/1.97 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[4959, 4916, 961, 4717, 88, 714, 1853])).
% 1.74/1.97 tff(4961,plain,
% 1.74/1.97 (~r(s(s(s(z))), s(z))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[4960, 1852])).
% 1.74/1.97 tff(4962,plain,
% 1.74/1.97 (b(s(s(s(z))), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[52, 4961])).
% 1.74/1.97 tff(4963,plain,
% 1.74/1.97 (b(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[3661, 4962, 88])).
% 1.74/1.97 tff(4964,plain,
% 1.74/1.97 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.97 inference(symmetry,[status(thm)],[1797])).
% 1.74/1.97 tff(4965,plain,
% 1.74/1.97 ((~b(s(s(s(elem!1))), s(s(elem!1)))) <=> (~b(s(s(s(z))), s(s(elem!1))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[4964])).
% 1.74/1.97 tff(4966,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(4967,plain,
% 1.74/1.97 (((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(4968,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[4967])).
% 1.74/1.97 tff(4969,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[4968, 4966])).
% 1.74/1.97 tff(4970,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(4971,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[4970, 4969])).
% 1.74/1.98 tff(4972,plain,
% 1.74/1.98 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[4971, 246, 2362, 1937, 946, 1574, 1658])).
% 1.74/1.98 tff(4973,plain,
% 1.74/1.98 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[4972, 4965])).
% 1.74/1.98 tff(4974,plain,
% 1.74/1.98 (r(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[689, 4973, 416])).
% 1.74/1.98 tff(4975,plain,
% 1.74/1.98 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[4974, 1309])).
% 1.74/1.98 tff(4976,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(4977,plain,
% 1.74/1.98 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(4978,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[4977])).
% 1.74/1.98 tff(4979,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.74/1.98 inference(transitivity,[status(thm)],[4978, 4976])).
% 1.74/1.98 tff(4980,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(4981,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[4980, 4979])).
% 1.74/1.98 tff(4982,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[4981, 246, 2362, 947, 714, 946])).
% 1.74/1.98 tff(4983,plain,((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(4984,plain,
% 1.74/1.98 (~b(elem!1, s(s(elem!1)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[4983, 946, 2362, 714])).
% 1.74/1.98 tff(4985,plain,
% 1.74/1.98 (r(elem!1, s(s(elem!1)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1268, 4984, 3739])).
% 1.74/1.98 tff(4986,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[3100, 183, 4985, 4975, 3427])).
% 1.74/1.98 tff(4987,plain,((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~(z = elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(4988,plain,
% 1.74/1.98 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[4987, 4963, 88, 2362, 3427, 4930, 4919, 714])).
% 1.74/1.98 tff(4989,plain,
% 1.74/1.98 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1557, 4988, 358])).
% 1.74/1.98 tff(4990,plain,
% 1.74/1.98 (~r(z, s(s(elem!1)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[3325, 4989, 4920])).
% 1.74/1.98 tff(4991,plain,
% 1.74/1.98 (~r(elem!1, s(s(elem!1)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[4879, 4990, 88])).
% 1.74/1.98 tff(4992,plain,
% 1.74/1.98 (b(elem!1, s(s(elem!1)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1268, 4991, 3739])).
% 1.74/1.98 tff(4993,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[4901, 246, 2362, 4992, 714, 961, 4919])).
% 1.74/1.98 tff(4994,plain,(b(elem!1, s(s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~(z = elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(4995,plain,
% 1.74/1.98 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[4994, 4915, 714, 961, 88, 2362, 1853, 4865])).
% 1.74/1.98 tff(4996,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[4995, 4914])).
% 1.74/1.98 tff(4997,plain,((~b(s(s(s(elem!1))), elem!1)) | (~(z = elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(4998,plain,
% 1.74/1.98 (~b(s(s(s(elem!1))), elem!1)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[4997, 1853, 714, 2362, 88])).
% 1.74/1.98 tff(4999,plain,
% 1.74/1.98 (~b(s(s(s(z))), elem!1)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[3701, 4998, 88])).
% 1.74/1.98 tff(5000,plain,
% 1.74/1.98 (r(s(s(s(z))), elem!1)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[647, 1, 554])).
% 1.74/1.98 tff(5001,plain,
% 1.74/1.98 (r(s(z), elem!1)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1034, 1445, 3678])).
% 1.74/1.98 tff(5002,plain,
% 1.74/1.98 (~r(s(s(s(z))), s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[3017, 5000, 5001])).
% 1.74/1.98 tff(5003,plain,
% 1.74/1.98 (b(s(s(s(z))), s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[52, 5002])).
% 1.74/1.98 tff(5004,plain,
% 1.74/1.98 (b(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[3661, 5003, 88])).
% 1.74/1.98 tff(5005,assumption,(s(elem!1) = s(s(s(elem!1)))), introduced(assumption)).
% 1.74/1.98 tff(5006,plain,
% 1.74/1.98 (s(elem!1) = s(s(s(z)))),
% 1.74/1.98 inference(transitivity,[status(thm)],[5005, 410])).
% 1.74/1.98 tff(5007,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1735, 5006])).
% 1.74/1.98 tff(5008,plain,((~(s(elem!1) = s(s(s(elem!1))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(5009,plain,
% 1.74/1.98 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5008, 88])).
% 1.74/1.98 tff(5010,plain,
% 1.74/1.98 (r(s(s(s(z))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 1.74/1.98 inference(transitivity,[status(thm)],[1777, 1775])).
% 1.74/1.98 tff(5011,plain,
% 1.74/1.98 (r(s(s(s(elem!1))), elem!1)),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[5000, 5010])).
% 1.74/1.98 tff(5012,plain,
% 1.74/1.98 (r(s(elem!1), elem!1)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[4450, 5001, 88])).
% 1.74/1.98 tff(5013,plain,
% 1.74/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(5014,plain,
% 1.74/1.98 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(5015,plain,
% 1.74/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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)))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5014])).
% 1.74/1.98 tff(5016,plain,
% 1.74/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[5015, 5013])).
% 1.74/1.98 tff(5017,plain,
% 1.74/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(5018,plain,
% 1.74/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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)))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[5017, 5016])).
% 1.74/1.98 tff(5019,plain,
% 1.74/1.98 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5018, 183, 5012, 5011])).
% 1.74/1.98 tff(5020,plain,
% 1.74/1.98 (((~![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)))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(5021,plain,
% 1.74/1.98 ((~![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)))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(5022,plain,
% 1.74/1.98 ((~![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))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[5021, 5020])).
% 1.74/1.98 tff(5023,plain,
% 1.74/1.98 (b(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5022, 47, 5019, 5009])).
% 1.74/1.98 tff(5024,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(5025,plain,
% 1.74/1.98 (((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(5026,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1)))))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5025])).
% 1.74/1.98 tff(5027,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[5026, 5024])).
% 1.74/1.98 tff(5028,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(5029,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1)))))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[5028, 5027])).
% 1.74/1.98 tff(5030,plain,
% 1.74/1.98 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5029, 246, 2362, 714, 3422])).
% 1.74/1.98 tff(5031,plain,
% 1.74/1.98 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1557, 5030, 358])).
% 1.74/1.98 tff(5032,plain,
% 1.74/1.98 (~r(s(s(elem!1)), s(elem!1))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1959, 5031, 1853])).
% 1.74/1.98 tff(5033,plain,
% 1.74/1.98 (~r(s(s(elem!1)), s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[3806, 5032, 88])).
% 1.74/1.98 tff(5034,plain,
% 1.74/1.98 (b(s(s(elem!1)), s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[197, 5033])).
% 1.74/1.98 tff(5035,assumption,(~b(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 1.74/1.98 tff(5036,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5035, 4182])).
% 1.74/1.98 tff(5037,plain,((~b(s(s(elem!1)), s(z))) | b(s(s(elem!1)), s(elem!1)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(5038,plain,
% 1.74/1.98 (b(s(s(elem!1)), s(elem!1))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5037, 5034, 88])).
% 1.74/1.98 tff(5039,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(5040,plain,
% 1.74/1.98 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(5041,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1)))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5040])).
% 1.74/1.98 tff(5042,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[5041, 5039])).
% 1.74/1.98 tff(5043,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(5044,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[5043, 5042])).
% 1.74/1.98 tff(5045,plain,
% 1.74/1.98 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5044, 246, 5038, 2751, 1937])).
% 1.74/1.98 tff(5046,plain,
% 1.74/1.98 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[4488, 5045, 3816, 4854, 1817])).
% 1.74/1.98 tff(5047,plain,
% 1.74/1.98 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[3693, 5046, 771])).
% 1.74/1.98 tff(5048,plain,
% 1.74/1.98 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[4455, 5045, 1817])).
% 1.74/1.98 tff(5049,plain,
% 1.74/1.98 (b(elem!1, s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[214, 2265, 3729])).
% 1.74/1.98 tff(5050,plain,
% 1.74/1.98 (b(s(z), elem!1)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1034, 3018, 3678])).
% 1.74/1.98 tff(5051,plain,
% 1.74/1.98 (~b(s(s(elem!1)), s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[3799, 5050, 2362, 5049])).
% 1.74/1.98 tff(5052,plain,
% 1.74/1.98 (r(s(s(elem!1)), s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[197, 5051])).
% 1.74/1.98 tff(5053,plain,
% 1.74/1.98 (r(s(s(elem!1)), s(elem!1))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[3806, 5052, 88])).
% 1.74/1.98 tff(5054,plain,
% 1.74/1.98 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[3841, 5053, 3833])).
% 1.74/1.98 tff(5055,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5054, 4139])).
% 1.74/1.98 tff(5056,plain,((~r(s(s(s(z))), s(z))) | (~(z = elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(5057,plain,
% 1.74/1.98 (~r(s(s(s(z))), s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5056, 634, 3833, 2362, 88])).
% 1.74/1.98 tff(5058,plain,
% 1.74/1.98 (b(s(s(s(z))), s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[52, 5057])).
% 1.74/1.98 tff(5059,plain,
% 1.74/1.98 (r(elem!1, s(s(s(elem!1))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[4414, 413, 88])).
% 1.74/1.98 tff(5060,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[462, 183, 216, 3833, 3427])).
% 1.74/1.98 tff(5061,plain,((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(5062,plain,
% 1.74/1.98 (~r(s(s(elem!1)), elem!1)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5061, 5059, 3833])).
% 1.74/1.98 tff(5063,plain,
% 1.74/1.98 (~r(s(z), elem!1)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2917, 5062, 88, 358, 568, 634, 4033, 5058])).
% 1.74/1.98 tff(5064,plain,
% 1.74/1.98 (b(s(z), elem!1)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1034, 5063, 3678])).
% 1.74/1.98 tff(5065,plain,
% 1.74/1.98 (b(s(elem!1), elem!1)),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[5064, 1452])).
% 1.74/1.98 tff(5066,plain,
% 1.74/1.98 (b(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[3661, 5058, 88])).
% 1.74/1.98 tff(5067,plain,
% 1.74/1.98 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[4436, 5065, 5059, 1658, 5066, 88])).
% 1.74/1.98 tff(5068,plain,
% 1.74/1.98 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1795, 5067, 1787])).
% 1.74/1.98 tff(5069,plain,
% 1.74/1.98 (~r(elem!1, s(s(elem!1)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[3651, 183, 3833, 5059])).
% 1.74/1.98 tff(5070,plain,
% 1.74/1.98 (b(elem!1, s(s(elem!1)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1268, 5069, 3739])).
% 1.74/1.98 tff(5071,plain,
% 1.74/1.98 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[4983, 5070, 2362, 714])).
% 1.74/1.98 tff(5072,plain,
% 1.74/1.98 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1557, 5071, 358])).
% 1.74/1.98 tff(5073,plain,
% 1.74/1.98 (~r(s(s(elem!1)), s(elem!1))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1959, 5072, 5068])).
% 1.74/1.98 tff(5074,plain,
% 1.74/1.98 (~r(s(s(elem!1)), s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[3806, 5073, 88])).
% 1.74/1.98 tff(5075,plain,
% 1.74/1.98 (b(s(s(elem!1)), s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[197, 5074])).
% 1.74/1.98 tff(5076,plain,
% 1.74/1.98 (b(s(s(elem!1)), s(elem!1))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[5075, 3677])).
% 1.74/1.98 tff(5077,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[4060, 246, 2362, 5070, 5076, 5065])).
% 1.74/1.98 tff(5078,plain,((~r(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~(z = 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))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(5079,plain,
% 1.74/1.98 (~r(elem!1, s(s(s(z))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5078, 5047, 88, 714, 2362, 5048, 634])).
% 1.74/1.98 tff(5080,plain,
% 1.74/1.98 (b(elem!1, s(s(s(z))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[470, 5079, 718])).
% 1.74/1.98 tff(5081,plain,
% 1.74/1.98 (b(elem!1, s(s(s(elem!1))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[4114, 5080, 88])).
% 1.74/1.98 tff(5082,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(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))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(5083,plain,
% 1.74/1.98 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(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))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(5084,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(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)))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5083])).
% 1.74/1.98 tff(5085,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(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))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[5084, 5082])).
% 1.74/1.98 tff(5086,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(5087,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[5086, 5085])).
% 1.74/1.98 tff(5088,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5087, 246, 2751, 5081, 714, 1937, 5047])).
% 1.74/1.98 tff(5089,plain,((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~(z = elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(5090,plain,
% 1.74/1.98 (~b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5089, 5023, 714, 5004, 88, 2362, 5000, 1853])).
% 1.74/1.98 tff(5091,plain,
% 1.74/1.98 (r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[3407, 47, 5090, 4838])).
% 1.74/1.98 tff(5092,plain,
% 1.74/1.98 (b(z, s(s(s(z))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[3497, 2213, 56, 568, 358, 1445, 1, 1735])).
% 1.74/1.98 tff(5093,plain,
% 1.74/1.98 (b(elem!1, s(s(s(z))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[5092, 2190])).
% 1.74/1.98 tff(5094,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2213, 5093])).
% 1.74/1.98 tff(5095,plain,(b(elem!1, s(s(s(z)))) | (~(z = elem!1)) | r(z, elem!1) | b(s(z), elem!1) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(5096,plain,
% 1.74/1.99 (b(elem!1, s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5095, 1, 56, 1445, 88])).
% 1.74/1.99 tff(5097,plain,
% 1.74/1.99 (b(elem!1, s(s(s(elem!1))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[4114, 5096, 88])).
% 1.74/1.99 tff(5098,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, 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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(5099,plain,
% 1.74/1.99 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(5100,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, 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)))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5099])).
% 1.74/1.99 tff(5101,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, 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))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[5100, 5098])).
% 1.74/1.99 tff(5102,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(5103,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[5102, 5101])).
% 1.74/1.99 tff(5104,plain,
% 1.74/1.99 (~b(elem!1, s(elem!1))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5103, 246, 5023, 5097, 5004])).
% 1.74/1.99 tff(5105,plain,
% 1.74/1.99 (r(elem!1, s(elem!1))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2864, 5104, 2829])).
% 1.74/1.99 tff(5106,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[4926, 183, 1853, 5105, 5091])).
% 1.74/1.99 tff(5107,plain,(b(s(s(s(z))), elem!1) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~(z = elem!1)) | r(z, elem!1) | b(s(z), elem!1) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(5108,plain,
% 1.74/1.99 (b(s(z), elem!1)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5107, 4999, 88, 56, 1853, 714, 2362])).
% 1.74/1.99 tff(5109,plain,
% 1.74/1.99 (b(s(elem!1), elem!1)),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[5108, 1452])).
% 1.74/1.99 tff(5110,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(5111,plain,
% 1.74/1.99 (((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(5112,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1)))))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5111])).
% 1.74/1.99 tff(5113,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[5112, 5110])).
% 1.74/1.99 tff(5114,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(5115,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1)))))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[5114, 5113])).
% 1.74/1.99 tff(5116,plain,
% 1.74/1.99 (~b(s(s(elem!1)), s(elem!1))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5115, 246, 2362, 714, 1200, 3422])).
% 1.74/1.99 tff(5117,plain,
% 1.74/1.99 (~b(s(s(elem!1)), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5037, 5116, 88])).
% 1.74/1.99 tff(5118,plain,
% 1.74/1.99 (r(s(s(elem!1)), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[197, 5117])).
% 1.74/1.99 tff(5119,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[3806, 5118, 5032, 88])).
% 1.74/1.99 tff(5120,plain,((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~(z = elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(5121,plain,
% 1.74/1.99 (~b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5120, 1853, 88, 2362, 714, 5109])).
% 1.74/1.99 tff(5122,assumption,(~r(elem!1, s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.74/1.99 tff(5123,assumption,(~(elem!1 = s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.74/1.99 tff(5124,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[3407, 47, 4916, 5123, 5122])).
% 1.74/1.99 tff(5125,plain,(r(elem!1, s(s(s(s(s(elem!1)))))) | b(elem!1, s(s(s(s(s(elem!1)))))) | (elem!1 = s(s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(5126,plain,
% 1.74/1.99 (r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5125, 5121, 4838])).
% 1.74/1.99 tff(5127,plain,
% 1.74/1.99 (~r(elem!1, s(elem!1))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[4928, 5126, 1853])).
% 1.74/1.99 tff(5128,plain,
% 1.74/1.99 (b(elem!1, s(elem!1))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2864, 5127, 2829])).
% 1.74/1.99 tff(5129,plain,
% 1.74/1.99 (b(z, s(z))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[5128, 3974])).
% 1.74/1.99 tff(5130,plain,
% 1.74/1.99 (~r(elem!1, s(elem!1))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[4928, 4837, 1853])).
% 1.74/1.99 tff(5131,plain,
% 1.74/1.99 (b(elem!1, s(elem!1))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2864, 5130, 2829])).
% 1.74/1.99 tff(5132,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(5133,plain,
% 1.74/1.99 (((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~b(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))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(5134,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5133])).
% 1.74/1.99 tff(5135,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.74/1.99 inference(transitivity,[status(thm)],[5134, 5132])).
% 1.74/1.99 tff(5136,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(5137,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[5136, 5135])).
% 1.74/1.99 tff(5138,plain,
% 1.74/1.99 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5137, 246, 2362, 714, 1200, 5131])).
% 1.74/1.99 tff(5139,plain,
% 1.74/1.99 (r(z, s(s(s(s(s(elem!1))))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[4837, 4339])).
% 1.74/1.99 tff(5140,plain,
% 1.74/1.99 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[3325, 5139, 266])).
% 1.74/1.99 tff(5141,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[1557, 5140, 5138, 358])).
% 1.74/1.99 tff(5142,plain,((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~(z = elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(5143,plain,
% 1.74/1.99 (~r(z, s(s(elem!1)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5142, 5126, 2362, 714, 5109, 88, 1853])).
% 1.74/1.99 tff(5144,plain,
% 1.74/1.99 (b(z, s(s(elem!1)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[264, 5143])).
% 1.74/1.99 tff(5145,plain,
% 1.74/1.99 (b(s(z), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2120, 5108, 88])).
% 1.74/1.99 tff(5146,plain,
% 1.74/1.99 (~r(elem!1, s(s(elem!1)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[4879, 5143, 88])).
% 1.74/1.99 tff(5147,plain,
% 1.74/1.99 (b(elem!1, s(s(elem!1)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[1268, 5146, 3739])).
% 1.74/1.99 tff(5148,plain,
% 1.74/1.99 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[4983, 5147, 2362, 714])).
% 1.74/1.99 tff(5149,plain,
% 1.74/1.99 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[1557, 5148, 358])).
% 1.74/1.99 tff(5150,plain,
% 1.74/1.99 (~r(s(s(elem!1)), s(elem!1))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[1959, 5149, 1853])).
% 1.74/1.99 tff(5151,plain,
% 1.74/1.99 (~r(s(s(elem!1)), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[3806, 5150, 88])).
% 1.74/1.99 tff(5152,plain,
% 1.74/1.99 (b(s(s(elem!1)), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[197, 5151])).
% 1.74/1.99 tff(5153,plain,
% 1.74/1.99 (~b(z, s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[1154, 5152, 5145, 5144])).
% 1.74/1.99 tff(5154,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5153, 5129])).
% 1.74/1.99 tff(5155,plain,((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~(z = elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(5156,plain,
% 1.74/1.99 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5155, 88, 2362, 714, 56])).
% 1.74/1.99 tff(5157,plain,
% 1.74/1.99 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[1795, 5156, 1787])).
% 1.74/1.99 tff(5158,plain,
% 1.74/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(5159,plain,
% 1.74/1.99 (((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(elem!1)))))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(5160,plain,
% 1.74/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(elem!1)))))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5159])).
% 1.74/1.99 tff(5161,plain,
% 1.74/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[5160, 5158])).
% 1.74/1.99 tff(5162,plain,
% 1.74/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(5163,plain,
% 1.74/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(elem!1)))))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[5162, 5161])).
% 1.74/1.99 tff(5164,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5163, 183, 602, 959, 4837])).
% 1.74/1.99 tff(5165,plain,((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(5166,plain,
% 1.74/1.99 (~r(elem!1, s(s(elem!1)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5165, 959, 4837])).
% 1.74/1.99 tff(5167,plain,
% 1.74/1.99 (b(elem!1, s(s(elem!1)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[1268, 5166, 3739])).
% 1.74/1.99 tff(5168,plain,
% 1.74/1.99 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[4890, 5167, 714, 2362])).
% 1.74/1.99 tff(5169,plain,
% 1.74/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(5170,plain,
% 1.74/1.99 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(5171,plain,
% 1.74/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5170])).
% 1.74/1.99 tff(5172,plain,
% 1.74/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[5171, 5169])).
% 1.74/1.99 tff(5173,plain,
% 1.74/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(5174,plain,
% 1.74/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[5173, 5172])).
% 1.74/1.99 tff(5175,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5174, 183, 3076, 3412, 959])).
% 1.74/1.99 tff(5176,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(5177,plain,
% 1.74/1.99 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5176, 3412, 959])).
% 1.74/1.99 tff(5178,plain,
% 1.74/1.99 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[5177, 4213])).
% 1.74/1.99 tff(5179,plain,
% 1.74/1.99 (b(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[689, 5178, 416])).
% 1.74/1.99 tff(5180,plain,
% 1.74/1.99 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[5179, 1797])).
% 1.74/1.99 tff(5181,plain,
% 1.74/1.99 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[4488, 3412, 3816, 4477, 1817])).
% 1.74/1.99 tff(5182,plain,
% 1.74/1.99 (~r(elem!1, s(s(s(elem!1))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[4869, 3412, 4837])).
% 1.74/1.99 tff(5183,plain,
% 1.74/1.99 (~r(elem!1, s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[4414, 5182, 88])).
% 1.74/1.99 tff(5184,plain,
% 1.74/1.99 (b(elem!1, s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[470, 5183, 718])).
% 1.74/1.99 tff(5185,plain,
% 1.74/1.99 (b(elem!1, s(s(s(elem!1))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[4114, 5184, 88])).
% 1.74/1.99 tff(5186,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(5187,plain,
% 1.74/1.99 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(5188,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5187])).
% 1.74/1.99 tff(5189,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[5188, 5186])).
% 1.74/2.00 tff(5190,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(5191,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5190, 5189])).
% 1.74/2.00 tff(5192,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5191, 246, 2362, 5167, 5185, 5181, 5180])).
% 1.74/2.00 tff(5193,plain,((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~(z = elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(5194,plain,
% 1.74/2.00 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5193, 959, 88, 2362, 5168, 4837])).
% 1.74/2.00 tff(5195,plain,
% 1.74/2.00 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[3693, 5194, 771])).
% 1.74/2.00 tff(5196,plain,
% 1.74/2.00 (~b(s(s(s(elem!1))), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4903, 5195, 714, 2362, 5167])).
% 1.74/2.00 tff(5197,plain,
% 1.74/2.00 (~b(s(s(s(z))), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[3701, 5196, 88])).
% 1.74/2.00 tff(5198,plain,
% 1.74/2.00 (r(s(s(s(z))), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[647, 5197, 554])).
% 1.74/2.00 tff(5199,plain,
% 1.74/2.00 (b(s(elem!1), elem!1) <=> b(s(z), elem!1)),
% 1.74/2.00 inference(symmetry,[status(thm)],[1452])).
% 1.74/2.00 tff(5200,plain,
% 1.74/2.00 ((~b(s(elem!1), elem!1)) <=> (~b(s(z), elem!1))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5199])).
% 1.74/2.00 tff(5201,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(5202,plain,
% 1.74/2.00 (((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(5203,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5202])).
% 1.74/2.00 tff(5204,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[5203, 5201])).
% 1.74/2.00 tff(5205,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(5206,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5205, 5204])).
% 1.74/2.00 tff(5207,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5206, 246, 2362, 947, 714, 1200, 2866])).
% 1.74/2.00 tff(5208,plain,((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(5209,plain,
% 1.74/2.00 (~b(s(elem!1), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5208, 5167, 2362, 714, 2866])).
% 1.74/2.00 tff(5210,plain,
% 1.74/2.00 (~b(s(z), elem!1)),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5209, 5200])).
% 1.74/2.00 tff(5211,plain,
% 1.74/2.00 (r(s(z), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1034, 5210, 3678])).
% 1.74/2.00 tff(5212,plain,
% 1.74/2.00 (~r(s(s(s(z))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[3017, 5211, 5198])).
% 1.74/2.00 tff(5213,plain,
% 1.74/2.00 (b(s(s(s(z))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[52, 5212])).
% 1.74/2.00 tff(5214,plain,
% 1.74/2.00 (b(s(s(s(elem!1))), s(elem!1))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[3661, 5213, 88])).
% 1.74/2.00 tff(5215,plain,
% 1.74/2.00 (r(s(s(s(elem!1))), elem!1)),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5198, 5010])).
% 1.74/2.00 tff(5216,plain,
% 1.74/2.00 (r(s(elem!1), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[3437, 47, 5209, 3954])).
% 1.74/2.00 tff(5217,plain,
% 1.74/2.00 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5018, 183, 5216, 5215])).
% 1.74/2.00 tff(5218,plain,
% 1.74/2.00 (b(s(elem!1), s(s(s(elem!1))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5022, 47, 5217, 5009])).
% 1.74/2.00 tff(5219,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(5220,plain,
% 1.74/2.00 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(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))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(5221,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5220])).
% 1.74/2.00 tff(5222,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[5221, 5219])).
% 1.74/2.00 tff(5223,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(5224,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5223, 5222])).
% 1.74/2.00 tff(5225,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5224, 246, 5218, 5214, 2866, 5195])).
% 1.74/2.00 tff(5226,plain,((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~(z = elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~r(elem!1, s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(5227,plain,
% 1.74/2.00 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5226, 4837, 88, 2362, 714, 5157])).
% 1.74/2.00 tff(5228,plain,
% 1.74/2.00 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1557, 5227, 358])).
% 1.74/2.00 tff(5229,plain,
% 1.74/2.00 (~r(s(s(s(z))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[3017, 5001, 5000])).
% 1.74/2.00 tff(5230,plain,
% 1.74/2.00 (b(elem!1, s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5095, 1445, 56, 1, 88])).
% 1.74/2.00 tff(5231,plain,
% 1.74/2.00 (b(elem!1, s(s(s(elem!1))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4114, 2002, 88])).
% 1.74/2.00 tff(5232,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(5233,plain,
% 1.74/2.00 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(5234,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5233])).
% 1.74/2.00 tff(5235,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.74/2.00 inference(transitivity,[status(thm)],[5234, 5232])).
% 1.74/2.00 tff(5236,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(5237,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5236, 5235])).
% 1.74/2.00 tff(5238,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5237, 246, 2362, 363, 960, 714, 1937, 946])).
% 1.74/2.00 tff(5239,plain,((~b(s(s(elem!1)), s(elem!1))) | (~b(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))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(5240,plain,
% 1.74/2.00 (~b(s(s(elem!1)), s(elem!1))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5239, 5231, 2362, 714, 3736, 946])).
% 1.74/2.00 tff(5241,plain,
% 1.74/2.00 (~b(s(s(elem!1)), s(z))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5240, 4019])).
% 1.74/2.00 tff(5242,plain,
% 1.74/2.00 (r(s(s(elem!1)), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[197, 5241])).
% 1.74/2.00 tff(5243,plain,
% 1.74/2.00 (~r(elem!1, s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4199, 5242, 602])).
% 1.74/2.00 tff(5244,plain,
% 1.74/2.00 (b(elem!1, s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[214, 5243, 3729])).
% 1.74/2.00 tff(5245,plain,
% 1.74/2.00 (b(elem!1, s(elem!1))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5244, 1449])).
% 1.74/2.00 tff(5246,plain,
% 1.74/2.00 (~b(s(z), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2011, 5244, 2003, 2002])).
% 1.74/2.00 tff(5247,plain,
% 1.74/2.00 (r(s(z), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1034, 5246, 3678])).
% 1.74/2.00 tff(5248,plain,
% 1.74/2.00 (r(s(elem!1), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4450, 5247, 88])).
% 1.74/2.00 tff(5249,plain,
% 1.74/2.00 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5018, 183, 5248, 4357])).
% 1.74/2.00 tff(5250,plain,
% 1.74/2.00 (~r(s(z), s(s(s(z))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5249, 1931])).
% 1.74/2.00 tff(5251,plain,
% 1.74/2.00 (b(s(z), s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1291, 5250])).
% 1.74/2.00 tff(5252,plain,
% 1.74/2.00 (b(s(elem!1), s(s(s(elem!1))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5251, 1927])).
% 1.74/2.00 tff(5253,plain,
% 1.74/2.00 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, 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))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(5254,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, 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)))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5253])).
% 1.74/2.00 tff(5255,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, 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))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[5254, 5098])).
% 1.74/2.00 tff(5256,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(5257,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5256, 5255])).
% 1.74/2.00 tff(5258,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5257, 246, 5252, 5231, 3736, 5245])).
% 1.74/2.00 tff(5259,plain,((~b(elem!1, s(s(s(z))))) | (~(z = elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(5260,plain,
% 1.74/2.00 (~r(elem!1, s(s(elem!1)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5259, 946, 4357, 2003, 88, 2362, 714, 2002])).
% 1.74/2.00 tff(5261,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1268, 5260, 4984, 3739])).
% 1.74/2.00 tff(5262,plain,((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), s(z))) | (~(z = elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(5263,plain,
% 1.74/2.00 (~b(s(s(s(z))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5262, 5230, 946, 88, 2362, 714, 5011])).
% 1.74/2.00 tff(5264,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[52, 5263, 5229])).
% 1.74/2.00 tff(5265,plain,(b(s(z), elem!1) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~(z = elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | r(z, elem!1) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(5266,plain,
% 1.74/2.00 (b(s(z), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5265, 1, 88, 2362, 714, 56, 946])).
% 1.74/2.00 tff(5267,assumption,(~b(s(elem!1), elem!1)), introduced(assumption)).
% 1.74/2.00 tff(5268,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5267, 3731])).
% 1.74/2.00 tff(5269,plain,((~b(s(z), elem!1)) | b(s(elem!1), elem!1) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(5270,plain,
% 1.74/2.00 (b(s(elem!1), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5269, 5266, 88])).
% 1.74/2.00 tff(5271,plain,
% 1.74/2.00 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(5272,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5271])).
% 1.74/2.00 tff(5273,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[5272, 1788])).
% 1.74/2.00 tff(5274,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(5275,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5274, 5273])).
% 1.74/2.00 tff(5276,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5275, 246, 714, 1200, 2866, 1574])).
% 1.74/2.00 tff(5277,plain,((~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(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(5278,plain,
% 1.74/2.00 (~b(elem!1, s(elem!1))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5277, 5270, 714, 5157])).
% 1.74/2.00 tff(5279,plain,
% 1.74/2.00 (r(elem!1, s(elem!1))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2864, 5278, 2829])).
% 1.74/2.00 tff(5280,plain,
% 1.74/2.00 (~r(s(s(s(z))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4517, 5279, 2362, 714, 88, 946])).
% 1.74/2.00 tff(5281,plain,
% 1.74/2.00 (b(s(s(s(z))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[52, 5280])).
% 1.74/2.00 tff(5282,plain,
% 1.74/2.00 (b(s(s(s(elem!1))), s(elem!1))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[3661, 5281, 88])).
% 1.74/2.00 tff(5283,plain,
% 1.74/2.00 (~r(elem!1, s(s(s(elem!1))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4436, 5282, 5157, 1658, 5270, 88])).
% 1.74/2.00 tff(5284,plain,
% 1.74/2.00 (~b(elem!1, s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5262, 5281, 946, 88, 2362, 714, 5011])).
% 1.74/2.00 tff(5285,plain,
% 1.74/2.00 (r(elem!1, s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[470, 5284, 718])).
% 1.74/2.00 tff(5286,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4414, 5285, 5283, 88])).
% 1.74/2.00 tff(5287,plain,(b(s(s(s(z))), elem!1) | (~(z = elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(5288,plain,
% 1.74/2.00 (b(s(s(s(z))), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5287, 1658, 88, 946, 2362, 714, 56])).
% 1.74/2.00 tff(5289,plain,
% 1.74/2.00 (b(s(s(s(elem!1))), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[3701, 5288, 88])).
% 1.74/2.00 tff(5290,plain,
% 1.74/2.00 (~b(elem!1, s(s(s(elem!1))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4537, 5289, 2362, 714, 946])).
% 1.74/2.00 tff(5291,plain,
% 1.74/2.00 (~b(elem!1, s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4114, 5290, 88])).
% 1.74/2.00 tff(5292,plain,
% 1.74/2.00 (r(elem!1, s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[470, 5291, 718])).
% 1.74/2.00 tff(5293,plain,
% 1.74/2.00 (r(elem!1, s(s(s(elem!1))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4414, 5292, 88])).
% 1.74/2.00 tff(5294,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[3651, 183, 602, 3833, 3427])).
% 1.74/2.00 tff(5295,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(5296,plain,
% 1.74/2.00 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5295, 5293, 4985])).
% 1.74/2.00 tff(5297,plain,
% 1.74/2.00 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4455, 5296, 1817])).
% 1.74/2.00 tff(5298,plain,
% 1.74/2.00 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1667, 5297, 946, 1658])).
% 1.74/2.00 tff(5299,plain,
% 1.74/2.00 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5298, 4965])).
% 1.74/2.00 tff(5300,plain,
% 1.74/2.00 (r(s(s(s(z))), s(s(elem!1)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[689, 5299, 416])).
% 1.74/2.00 tff(5301,plain,
% 1.74/2.00 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5300, 1309])).
% 1.74/2.00 tff(5302,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[3100, 183, 4985, 5301, 5293])).
% 1.74/2.00 tff(5303,plain,((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~(z = elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(5304,plain,
% 1.74/2.00 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5303, 5228, 88, 2362, 714, 56])).
% 1.74/2.00 tff(5305,plain,
% 1.74/2.00 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[3693, 5304, 771])).
% 1.74/2.00 tff(5306,plain,
% 1.74/2.00 (~r(elem!1, s(s(s(elem!1))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4869, 5305, 4837])).
% 1.74/2.00 tff(5307,plain,
% 1.74/2.00 (~r(elem!1, s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4414, 5306, 88])).
% 1.74/2.00 tff(5308,plain,
% 1.74/2.00 (b(elem!1, s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[470, 5307, 718])).
% 1.74/2.00 tff(5309,plain,
% 1.74/2.00 (b(elem!1, s(s(s(elem!1))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4114, 5308, 88])).
% 1.74/2.00 tff(5310,plain,
% 1.74/2.00 (~b(s(s(s(elem!1))), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4893, 5305, 2362, 714, 88])).
% 1.74/2.00 tff(5311,plain,
% 1.74/2.00 (~b(s(s(s(z))), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[3701, 5310, 88])).
% 1.74/2.00 tff(5312,plain,
% 1.74/2.00 (b(s(z), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5265, 5311, 88, 2362, 714, 56, 5228])).
% 1.74/2.01 tff(5313,plain,
% 1.74/2.01 (b(s(elem!1), elem!1)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5269, 5312, 88])).
% 1.74/2.01 tff(5314,plain,
% 1.74/2.01 (~b(elem!1, s(elem!1))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5277, 5313, 714, 5157])).
% 1.74/2.01 tff(5315,plain,
% 1.74/2.01 (r(elem!1, s(elem!1))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2864, 5314, 2829])).
% 1.74/2.01 tff(5316,plain,
% 1.74/2.01 (~r(s(s(s(z))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[4517, 5315, 2362, 714, 88, 5228])).
% 1.74/2.01 tff(5317,plain,
% 1.74/2.01 (b(s(s(s(z))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[52, 5316])).
% 1.74/2.01 tff(5318,plain,
% 1.74/2.01 (b(s(s(s(elem!1))), s(elem!1))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[3661, 5317, 88])).
% 1.74/2.01 tff(5319,plain,
% 1.74/2.01 (~b(s(s(elem!1)), s(elem!1))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5239, 5318, 2362, 714, 5228, 5309])).
% 1.74/2.01 tff(5320,plain,
% 1.74/2.01 (~b(s(s(elem!1)), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5037, 5319, 88])).
% 1.74/2.01 tff(5321,plain,
% 1.74/2.01 (~b(elem!1, s(s(elem!1)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[4983, 5228, 2362, 714])).
% 1.74/2.01 tff(5322,plain,
% 1.74/2.01 (r(elem!1, s(s(elem!1)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[1268, 5321, 3739])).
% 1.74/2.01 tff(5323,plain,
% 1.74/2.01 (~b(elem!1, s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2011, 5317, 5312, 5308])).
% 1.74/2.01 tff(5324,plain,
% 1.74/2.01 (r(elem!1, s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[214, 5323, 3729])).
% 1.74/2.01 tff(5325,plain,
% 1.74/2.01 (~r(s(s(elem!1)), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[4199, 5324, 5322])).
% 1.74/2.01 tff(5326,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[197, 5325, 5320])).
% 1.74/2.01 tff(5327,plain,((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~(z = elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(5328,plain,
% 1.74/2.01 (~r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5327, 61, 3726, 4836, 56])).
% 1.74/2.01 tff(5329,plain,
% 1.74/2.01 (b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5125, 5328, 72])).
% 1.74/2.01 tff(5330,plain,
% 1.74/2.01 (~b(s(s(s(elem!1))), elem!1)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[4864, 5329, 4474, 3643, 4836, 3616, 3726])).
% 1.74/2.01 tff(5331,plain,
% 1.74/2.01 (~b(s(s(s(z))), elem!1)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[3701, 5330, 61])).
% 1.74/2.01 tff(5332,plain,
% 1.74/2.01 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[4853, 5329, 4836, 3726])).
% 1.74/2.01 tff(5333,plain,
% 1.74/2.01 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5155, 61, 3726, 4836, 56])).
% 1.74/2.01 tff(5334,plain,
% 1.74/2.01 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[1795, 5333, 3602])).
% 1.74/2.01 tff(5335,plain,
% 1.74/2.01 (b(s(s(s(z))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[52, 5229])).
% 1.74/2.01 tff(5336,plain,
% 1.74/2.01 (b(s(s(s(elem!1))), s(elem!1))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[3661, 5335, 88])).
% 1.74/2.01 tff(5337,plain,
% 1.74/2.01 (b(elem!1, s(s(s(elem!1))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[4114, 5230, 88])).
% 1.74/2.01 tff(5338,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(5339,plain,
% 1.74/2.01 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(5340,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1)))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[5339])).
% 1.74/2.01 tff(5341,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.74/2.01 inference(transitivity,[status(thm)],[5340, 5338])).
% 1.74/2.01 tff(5342,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(5343,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[5342, 5341])).
% 1.74/2.01 tff(5344,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5343, 246, 2362, 2751, 960, 1937, 1657])).
% 1.74/2.01 tff(5345,plain,((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(5346,plain,
% 1.74/2.01 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5345, 5023, 5337, 2362, 5336])).
% 1.74/2.01 tff(5347,plain,
% 1.74/2.01 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[4488, 5346, 3816, 4477, 1817])).
% 1.74/2.01 tff(5348,plain,
% 1.74/2.01 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[3693, 5347, 771])).
% 1.74/2.01 tff(5349,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5224, 246, 5023, 5336, 2866, 5348])).
% 1.74/2.01 tff(5350,plain,(b(s(z), elem!1) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | b(s(s(elem!1)), s(s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~(z = elem!1)) | r(z, elem!1) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(5351,plain,
% 1.74/2.01 (b(s(z), elem!1)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5350, 5334, 5332, 3726, 61, 56, 5331])).
% 1.74/2.01 tff(5352,plain,
% 1.74/2.01 (b(s(elem!1), elem!1)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5269, 5351, 61])).
% 1.74/2.01 tff(5353,plain,
% 1.74/2.01 (~b(elem!1, s(s(elem!1)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5208, 5352, 3726, 4836, 5334])).
% 1.74/2.01 tff(5354,plain,
% 1.74/2.01 (r(elem!1, s(s(elem!1)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[1268, 5353, 140])).
% 1.74/2.01 tff(5355,plain,
% 1.74/2.01 (r(elem!1, s(z)) <=> r(elem!1, s(elem!1))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[141])).
% 1.74/2.01 tff(5356,plain,
% 1.74/2.01 (r(elem!1, s(elem!1)) <=> r(elem!1, s(z))),
% 1.74/2.01 inference(symmetry,[status(thm)],[5355])).
% 1.74/2.01 tff(5357,plain,
% 1.74/2.01 (~b(elem!1, s(elem!1))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5277, 5352, 4836, 5334])).
% 1.74/2.01 tff(5358,plain,
% 1.74/2.01 (r(elem!1, s(elem!1))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2864, 5357, 4472])).
% 1.74/2.01 tff(5359,plain,
% 1.74/2.01 (r(elem!1, s(z))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[5358, 5356])).
% 1.74/2.01 tff(5360,plain,
% 1.74/2.01 (~r(s(s(elem!1)), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[4199, 5359, 5354])).
% 1.74/2.01 tff(5361,plain,
% 1.74/2.01 (b(s(s(elem!1)), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[197, 5360])).
% 1.74/2.01 tff(5362,plain,
% 1.74/2.01 (b(s(s(elem!1)), s(elem!1))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5037, 5361, 61])).
% 1.74/2.01 tff(5363,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5115, 246, 3726, 5362, 4836, 5352, 5329])).
% 1.74/2.01 tff(5364,plain,(r(z, elem!1) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(5365,plain,
% 1.74/2.01 (r(z, elem!1)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5364, 55])).
% 1.74/2.01 tff(5366,plain,
% 1.74/2.01 ((z = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = z)),
% 1.74/2.01 inference(commutativity,[status(thm)],[])).
% 1.74/2.01 tff(5367,plain,
% 1.74/2.01 ((s(s(s(elem!1))) = z) <=> (z = s(s(s(elem!1))))),
% 1.74/2.01 inference(symmetry,[status(thm)],[5366])).
% 1.74/2.01 tff(5368,plain,
% 1.74/2.01 ((~(s(s(s(elem!1))) = z)) <=> (~(z = s(s(s(elem!1)))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[5367])).
% 1.74/2.01 tff(5369,plain,
% 1.74/2.01 (~(z = s(s(s(elem!1))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[355, 5368])).
% 1.74/2.01 tff(5370,plain,
% 1.74/2.01 (~r(s(s(s(z))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2274, 6, 2232])).
% 1.74/2.01 tff(5371,plain,
% 1.74/2.01 (~b(s(s(s(z))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2290, 6, 1])).
% 1.74/2.01 tff(5372,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[52, 5371, 5370])).
% 1.74/2.01 tff(5373,plain,((~(s(z) = elem!1)) | b(s(s(s(z))), elem!1) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(5374,plain,
% 1.74/2.01 (~(s(z) = elem!1)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5373, 1, 2232])).
% 1.74/2.01 tff(5375,plain,
% 1.74/2.01 (~(elem!1 = s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2279, 5374])).
% 1.74/2.01 tff(5376,plain,
% 1.74/2.01 (~b(elem!1, s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2130, 2125, 2124])).
% 1.74/2.01 tff(5377,plain,
% 1.74/2.01 (r(elem!1, s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[214, 5376, 5375])).
% 1.74/2.01 tff(5378,plain,
% 1.74/2.01 (s(s(s(s(z)))) = s(elem!1)),
% 1.74/2.01 inference(monotonicity,[status(thm)],[1673])).
% 1.74/2.01 tff(5379,plain,
% 1.74/2.01 (s(elem!1) = s(s(s(s(z))))),
% 1.74/2.01 inference(symmetry,[status(thm)],[5378])).
% 1.74/2.01 tff(5380,plain,
% 1.74/2.01 (elem!1 = s(s(elem!1))),
% 1.74/2.01 inference(symmetry,[status(thm)],[2125])).
% 1.74/2.01 tff(5381,plain,
% 1.74/2.01 (s(s(s(z))) = s(s(elem!1))),
% 1.74/2.01 inference(transitivity,[status(thm)],[1673, 5380])).
% 1.74/2.01 tff(5382,plain,
% 1.74/2.01 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[5381])).
% 1.74/2.01 tff(5383,plain,
% 1.74/2.01 (s(s(z)) = s(s(s(s(z))))),
% 1.74/2.01 inference(transitivity,[status(thm)],[25, 5382, 92, 5379])).
% 1.74/2.01 tff(5384,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[1526, 5383])).
% 1.74/2.01 tff(5385,plain,((~(s(s(elem!1)) = elem!1)) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(5386,plain,
% 1.74/2.01 (~(s(s(s(z))) = elem!1)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5385, 2125])).
% 1.74/2.01 tff(5387,plain,
% 1.74/2.01 (r(s(s(s(z))), elem!1)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[647, 5386, 1])).
% 1.74/2.01 tff(5388,plain,
% 1.74/2.01 (r(z, elem!1) <=> r(z, z)),
% 1.74/2.01 inference(monotonicity,[status(thm)],[1038])).
% 1.74/2.01 tff(5389,plain,
% 1.74/2.01 (r(z, z) <=> r(z, elem!1)),
% 1.74/2.01 inference(symmetry,[status(thm)],[5388])).
% 1.74/2.01 tff(5390,plain,
% 1.74/2.01 ((~r(z, z)) <=> (~r(z, elem!1))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[5389])).
% 1.74/2.01 tff(5391,plain,
% 1.74/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, z)))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(5392,plain,
% 1.74/2.01 (((~r(z, elem!1)) | (~r(z, elem!1)) | (~r(z, elem!1)) | (~r(z, z))) <=> ((~r(z, elem!1)) | (~r(z, z)))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(5393,plain,
% 1.74/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, elem!1)) | (~r(z, elem!1)) | (~r(z, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, z))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[5392])).
% 1.74/2.01 tff(5394,plain,
% 1.74/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, elem!1)) | (~r(z, elem!1)) | (~r(z, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, z)))),
% 1.74/2.01 inference(transitivity,[status(thm)],[5393, 5391])).
% 1.74/2.01 tff(5395,plain,
% 1.74/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, elem!1)) | (~r(z, elem!1)) | (~r(z, z)))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(5396,plain,
% 1.74/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, z))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[5395, 5394])).
% 1.74/2.01 tff(5397,plain,
% 1.74/2.01 (~r(z, z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5396, 183, 267])).
% 1.74/2.01 tff(5398,plain,
% 1.74/2.01 (~r(z, elem!1)),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[5397, 5390])).
% 1.74/2.01 tff(5399,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[267, 5398])).
% 1.74/2.01 tff(5400,plain,((~(elem!1 = z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(5401,plain,
% 1.74/2.01 (~(elem!1 = z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5400, 267])).
% 1.74/2.01 tff(5402,plain,
% 1.74/2.01 (~r(s(s(s(z))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2282, 5387, 2232, 5376])).
% 1.74/2.01 tff(5403,plain,
% 1.74/2.01 (b(s(s(s(z))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[52, 5402])).
% 1.74/2.01 tff(5404,plain,
% 1.74/2.01 (~r(z, s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[292, 5377, 267])).
% 1.74/2.01 tff(5405,plain,
% 1.74/2.01 (b(z, s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[169, 5404])).
% 1.74/2.01 tff(5406,plain,
% 1.74/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(5407,plain,
% 1.74/2.01 (((~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z))) <=> ((~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(5408,plain,
% 1.74/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[5407])).
% 1.74/2.01 tff(5409,plain,
% 1.74/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))),
% 1.74/2.01 inference(transitivity,[status(thm)],[5408, 5406])).
% 1.74/2.01 tff(5410,plain,
% 1.74/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(5411,plain,
% 1.74/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[5410, 5409])).
% 1.74/2.01 tff(5412,plain,
% 1.74/2.01 (~r(s(s(s(z))), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5411, 183, 267, 634])).
% 1.74/2.01 tff(5413,plain,
% 1.74/2.01 (b(s(s(s(z))), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[995, 5412])).
% 1.74/2.01 tff(5414,plain,
% 1.74/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(5415,plain,
% 1.74/2.01 (((~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z)))))) <=> ((~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(5416,plain,
% 1.74/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), elem!1))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[5415])).
% 1.74/2.01 tff(5417,plain,
% 1.74/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 1.74/2.01 inference(transitivity,[status(thm)],[5416, 5414])).
% 1.74/2.01 tff(5418,plain,
% 1.74/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(5419,plain,
% 1.74/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), elem!1))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[5418, 5417])).
% 1.74/2.01 tff(5420,plain,
% 1.74/2.01 (~r(z, s(s(s(z))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5419, 183, 267, 634])).
% 1.74/2.01 tff(5421,plain,
% 1.74/2.01 ((z = s(s(s(z)))) | b(z, s(s(s(z))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2221, 47, 5420])).
% 1.74/2.01 tff(5422,plain,
% 1.74/2.01 (b(z, s(s(s(z))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5421, 2218])).
% 1.74/2.01 tff(5423,plain,
% 1.74/2.01 (~b(s(z), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2098, 5413, 2003, 236])).
% 1.74/2.01 tff(5424,plain,
% 1.74/2.01 (r(s(z), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[1069, 5423])).
% 1.74/2.01 tff(5425,plain,
% 1.74/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1)))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(5426,plain,
% 1.74/2.01 (((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), z))) <=> ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1)))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(5427,plain,
% 1.74/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[5426])).
% 1.74/2.01 tff(5428,plain,
% 1.74/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1)))),
% 1.74/2.01 inference(transitivity,[status(thm)],[5427, 5425])).
% 1.74/2.01 tff(5429,plain,
% 1.74/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), z)))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(5430,plain,
% 1.74/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[5429, 5428])).
% 1.74/2.01 tff(5431,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5430, 183, 267, 1114, 217])).
% 1.74/2.01 tff(5432,plain,((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(5433,plain,
% 1.74/2.01 (~r(s(z), elem!1)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5432, 5424, 267])).
% 1.74/2.01 tff(5434,plain,
% 1.74/2.01 (b(s(z), elem!1)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[1034, 5433, 2277])).
% 1.74/2.01 tff(5435,plain,
% 1.74/2.01 (~r(elem!1, z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[1163, 5424, 474])).
% 1.74/2.01 tff(5436,plain,
% 1.74/2.01 (b(elem!1, z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[1143, 5435, 1438])).
% 1.74/2.01 tff(5437,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(5438,plain,
% 1.74/2.01 (((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))) <=> ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(5439,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[5438])).
% 1.74/2.01 tff(5440,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.74/2.01 inference(transitivity,[status(thm)],[5439, 5437])).
% 1.74/2.01 tff(5441,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(5442,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[5441, 5440])).
% 1.74/2.01 tff(5443,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5442, 246, 5436, 5434, 236, 2003, 5422, 5413])).
% 1.74/2.02 tff(5444,plain,((~r(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (elem!1 = z) | (s(z) = elem!1) | (~r(elem!1, s(z))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(5445,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[5444, 5405, 5403, 267, 5401, 5374, 5387, 5377])).
% 1.74/2.02 tff(5446,plain,((~(s(s(elem!1)) = elem!1)) | (~r(z, elem!1)) | r(s(s(elem!1)), elem!1) | b(s(s(s(z))), elem!1) | b(s(s(elem!1)), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(5447,plain,
% 1.74/2.02 (~(s(s(elem!1)) = elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[5446, 1, 2232, 5365, 2124])).
% 1.74/2.02 tff(5448,plain,
% 1.74/2.02 (s(s(elem!1)) = elem!1),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[2392, 133])).
% 1.74/2.02 tff(5449,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[199, 5448])).
% 1.74/2.02 tff(5450,plain,((~(elem!1 = s(s(elem!1)))) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(5451,plain,
% 1.74/2.02 (~(elem!1 = s(s(elem!1)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[5450, 5447])).
% 1.74/2.02 tff(5452,plain,
% 1.74/2.02 (~(elem!1 = s(s(s(s(s(elem!1))))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[71, 69])).
% 1.74/2.02 tff(5453,plain,
% 1.74/2.02 (r(elem!1, s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[214, 5375, 210])).
% 1.74/2.02 tff(5454,plain,
% 1.74/2.02 (~r(elem!1, s(s(elem!1)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[4199, 5453, 173])).
% 1.74/2.02 tff(5455,plain,
% 1.74/2.02 (~r(z, s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[292, 5453, 5365])).
% 1.74/2.02 tff(5456,plain,
% 1.74/2.02 (b(z, s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[169, 5455])).
% 1.74/2.02 tff(5457,plain,
% 1.74/2.02 (~(s(s(elem!1)) = elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[5385, 1673])).
% 1.74/2.02 tff(5458,plain,
% 1.74/2.02 (b(s(s(elem!1)), elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[156, 5457, 2232])).
% 1.74/2.02 tff(5459,assumption,(~r(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.74/2.02 tff(5460,plain,
% 1.74/2.02 (~(elem!1 = s(s(elem!1)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[5450, 5457])).
% 1.74/2.02 tff(5461,plain,
% 1.74/2.02 (b(elem!1, s(s(elem!1)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1268, 5460, 5459])).
% 1.74/2.02 tff(5462,plain,
% 1.74/2.02 ((s(elem!1) = s(s(elem!1))) <=> (s(s(elem!1)) = s(elem!1))),
% 1.74/2.02 inference(commutativity,[status(thm)],[])).
% 1.74/2.02 tff(5463,plain,
% 1.74/2.02 ((s(s(elem!1)) = s(elem!1)) <=> (s(elem!1) = s(s(elem!1)))),
% 1.74/2.02 inference(symmetry,[status(thm)],[5462])).
% 1.74/2.02 tff(5464,plain,
% 1.74/2.02 ((~(s(s(elem!1)) = s(elem!1))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[5463])).
% 1.74/2.02 tff(5465,plain,
% 1.74/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(5466,plain,
% 1.74/2.02 (((~r(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), z))) <=> ((~r(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(5467,plain,
% 1.74/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[5466])).
% 1.74/2.02 tff(5468,plain,
% 1.74/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.74/2.02 inference(transitivity,[status(thm)],[5467, 5465])).
% 1.74/2.02 tff(5469,plain,
% 1.74/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(5470,plain,
% 1.74/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[5469, 5468])).
% 1.74/2.02 tff(5471,plain,
% 1.74/2.02 (~r(s(s(s(s(s(elem!1))))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[5470, 183, 267, 333])).
% 1.74/2.02 tff(5472,plain,
% 1.74/2.02 (b(s(s(s(s(s(elem!1))))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1601, 5471])).
% 1.74/2.02 tff(5473,assumption,(z = s(s(s(z)))), introduced(assumption)).
% 1.74/2.02 tff(5474,plain,
% 1.74/2.02 (s(s(s(z))) = z),
% 1.74/2.02 inference(symmetry,[status(thm)],[5473])).
% 1.74/2.02 tff(5475,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[80, 5474])).
% 1.74/2.02 tff(5476,plain,(~(z = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(5477,plain,
% 1.74/2.02 (b(z, s(s(s(z))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2221, 47, 5420, 5476])).
% 1.74/2.02 tff(5478,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(5479,plain,
% 1.74/2.02 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))) <=> ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(5480,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[5479])).
% 1.74/2.02 tff(5481,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.74/2.02 inference(transitivity,[status(thm)],[5480, 5478])).
% 1.74/2.02 tff(5482,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(5483,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[5482, 5481])).
% 1.74/2.02 tff(5484,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[5483, 246, 5477, 5413, 5472, 2320])).
% 1.74/2.02 tff(5485,plain,((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(5486,plain,
% 1.74/2.02 (~r(s(s(s(z))), elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[5485, 333, 267])).
% 1.74/2.02 tff(5487,plain,
% 1.74/2.02 (s(s(s(z))) = elem!1),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[647, 5486, 1])).
% 1.74/2.02 tff(5488,plain,
% 1.74/2.02 (s(s(s(s(z)))) = s(elem!1)),
% 1.74/2.02 inference(monotonicity,[status(thm)],[5487])).
% 1.74/2.02 tff(5489,plain,
% 1.74/2.02 ((s(s(s(s(z)))) = elem!1) <=> (s(elem!1) = elem!1)),
% 1.74/2.02 inference(monotonicity,[status(thm)],[5488])).
% 1.74/2.02 tff(5490,plain,
% 1.74/2.02 ((s(s(s(s(z)))) = elem!1) <=> (elem!1 = s(elem!1))),
% 1.74/2.02 inference(transitivity,[status(thm)],[5489, 2825])).
% 1.74/2.02 tff(5491,plain,
% 1.74/2.02 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(elem!1 = s(elem!1)))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[5490])).
% 1.74/2.02 tff(5492,plain,
% 1.74/2.02 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.74/2.02 inference(monotonicity,[status(thm)],[5487])).
% 1.74/2.02 tff(5493,plain,
% 1.74/2.02 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[5492])).
% 1.74/2.02 tff(5494,plain,
% 1.74/2.02 (~(s(s(s(s(z)))) = elem!1)),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[1697, 5493])).
% 1.74/2.02 tff(5495,plain,
% 1.74/2.02 (~(elem!1 = s(elem!1))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[5494, 5491])).
% 1.74/2.02 tff(5496,assumption,(s(s(elem!1)) = s(elem!1)), introduced(assumption)).
% 1.74/2.02 tff(5497,plain,
% 1.74/2.02 (s(elem!1) = s(s(elem!1))),
% 1.74/2.02 inference(symmetry,[status(thm)],[5496])).
% 1.74/2.02 tff(5498,plain,
% 1.74/2.02 (inj_0(s(elem!1)) = inj_0(s(s(elem!1)))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[5497])).
% 1.74/2.02 tff(5499,plain,
% 1.74/2.02 (elem!1 = s(elem!1)),
% 1.74/2.02 inference(transitivity,[status(thm)],[3154, 5498, 92])).
% 1.74/2.02 tff(5500,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[3425, 5499])).
% 1.74/2.02 tff(5501,plain,((~(s(s(elem!1)) = s(elem!1))) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(5502,plain,
% 1.74/2.02 (~(s(s(elem!1)) = s(elem!1))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[5501, 5495])).
% 1.74/2.02 tff(5503,plain,
% 1.74/2.02 (~(s(elem!1) = s(s(elem!1)))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[5502, 5464])).
% 1.74/2.02 tff(5504,plain,
% 1.74/2.02 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(elem!1), elem!1)),
% 1.74/2.02 inference(monotonicity,[status(thm)],[5488, 5487])).
% 1.74/2.02 tff(5505,plain,
% 1.74/2.02 (s(elem!1) = s(s(s(s(z))))),
% 1.74/2.02 inference(symmetry,[status(thm)],[5488])).
% 1.74/2.02 tff(5506,plain,
% 1.74/2.02 ((s(s(s(s(s(elem!1))))) = s(elem!1)) <=> (s(s(s(s(s(elem!1))))) = s(s(s(s(z)))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[5505])).
% 1.74/2.02 tff(5507,plain,
% 1.74/2.02 ((s(s(s(s(s(elem!1))))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))),
% 1.74/2.02 inference(transitivity,[status(thm)],[5506, 1483])).
% 1.74/2.02 tff(5508,plain,
% 1.74/2.02 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(elem!1))),
% 1.74/2.02 inference(symmetry,[status(thm)],[5507])).
% 1.74/2.02 tff(5509,plain,
% 1.74/2.02 ((~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(s(elem!1))))) = s(elem!1)))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[5508])).
% 1.74/2.02 tff(5510,plain,
% 1.74/2.02 (~(s(s(s(s(s(elem!1))))) = s(elem!1))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[1501, 5509])).
% 1.74/2.02 tff(5511,plain,
% 1.74/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(5512,plain,
% 1.74/2.02 (((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(z, s(s(s(s(s(elem!1)))))))) <=> ((~r(z, elem!1)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(5513,plain,
% 1.74/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[5512])).
% 1.74/2.02 tff(5514,plain,
% 1.74/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.74/2.02 inference(transitivity,[status(thm)],[5513, 5511])).
% 1.74/2.02 tff(5515,plain,
% 1.74/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(z, s(s(s(s(s(elem!1))))))))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(5516,plain,
% 1.74/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[5515, 5514])).
% 1.74/2.02 tff(5517,plain,
% 1.74/2.02 (~r(z, s(s(s(s(s(elem!1))))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[5516, 183, 267, 333])).
% 1.74/2.02 tff(5518,plain,
% 1.74/2.02 ((z = s(s(s(s(s(elem!1)))))) | b(z, s(s(s(s(s(elem!1))))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2487, 47, 5517])).
% 1.74/2.02 tff(5519,plain,
% 1.74/2.02 (b(z, s(s(s(s(s(elem!1))))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[5518, 2477])).
% 1.74/2.02 tff(5520,plain,
% 1.74/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(5521,plain,
% 1.74/2.02 (((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1)))) <=> ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(5522,plain,
% 1.74/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1)))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[5521])).
% 1.74/2.02 tff(5523,plain,
% 1.74/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))))),
% 1.74/2.02 inference(transitivity,[status(thm)],[5522, 5520])).
% 1.74/2.02 tff(5524,plain,
% 1.74/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(5525,plain,
% 1.74/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1)))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[5524, 5523])).
% 1.74/2.02 tff(5526,plain,
% 1.74/2.02 (~r(z, s(elem!1))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[5525, 183, 267, 367])).
% 1.74/2.02 tff(5527,plain,
% 1.74/2.02 (b(z, s(elem!1))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2561, 5526])).
% 1.74/2.02 tff(5528,plain,
% 1.74/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(5529,plain,
% 1.74/2.02 (((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z))) <=> ((~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(5530,plain,
% 1.74/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[5529])).
% 1.74/2.02 tff(5531,plain,
% 1.74/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))),
% 1.74/2.02 inference(transitivity,[status(thm)],[5530, 5528])).
% 1.74/2.02 tff(5532,plain,
% 1.74/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(5533,plain,
% 1.74/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[5532, 5531])).
% 1.74/2.02 tff(5534,plain,
% 1.74/2.02 (~r(s(elem!1), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[5533, 183, 267, 367])).
% 1.74/2.02 tff(5535,plain,
% 1.74/2.02 (b(s(elem!1), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2581, 5534])).
% 1.74/2.02 tff(5536,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(5537,plain,
% 1.74/2.02 (((~b(z, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(s(elem!1)))))))) <=> ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(5538,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[5537])).
% 1.74/2.02 tff(5539,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.87/2.02 inference(transitivity,[status(thm)],[5538, 5536])).
% 1.87/2.02 tff(5540,plain,
% 1.87/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 1.87/2.02 inference(quant_inst,[status(thm)],[])).
% 1.87/2.02 tff(5541,plain,
% 1.87/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.87/2.02 inference(modus_ponens,[status(thm)],[5540, 5539])).
% 1.87/2.02 tff(5542,plain,
% 1.87/2.02 ($false),
% 1.87/2.02 inference(unit_resolution,[status(thm)],[5541, 246, 5535, 4038, 5527, 5519])).
% 1.87/2.02 tff(5543,plain,((~r(s(elem!1), elem!1)) | (s(s(s(s(s(elem!1))))) = s(elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.02 tff(5544,plain,
% 1.87/2.02 (~r(s(elem!1), elem!1)),
% 1.87/2.02 inference(unit_resolution,[status(thm)],[5543, 5510, 267, 333])).
% 1.87/2.02 tff(5545,plain,
% 1.87/2.02 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(elem!1), elem!1)),
% 1.87/2.02 inference(monotonicity,[status(thm)],[5378, 1673])).
% 1.87/2.02 tff(5546,plain,
% 1.87/2.02 (r(s(elem!1), elem!1)),
% 1.87/2.02 inference(modus_ponens,[status(thm)],[2593, 5545])).
% 1.87/2.02 tff(5547,plain,
% 1.87/2.02 ($false),
% 1.87/2.02 inference(unit_resolution,[status(thm)],[4448, 5546])).
% 1.87/2.02 tff(5548,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | r(s(elem!1), elem!1) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.02 tff(5549,plain,
% 1.87/2.02 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.87/2.02 inference(unit_resolution,[status(thm)],[5548, 5544, 5487])).
% 1.87/2.02 tff(5550,plain,
% 1.87/2.02 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.87/2.02 inference(unit_resolution,[status(thm)],[1702, 5549])).
% 1.87/2.02 tff(5551,plain,
% 1.87/2.02 (b(s(elem!1), elem!1)),
% 1.87/2.02 inference(modus_ponens,[status(thm)],[5550, 5504])).
% 1.87/2.02 tff(5552,plain,
% 1.87/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.87/2.02 inference(rewrite,[status(thm)],[])).
% 1.87/2.02 tff(5553,plain,
% 1.87/2.02 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.87/2.02 inference(rewrite,[status(thm)],[])).
% 1.87/2.02 tff(5554,plain,
% 1.87/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1))))),
% 1.87/2.02 inference(monotonicity,[status(thm)],[5553])).
% 1.87/2.02 tff(5555,plain,
% 1.87/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.87/2.03 inference(transitivity,[status(thm)],[5554, 5552])).
% 1.87/2.03 tff(5556,plain,
% 1.87/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.87/2.03 inference(quant_inst,[status(thm)],[])).
% 1.87/2.03 tff(5557,plain,
% 1.87/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1))),
% 1.87/2.03 inference(modus_ponens,[status(thm)],[5556, 5555])).
% 1.87/2.03 tff(5558,plain,
% 1.87/2.03 (~b(s(elem!1), s(s(elem!1)))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[5557, 246, 2362, 947, 5551])).
% 1.87/2.03 tff(5559,plain,
% 1.87/2.03 (((~![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))))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(5560,plain,
% 1.87/2.03 ((~![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))))),
% 1.87/2.03 inference(quant_inst,[status(thm)],[])).
% 1.87/2.03 tff(5561,plain,
% 1.87/2.03 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1)))),
% 1.87/2.03 inference(modus_ponens,[status(thm)],[5560, 5559])).
% 1.87/2.03 tff(5562,plain,
% 1.87/2.03 ((s(elem!1) = s(s(elem!1))) | r(s(elem!1), s(s(elem!1)))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[5561, 47, 5558])).
% 1.87/2.03 tff(5563,plain,
% 1.87/2.03 (r(s(elem!1), s(s(elem!1)))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[5562, 5503])).
% 1.87/2.03 tff(5564,plain,
% 1.87/2.03 (b(s(s(s(z))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.87/2.03 inference(monotonicity,[status(thm)],[97])).
% 1.87/2.03 tff(5565,plain,
% 1.87/2.03 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.87/2.03 inference(symmetry,[status(thm)],[5564])).
% 1.87/2.03 tff(5566,plain,
% 1.87/2.03 (b(s(s(s(z))), elem!1)),
% 1.87/2.03 inference(modus_ponens,[status(thm)],[2362, 5565])).
% 1.87/2.03 tff(5567,plain,
% 1.87/2.03 ($false),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[1, 5566])).
% 1.87/2.03 tff(5568,plain,((~(s(s(s(z))) = s(s(elem!1)))) | b(s(s(s(z))), elem!1) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.03 tff(5569,plain,
% 1.87/2.03 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[5568, 2362, 1])).
% 1.87/2.03 tff(5570,plain,
% 1.87/2.03 (~(s(z) = elem!1)),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[121, 5569])).
% 1.87/2.03 tff(5571,plain,
% 1.87/2.03 (~r(s(z), z)),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[5432, 217, 267])).
% 1.87/2.03 tff(5572,plain,
% 1.87/2.03 (b(s(z), z)),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[1069, 5571])).
% 1.87/2.03 tff(5573,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(5574,plain,
% 1.87/2.03 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z)))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(5575,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z)))))),
% 1.87/2.03 inference(monotonicity,[status(thm)],[5574])).
% 1.87/2.03 tff(5576,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 1.87/2.03 inference(transitivity,[status(thm)],[5575, 5573])).
% 1.87/2.03 tff(5577,plain,
% 1.87/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 1.87/2.03 inference(quant_inst,[status(thm)],[])).
% 1.87/2.03 tff(5578,plain,
% 1.87/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z)))),
% 1.87/2.03 inference(modus_ponens,[status(thm)],[5577, 5576])).
% 1.87/2.03 tff(5579,plain,
% 1.87/2.03 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[5578, 246, 5572, 236, 5472])).
% 1.87/2.03 tff(5580,plain,
% 1.87/2.03 ($false),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[2311, 47, 331, 2308, 5579])).
% 1.87/2.03 tff(5581,plain,((~r(s(z), elem!1)) | (~b(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.03 tff(5582,plain,
% 1.87/2.03 (~r(s(z), elem!1)),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[5581, 333, 236, 267])).
% 1.87/2.03 tff(5583,plain,
% 1.87/2.03 (b(s(z), elem!1)),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[1034, 5582, 5570])).
% 1.87/2.03 tff(5584,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(5585,plain,
% 1.87/2.03 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(5586,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1))))))),
% 1.87/2.03 inference(monotonicity,[status(thm)],[5585])).
% 1.87/2.03 tff(5587,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 1.87/2.03 inference(transitivity,[status(thm)],[5586, 5584])).
% 1.87/2.03 tff(5588,plain,
% 1.87/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 1.87/2.03 inference(quant_inst,[status(thm)],[])).
% 1.87/2.03 tff(5589,plain,
% 1.87/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1))))),
% 1.87/2.03 inference(modus_ponens,[status(thm)],[5588, 5587])).
% 1.87/2.03 tff(5590,plain,
% 1.87/2.03 (~b(s(z), s(s(elem!1)))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[5589, 246, 5583, 2362, 947])).
% 1.87/2.03 tff(5591,plain,
% 1.87/2.03 (r(s(z), s(s(elem!1)))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[233, 5590])).
% 1.87/2.03 tff(5592,plain,
% 1.87/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(5593,plain,
% 1.87/2.03 (((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z)))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(5594,plain,
% 1.87/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.87/2.03 inference(monotonicity,[status(thm)],[5593])).
% 1.87/2.03 tff(5595,plain,
% 1.87/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.87/2.03 inference(transitivity,[status(thm)],[5594, 5592])).
% 1.87/2.03 tff(5596,plain,
% 1.87/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))))),
% 1.87/2.03 inference(quant_inst,[status(thm)],[])).
% 1.87/2.03 tff(5597,plain,
% 1.87/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1))))),
% 1.87/2.03 inference(modus_ponens,[status(thm)],[5596, 5595])).
% 1.87/2.03 tff(5598,plain,
% 1.87/2.03 (~r(s(elem!1), s(z))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[5597, 183, 5591, 5563])).
% 1.87/2.03 tff(5599,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(5600,plain,
% 1.87/2.03 (((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(5601,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z)))))),
% 1.87/2.03 inference(monotonicity,[status(thm)],[5600])).
% 1.87/2.03 tff(5602,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.87/2.03 inference(transitivity,[status(thm)],[5601, 5599])).
% 1.87/2.03 tff(5603,plain,
% 1.87/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.87/2.03 inference(quant_inst,[status(thm)],[])).
% 1.87/2.03 tff(5604,plain,
% 1.87/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z)))),
% 1.87/2.03 inference(modus_ponens,[status(thm)],[5603, 5602])).
% 1.87/2.03 tff(5605,plain,
% 1.87/2.03 (~b(s(elem!1), s(z))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[5604, 246, 5583, 2362, 947, 5551])).
% 1.87/2.03 tff(5606,plain,
% 1.87/2.03 ((s(elem!1) = s(z)) | r(s(elem!1), s(z))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[2989, 47, 5605])).
% 1.87/2.03 tff(5607,plain,
% 1.87/2.03 (s(elem!1) = s(z)),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[5606, 5598])).
% 1.87/2.03 tff(5608,plain,
% 1.87/2.03 (s(s(s(s(z)))) = s(z)),
% 1.87/2.03 inference(transitivity,[status(thm)],[5488, 5607])).
% 1.87/2.03 tff(5609,plain,
% 1.87/2.03 ($false),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[1713, 5608])).
% 1.87/2.03 tff(5610,plain,((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(z))) | (~r(z, elem!1)) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.87/2.03 tff(5611,plain,
% 1.87/2.03 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[5610, 5461, 5365, 5458, 5456, 1])).
% 1.87/2.03 tff(5612,plain,
% 1.87/2.03 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[86, 5611, 69])).
% 1.87/2.03 tff(5613,plain,
% 1.87/2.03 (s(s(s(s(elem!1)))) = s(elem!1)),
% 1.87/2.03 inference(transitivity,[status(thm)],[326, 345, 92])).
% 1.87/2.03 tff(5614,plain,
% 1.87/2.03 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(elem!1))),
% 1.87/2.03 inference(monotonicity,[status(thm)],[5613])).
% 1.87/2.03 tff(5615,plain,
% 1.87/2.03 (inj_0(s(elem!1)) = inj_0(s(s(s(s(elem!1)))))),
% 1.87/2.03 inference(symmetry,[status(thm)],[5614])).
% 1.87/2.03 tff(5616,plain,
% 1.87/2.03 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.87/2.03 inference(transitivity,[status(thm)],[1673, 3154, 5615, 351])).
% 1.87/2.03 tff(5617,plain,
% 1.87/2.03 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 1.87/2.03 inference(monotonicity,[status(thm)],[5616])).
% 1.87/2.03 tff(5618,plain,
% 1.87/2.03 (s(s(z)) = s(s(elem!1))),
% 1.87/2.03 inference(transitivity,[status(thm)],[25, 5617, 103])).
% 1.87/2.03 tff(5619,plain,
% 1.87/2.03 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 1.87/2.03 inference(monotonicity,[status(thm)],[5618])).
% 1.87/2.03 tff(5620,plain,
% 1.87/2.03 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.87/2.03 inference(symmetry,[status(thm)],[5619])).
% 1.87/2.03 tff(5621,plain,
% 1.87/2.03 (s(s(s(s(z)))) = s(z)),
% 1.87/2.03 inference(transitivity,[status(thm)],[5378, 108, 5620, 1486])).
% 1.87/2.03 tff(5622,plain,
% 1.87/2.03 ($false),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[1713, 5621])).
% 1.87/2.03 tff(5623,plain,((~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.03 tff(5624,plain,
% 1.87/2.03 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[5623, 1673])).
% 1.87/2.03 tff(5625,plain,
% 1.87/2.03 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[4983, 5612, 5458, 5461])).
% 1.87/2.03 tff(5626,plain,
% 1.87/2.03 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[1557, 5625, 5624])).
% 1.87/2.03 tff(5627,plain,
% 1.87/2.03 ((s(s(s(s(z)))) = elem!1) <=> (s(elem!1) = elem!1)),
% 1.87/2.03 inference(monotonicity,[status(thm)],[5378])).
% 1.87/2.03 tff(5628,plain,
% 1.87/2.03 ((s(s(s(s(z)))) = elem!1) <=> (elem!1 = s(elem!1))),
% 1.87/2.03 inference(transitivity,[status(thm)],[5627, 2825])).
% 1.87/2.03 tff(5629,plain,
% 1.87/2.03 ((s(s(s(s(z)))) = elem!1) <=> (s(elem!1) = elem!1)),
% 1.87/2.03 inference(transitivity,[status(thm)],[5628, 3423])).
% 1.87/2.03 tff(5630,plain,
% 1.87/2.03 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(s(elem!1) = elem!1))),
% 1.87/2.03 inference(monotonicity,[status(thm)],[5629])).
% 1.87/2.03 tff(5631,plain,
% 1.87/2.03 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.87/2.03 inference(monotonicity,[status(thm)],[1673])).
% 1.87/2.03 tff(5632,plain,
% 1.87/2.03 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 1.87/2.03 inference(monotonicity,[status(thm)],[5631])).
% 1.87/2.03 tff(5633,plain,
% 1.87/2.03 (~(s(s(s(s(z)))) = elem!1)),
% 1.87/2.03 inference(modus_ponens,[status(thm)],[1697, 5632])).
% 1.87/2.03 tff(5634,plain,
% 1.87/2.03 (~(s(elem!1) = elem!1)),
% 1.87/2.03 inference(modus_ponens,[status(thm)],[5633, 5630])).
% 1.87/2.03 tff(5635,plain,
% 1.87/2.03 (elem!1 = s(elem!1)),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[5501, 5496])).
% 1.87/2.03 tff(5636,plain,
% 1.87/2.03 ((s(s(elem!1)) = elem!1) <=> (s(s(elem!1)) = s(elem!1))),
% 1.87/2.03 inference(monotonicity,[status(thm)],[5635])).
% 1.87/2.03 tff(5637,plain,
% 1.87/2.03 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(elem!1)) = elem!1)),
% 1.87/2.03 inference(symmetry,[status(thm)],[5636])).
% 1.87/2.03 tff(5638,plain,
% 1.87/2.03 (s(s(elem!1)) = elem!1),
% 1.87/2.03 inference(modus_ponens,[status(thm)],[5496, 5637])).
% 1.87/2.03 tff(5639,plain,
% 1.87/2.03 ($false),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[199, 5638])).
% 1.87/2.03 tff(5640,plain,((~(s(s(elem!1)) = s(elem!1))) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.87/2.03 tff(5641,plain,
% 1.87/2.03 (~(s(s(elem!1)) = s(elem!1))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[5640, 5457])).
% 1.87/2.03 tff(5642,assumption,(~(s(s(elem!1)) = s(elem!1))), introduced(assumption)).
% 1.87/2.03 tff(5643,plain,
% 1.87/2.03 ($false),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[1949, 47, 5035, 3804, 5642])).
% 1.87/2.03 tff(5644,plain,(b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1)) | (s(s(elem!1)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.03 tff(5645,plain,
% 1.87/2.03 (r(s(s(elem!1)), s(elem!1))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[5644, 5641, 5035])).
% 1.87/2.03 tff(5646,plain,
% 1.87/2.03 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[1959, 5626, 5645])).
% 1.87/2.03 tff(5647,plain,
% 1.87/2.03 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(elem!1) = s(s(s(s(s(elem!1))))))),
% 1.87/2.03 inference(monotonicity,[status(thm)],[5378])).
% 1.87/2.03 tff(5648,plain,
% 1.87/2.03 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(elem!1))),
% 1.87/2.03 inference(transitivity,[status(thm)],[5647, 1800])).
% 1.87/2.03 tff(5649,plain,
% 1.87/2.03 ((~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(s(elem!1))))) = s(elem!1)))),
% 1.87/2.03 inference(monotonicity,[status(thm)],[5648])).
% 1.87/2.03 tff(5650,plain,
% 1.87/2.03 (~(s(s(s(s(s(elem!1))))) = s(elem!1))),
% 1.87/2.03 inference(modus_ponens,[status(thm)],[1501, 5649])).
% 1.87/2.03 tff(5651,plain,
% 1.87/2.03 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[1795, 5650, 5646])).
% 1.87/2.03 tff(5652,plain,
% 1.87/2.03 (~b(s(elem!1), elem!1)),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[5208, 5651, 5461, 5612, 5458])).
% 1.87/2.03 tff(5653,assumption,(~(s(elem!1) = elem!1)), introduced(assumption)).
% 1.87/2.03 tff(5654,plain,
% 1.87/2.03 ($false),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[3437, 47, 4448, 5267, 5653])).
% 1.87/2.03 tff(5655,plain,(r(s(elem!1), elem!1) | b(s(elem!1), elem!1) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.87/2.03 tff(5656,plain,
% 1.87/2.03 (r(s(elem!1), elem!1)),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[5655, 5652, 5634])).
% 1.87/2.03 tff(5657,plain,
% 1.87/2.03 (~r(z, s(elem!1))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[5525, 183, 5365, 5656])).
% 1.87/2.03 tff(5658,plain,
% 1.87/2.03 (b(z, s(elem!1))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[2561, 5657])).
% 1.87/2.03 tff(5659,plain,
% 1.87/2.03 (~r(s(elem!1), z)),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[5533, 183, 5365, 5656])).
% 1.87/2.03 tff(5660,plain,
% 1.87/2.03 (b(s(elem!1), z)),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[2581, 5659])).
% 1.87/2.03 tff(5661,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(5662,plain,
% 1.87/2.03 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), z))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(5663,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))))),
% 1.87/2.03 inference(monotonicity,[status(thm)],[5662])).
% 1.87/2.03 tff(5664,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.87/2.03 inference(transitivity,[status(thm)],[5663, 5661])).
% 1.87/2.03 tff(5665,plain,
% 1.87/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 1.87/2.03 inference(quant_inst,[status(thm)],[])).
% 1.87/2.03 tff(5666,plain,
% 1.87/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.87/2.03 inference(modus_ponens,[status(thm)],[5665, 5664])).
% 1.87/2.03 tff(5667,plain,
% 1.87/2.03 (~b(s(s(s(s(s(elem!1))))), z)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[5666, 246, 5456, 5660, 5651, 5658])).
% 1.87/2.04 tff(5668,plain,
% 1.87/2.04 (r(s(s(s(s(s(elem!1))))), z)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[1601, 5667])).
% 1.87/2.04 tff(5669,assumption,(r(s(s(s(s(s(elem!1))))), z)), introduced(assumption)).
% 1.87/2.04 tff(5670,plain,
% 1.87/2.04 ($false),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[2378, 183, 172, 959, 5669])).
% 1.87/2.04 tff(5671,plain,((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.04 tff(5672,plain,
% 1.87/2.04 (~r(s(s(elem!1)), z)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[5671, 5668, 5626])).
% 1.87/2.04 tff(5673,plain,
% 1.87/2.04 (b(s(s(elem!1)), z)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[523, 5672])).
% 1.87/2.04 tff(5674,plain,
% 1.87/2.04 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(elem!1), elem!1)),
% 1.87/2.04 inference(monotonicity,[status(thm)],[5378, 1673])).
% 1.87/2.04 tff(5675,plain,
% 1.87/2.04 (b(s(elem!1), elem!1)),
% 1.87/2.04 inference(modus_ponens,[status(thm)],[1833, 5674])).
% 1.87/2.04 tff(5676,plain,
% 1.87/2.04 ($false),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[5267, 5675])).
% 1.87/2.04 tff(5677,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | b(s(elem!1), elem!1) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.04 tff(5678,plain,
% 1.87/2.04 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[5677, 5652, 1673])).
% 1.87/2.04 tff(5679,plain,
% 1.87/2.04 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[1702, 5678])).
% 1.87/2.04 tff(5680,plain,
% 1.87/2.04 (b(elem!1, s(s(s(z)))) <=> b(elem!1, elem!1)),
% 1.87/2.04 inference(monotonicity,[status(thm)],[1673])).
% 1.87/2.04 tff(5681,plain,
% 1.87/2.04 (b(elem!1, elem!1) <=> b(elem!1, s(s(s(z))))),
% 1.87/2.04 inference(symmetry,[status(thm)],[5680])).
% 1.87/2.04 tff(5682,plain,
% 1.87/2.04 ((~b(elem!1, elem!1)) <=> (~b(elem!1, s(s(s(z)))))),
% 1.87/2.04 inference(monotonicity,[status(thm)],[5681])).
% 1.87/2.04 tff(5683,plain,
% 1.87/2.04 (^[X: $i] : refl((~b(X, X)) <=> (~b(X, X)))),
% 1.87/2.04 inference(bind,[status(th)],[])).
% 1.87/2.04 tff(5684,plain,
% 1.87/2.04 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 1.87/2.04 inference(quant_intro,[status(thm)],[5683])).
% 1.87/2.04 tff(5685,plain,
% 1.87/2.04 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 1.87/2.04 inference(rewrite,[status(thm)],[])).
% 1.87/2.04 tff(5686,axiom,(![X: $i] : (~b(X, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bi')).
% 1.87/2.04 tff(5687,plain,
% 1.87/2.04 (![X: $i] : (~b(X, X))),
% 1.87/2.04 inference(modus_ponens,[status(thm)],[5686, 5685])).
% 1.87/2.04 tff(5688,plain,(
% 1.87/2.04 ![X: $i] : (~b(X, X))),
% 1.87/2.04 inference(skolemize,[status(sab)],[5687])).
% 1.87/2.04 tff(5689,plain,
% 1.87/2.04 (![X: $i] : (~b(X, X))),
% 1.87/2.04 inference(modus_ponens,[status(thm)],[5688, 5684])).
% 1.87/2.04 tff(5690,plain,
% 1.87/2.04 ((~![X: $i] : (~b(X, X))) | (~b(elem!1, elem!1))),
% 1.87/2.04 inference(quant_inst,[status(thm)],[])).
% 1.87/2.04 tff(5691,plain,
% 1.87/2.04 (~b(elem!1, elem!1)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[5690, 5689])).
% 1.87/2.04 tff(5692,plain,
% 1.87/2.04 (~b(elem!1, s(s(s(z))))),
% 1.87/2.04 inference(modus_ponens,[status(thm)],[5691, 5682])).
% 1.87/2.04 tff(5693,plain,
% 1.87/2.04 ((s(elem!1) = s(s(s(z)))) <=> (s(elem!1) = elem!1)),
% 1.87/2.04 inference(monotonicity,[status(thm)],[1673])).
% 1.87/2.04 tff(5694,plain,
% 1.87/2.04 ((s(elem!1) = s(s(s(z)))) <=> (elem!1 = s(elem!1))),
% 1.87/2.04 inference(transitivity,[status(thm)],[5693, 2825])).
% 1.87/2.04 tff(5695,plain,
% 1.87/2.04 ((elem!1 = s(elem!1)) <=> (s(elem!1) = s(s(s(z))))),
% 1.87/2.04 inference(symmetry,[status(thm)],[5694])).
% 1.87/2.04 tff(5696,plain,
% 1.87/2.04 ((s(s(s(s(z)))) = elem!1) <=> (s(elem!1) = s(s(s(z))))),
% 1.87/2.04 inference(transitivity,[status(thm)],[5628, 5695])).
% 1.87/2.04 tff(5697,plain,
% 1.87/2.04 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(s(elem!1) = s(s(s(z)))))),
% 1.87/2.04 inference(monotonicity,[status(thm)],[5696])).
% 1.87/2.04 tff(5698,plain,
% 1.87/2.04 (~(s(elem!1) = s(s(s(z))))),
% 1.87/2.04 inference(modus_ponens,[status(thm)],[5633, 5697])).
% 1.87/2.04 tff(5699,plain,
% 1.87/2.04 ((~b(z, elem!1)) <=> (~b(z, s(s(s(z)))))),
% 1.87/2.04 inference(monotonicity,[status(thm)],[2238])).
% 1.87/2.04 tff(5700,plain,
% 1.87/2.04 (~b(z, s(s(s(z))))),
% 1.87/2.04 inference(modus_ponens,[status(thm)],[55, 5699])).
% 1.87/2.04 tff(5701,plain,
% 1.87/2.04 (~(elem!1 = z)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[5400, 5365])).
% 1.87/2.04 tff(5702,plain,
% 1.87/2.04 (~b(z, s(s(s(s(s(elem!1))))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[5541, 246, 5660, 5651, 5658])).
% 1.87/2.04 tff(5703,assumption,(z = s(s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.87/2.04 tff(5704,plain,
% 1.87/2.04 (s(s(s(s(s(elem!1))))) = z),
% 1.87/2.04 inference(symmetry,[status(thm)],[5703])).
% 1.87/2.04 tff(5705,plain,
% 1.87/2.04 ($false),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[65, 5704])).
% 1.87/2.04 tff(5706,plain,(~(z = s(s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.04 tff(5707,plain,
% 1.87/2.04 (r(z, s(s(s(s(s(elem!1))))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[2487, 47, 5706, 5702])).
% 1.87/2.04 tff(5708,plain,
% 1.87/2.04 (~r(z, s(s(elem!1)))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[3325, 5707, 5626])).
% 1.87/2.04 tff(5709,plain,
% 1.87/2.04 (b(z, s(s(elem!1)))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[264, 5708])).
% 1.87/2.04 tff(5710,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))))),
% 1.87/2.04 inference(rewrite,[status(thm)],[])).
% 1.87/2.04 tff(5711,plain,
% 1.87/2.04 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))))),
% 1.87/2.04 inference(rewrite,[status(thm)],[])).
% 1.87/2.04 tff(5712,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1))))))),
% 1.87/2.04 inference(monotonicity,[status(thm)],[5711])).
% 1.87/2.04 tff(5713,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))))),
% 1.87/2.04 inference(transitivity,[status(thm)],[5712, 5710])).
% 1.87/2.04 tff(5714,plain,
% 1.87/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))),
% 1.87/2.04 inference(quant_inst,[status(thm)],[])).
% 1.87/2.04 tff(5715,plain,
% 1.87/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1))))),
% 1.87/2.04 inference(modus_ponens,[status(thm)],[5714, 5713])).
% 1.87/2.04 tff(5716,plain,
% 1.87/2.04 ((~b(elem!1, z)) | (~b(z, s(s(elem!1))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[5715, 246, 5673, 5456, 5461])).
% 1.87/2.04 tff(5717,plain,
% 1.87/2.04 (~b(elem!1, z)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[5716, 5709])).
% 1.87/2.04 tff(5718,plain,
% 1.87/2.04 (r(elem!1, z)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[1143, 5717, 5701])).
% 1.87/2.04 tff(5719,plain,
% 1.87/2.04 (~r(s(z), z)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[1163, 5718, 5453])).
% 1.87/2.04 tff(5720,plain,
% 1.87/2.04 (b(s(z), z)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[1069, 5719])).
% 1.87/2.04 tff(5721,plain,
% 1.87/2.04 (~b(s(s(s(s(z)))), s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[3297, 246, 1056, 236, 2601])).
% 1.87/2.04 tff(5722,plain,
% 1.87/2.04 (r(s(s(s(s(z)))), s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[2411, 47, 1713, 5721])).
% 1.87/2.04 tff(5723,plain,
% 1.87/2.04 (~b(s(s(s(z))), s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[2660, 2593, 69, 1056, 2232, 1749, 1445, 236, 1555, 2214, 1, 2213, 210])).
% 1.87/2.04 tff(5724,plain,
% 1.87/2.04 (r(s(s(s(z))), s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[52, 5723])).
% 1.87/2.04 tff(5725,plain,
% 1.87/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.87/2.04 inference(rewrite,[status(thm)],[])).
% 1.87/2.04 tff(5726,plain,
% 1.87/2.04 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.87/2.04 inference(rewrite,[status(thm)],[])).
% 1.87/2.04 tff(5727,plain,
% 1.87/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.87/2.04 inference(monotonicity,[status(thm)],[5726])).
% 1.87/2.04 tff(5728,plain,
% 1.87/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.87/2.04 inference(transitivity,[status(thm)],[5727, 5725])).
% 1.87/2.04 tff(5729,plain,
% 1.87/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.87/2.04 inference(quant_inst,[status(thm)],[])).
% 1.87/2.04 tff(5730,plain,
% 1.87/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.87/2.04 inference(modus_ponens,[status(thm)],[5729, 5728])).
% 1.87/2.04 tff(5731,plain,
% 1.87/2.04 ($false),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[5730, 183, 5724, 2593, 5722])).
% 1.87/2.04 tff(5732,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(z))) | b(z, s(s(s(z)))) | (s(s(s(s(s(elem!1))))) = elem!1) | r(s(s(elem!1)), elem!1) | (s(elem!1) = s(s(s(z)))) | b(s(z), elem!1) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | b(s(s(s(z))), elem!1) | b(elem!1, s(s(s(z)))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.04 tff(5733,plain,
% 1.87/2.04 (b(s(z), elem!1)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[5732, 5720, 2232, 69, 210, 5456, 5700, 5698, 5624, 1, 5692, 5679])).
% 1.87/2.04 tff(5734,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.87/2.04 inference(rewrite,[status(thm)],[])).
% 1.87/2.04 tff(5735,plain,
% 1.87/2.04 (((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(z)))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.87/2.04 inference(rewrite,[status(thm)],[])).
% 1.87/2.04 tff(5736,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(elem!1))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.87/2.04 inference(monotonicity,[status(thm)],[5735])).
% 1.87/2.04 tff(5737,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(elem!1))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.87/2.04 inference(transitivity,[status(thm)],[5736, 5734])).
% 1.87/2.04 tff(5738,plain,
% 1.87/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 1.87/2.04 inference(quant_inst,[status(thm)],[])).
% 1.87/2.04 tff(5739,plain,
% 1.87/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 1.87/2.04 inference(modus_ponens,[status(thm)],[5738, 5737])).
% 1.87/2.04 tff(5740,plain,
% 1.87/2.04 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[5739, 246, 5720, 5733, 5673, 5461, 5612])).
% 1.87/2.04 tff(5741,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))),
% 1.87/2.04 inference(rewrite,[status(thm)],[])).
% 1.87/2.04 tff(5742,plain,
% 1.87/2.04 (((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))),
% 1.87/2.04 inference(rewrite,[status(thm)],[])).
% 1.87/2.04 tff(5743,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1))))))),
% 1.87/2.04 inference(monotonicity,[status(thm)],[5742])).
% 1.87/2.04 tff(5744,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))),
% 1.87/2.04 inference(transitivity,[status(thm)],[5743, 5741])).
% 1.87/2.04 tff(5745,plain,
% 1.87/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))),
% 1.87/2.04 inference(quant_inst,[status(thm)],[])).
% 1.87/2.04 tff(5746,plain,
% 1.87/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1))))),
% 1.87/2.04 inference(modus_ponens,[status(thm)],[5745, 5744])).
% 1.87/2.04 tff(5747,plain,
% 1.87/2.04 (~b(s(z), s(s(elem!1)))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[5746, 246, 5720, 5673, 5456])).
% 1.87/2.04 tff(5748,plain,
% 1.87/2.04 (r(s(z), s(s(elem!1)))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[233, 5747])).
% 1.87/2.04 tff(5749,plain,
% 1.87/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.87/2.04 inference(rewrite,[status(thm)],[])).
% 1.87/2.04 tff(5750,plain,
% 1.87/2.04 (((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(z)))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.87/2.04 inference(rewrite,[status(thm)],[])).
% 1.87/2.04 tff(5751,plain,
% 1.87/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 1.87/2.04 inference(monotonicity,[status(thm)],[5750])).
% 1.87/2.04 tff(5752,plain,
% 1.87/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.87/2.04 inference(transitivity,[status(thm)],[5751, 5749])).
% 1.87/2.04 tff(5753,plain,
% 1.87/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 1.87/2.04 inference(quant_inst,[status(thm)],[])).
% 1.87/2.04 tff(5754,plain,
% 1.87/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 1.87/2.04 inference(modus_ponens,[status(thm)],[5753, 5752])).
% 1.87/2.04 tff(5755,plain,
% 1.87/2.04 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[5754, 183, 5748, 5626])).
% 1.87/2.04 tff(5756,plain,
% 1.87/2.04 ($false),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[2311, 47, 331, 5755, 5740])).
% 1.87/2.04 tff(5757,plain,((~(s(s(s(z))) = elem!1)) | r(s(s(elem!1)), elem!1) | (s(s(s(s(s(elem!1))))) = elem!1) | b(elem!1, s(z)) | b(s(s(s(z))), elem!1) | b(z, elem!1) | b(s(s(elem!1)), s(elem!1)) | r(elem!1, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.04 tff(5758,plain,
% 1.87/2.04 (~(s(s(s(z))) = elem!1)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[5757, 1, 69, 210, 2232, 55, 5035, 5454])).
% 1.87/2.04 tff(5759,plain,
% 1.87/2.04 (r(s(s(s(z))), elem!1)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[647, 5758, 1])).
% 1.87/2.04 tff(5760,plain,
% 1.87/2.04 (~r(s(s(s(z))), s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[2282, 5759, 2232, 210])).
% 1.87/2.04 tff(5761,plain,
% 1.87/2.04 (~b(s(s(s(z))), s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[5444, 5759, 5365, 5701, 5374, 5453, 5456])).
% 1.87/2.04 tff(5762,plain,
% 1.87/2.04 ($false),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[52, 5761, 5760])).
% 1.87/2.04 tff(5763,plain,(b(s(s(s(z))), elem!1) | r(s(s(elem!1)), elem!1) | b(elem!1, s(z)) | (s(s(s(s(s(elem!1))))) = elem!1) | b(z, elem!1) | b(s(s(elem!1)), s(elem!1)) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.04 tff(5764,plain,
% 1.87/2.04 (b(s(s(s(z))), elem!1)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[5763, 210, 2232, 69, 55, 5035, 2133])).
% 1.87/2.04 tff(5765,plain,
% 1.87/2.04 ((~b(s(s(elem!1)), s(z))) <=> (~b(s(s(elem!1)), elem!1))),
% 1.87/2.04 inference(monotonicity,[status(thm)],[204])).
% 1.87/2.04 tff(5766,plain,
% 1.87/2.04 (~b(s(s(elem!1)), elem!1)),
% 1.87/2.04 inference(modus_ponens,[status(thm)],[2124, 5765])).
% 1.87/2.04 tff(5767,plain,
% 1.87/2.04 ((~b(s(s(elem!1)), elem!1)) <=> (~b(s(s(s(z))), elem!1))),
% 1.87/2.04 inference(monotonicity,[status(thm)],[5565])).
% 1.87/2.04 tff(5768,plain,
% 1.87/2.04 (~b(s(s(s(z))), elem!1)),
% 1.87/2.04 inference(modus_ponens,[status(thm)],[145, 5767])).
% 1.87/2.04 tff(5769,plain,
% 1.87/2.04 ($false),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[3697, 5768])).
% 1.87/2.04 tff(5770,plain,((~(s(s(s(z))) = s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.87/2.04 tff(5771,plain,
% 1.87/2.04 (b(s(s(elem!1)), elem!1)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[5770, 3452, 3697])).
% 1.87/2.04 tff(5772,plain,
% 1.87/2.04 ($false),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[5771, 5766])).
% 1.87/2.04 tff(5773,plain,((~(elem!1 = s(z))) | b(s(s(elem!1)), s(z)) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.04 tff(5774,plain,
% 1.87/2.04 (~(elem!1 = s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[5773, 5764, 2124])).
% 1.87/2.04 tff(5775,plain,
% 1.87/2.04 (r(elem!1, s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[214, 5774, 210])).
% 1.87/2.04 tff(5776,plain,
% 1.87/2.04 (~r(z, s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[292, 5775, 5365])).
% 1.87/2.04 tff(5777,plain,
% 1.87/2.04 (b(z, s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[169, 5776])).
% 1.87/2.04 tff(5778,plain,
% 1.87/2.04 (~(s(z) = elem!1)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[9, 5774])).
% 1.87/2.04 tff(5779,plain,
% 1.87/2.04 (s(s(s(z))) = elem!1),
% 1.87/2.04 inference(symmetry,[status(thm)],[2292])).
% 1.87/2.04 tff(5780,plain,
% 1.87/2.04 (b(s(s(s(z))), elem!1) <=> b(elem!1, elem!1)),
% 1.87/2.04 inference(monotonicity,[status(thm)],[5779])).
% 1.87/2.04 tff(5781,plain,
% 1.87/2.04 (b(elem!1, elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.87/2.04 inference(symmetry,[status(thm)],[5780])).
% 1.87/2.04 tff(5782,plain,
% 1.87/2.04 ((~b(elem!1, elem!1)) <=> (~b(s(s(s(z))), elem!1))),
% 1.87/2.04 inference(monotonicity,[status(thm)],[5781])).
% 1.87/2.04 tff(5783,plain,
% 1.87/2.04 (~b(s(s(s(z))), elem!1)),
% 1.87/2.04 inference(modus_ponens,[status(thm)],[5691, 5782])).
% 1.87/2.04 tff(5784,plain,
% 1.87/2.04 ($false),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[3697, 5783])).
% 1.87/2.04 tff(5785,plain,((~(elem!1 = s(s(s(z))))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.04 tff(5786,plain,
% 1.87/2.04 (~(elem!1 = s(s(s(z))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[5785, 5764])).
% 1.87/2.04 tff(5787,plain,
% 1.87/2.04 ((s(z) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(z))),
% 1.87/2.04 inference(commutativity,[status(thm)],[])).
% 1.87/2.04 tff(5788,plain,
% 1.87/2.04 ((s(s(s(s(z)))) = s(z)) <=> (s(z) = s(s(s(s(z)))))),
% 1.87/2.04 inference(symmetry,[status(thm)],[5787])).
% 1.87/2.04 tff(5789,plain,
% 1.87/2.04 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(z) = s(s(s(s(z))))))),
% 1.87/2.04 inference(monotonicity,[status(thm)],[5788])).
% 1.87/2.04 tff(5790,plain,
% 1.87/2.04 (~(s(z) = s(s(s(s(z)))))),
% 1.87/2.04 inference(modus_ponens,[status(thm)],[1713, 5789])).
% 1.87/2.04 tff(5791,plain,
% 1.87/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(5792,plain,
% 1.87/2.05 (((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(5793,plain,
% 1.87/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[5792])).
% 1.87/2.05 tff(5794,plain,
% 1.87/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.87/2.05 inference(transitivity,[status(thm)],[5793, 5791])).
% 1.87/2.05 tff(5795,plain,
% 1.87/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))))),
% 1.87/2.05 inference(quant_inst,[status(thm)],[])).
% 1.87/2.05 tff(5796,plain,
% 1.87/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 1.87/2.05 inference(modus_ponens,[status(thm)],[5795, 5794])).
% 1.87/2.05 tff(5797,plain,
% 1.87/2.05 (~r(elem!1, s(s(s(z))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[5796, 183, 474, 430])).
% 1.87/2.05 tff(5798,plain,
% 1.87/2.05 (b(elem!1, s(s(s(z))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[470, 5797, 1675])).
% 1.87/2.05 tff(5799,plain,
% 1.87/2.05 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[97])).
% 1.87/2.05 tff(5800,plain,
% 1.87/2.05 (s(s(z)) = s(elem!1)),
% 1.87/2.05 inference(transitivity,[status(thm)],[25, 5799, 92])).
% 1.87/2.05 tff(5801,plain,
% 1.87/2.05 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[5800])).
% 1.87/2.05 tff(5802,plain,
% 1.87/2.05 (s(z) = elem!1),
% 1.87/2.05 inference(transitivity,[status(thm)],[1523, 5801, 343])).
% 1.87/2.05 tff(5803,plain,
% 1.87/2.05 ($false),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[2277, 5802])).
% 1.87/2.05 tff(5804,plain,((~(s(s(s(z))) = s(s(elem!1)))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.87/2.05 tff(5805,plain,
% 1.87/2.05 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[5804, 2277])).
% 1.87/2.05 tff(5806,plain,
% 1.87/2.05 (~(s(s(elem!1)) = s(s(s(z))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[421, 5805])).
% 1.87/2.05 tff(5807,plain,
% 1.87/2.05 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[4240, 183, 173, 430])).
% 1.87/2.05 tff(5808,plain,
% 1.87/2.05 (b(s(s(elem!1)), s(s(s(z))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[454, 5807, 5806])).
% 1.87/2.05 tff(5809,plain,
% 1.87/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(5810,plain,
% 1.87/2.05 (((~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(5811,plain,
% 1.87/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[5810])).
% 1.87/2.05 tff(5812,plain,
% 1.87/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.87/2.05 inference(transitivity,[status(thm)],[5811, 5809])).
% 1.87/2.05 tff(5813,plain,
% 1.87/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(elem!1)))))),
% 1.87/2.05 inference(quant_inst,[status(thm)],[])).
% 1.87/2.05 tff(5814,plain,
% 1.87/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.87/2.05 inference(modus_ponens,[status(thm)],[5813, 5812])).
% 1.87/2.05 tff(5815,plain,
% 1.87/2.05 (~b(elem!1, s(s(elem!1)))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[5814, 246, 5798, 3697, 5808])).
% 1.87/2.05 tff(5816,plain,
% 1.87/2.05 (elem!1 = s(s(elem!1))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[1268, 5815, 4200])).
% 1.87/2.05 tff(5817,plain,
% 1.87/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(5818,plain,
% 1.87/2.05 (((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(5819,plain,
% 1.87/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[5818])).
% 1.87/2.05 tff(5820,plain,
% 1.87/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.87/2.05 inference(transitivity,[status(thm)],[5819, 5817])).
% 1.87/2.05 tff(5821,plain,
% 1.87/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)))),
% 1.87/2.05 inference(quant_inst,[status(thm)],[])).
% 1.87/2.05 tff(5822,plain,
% 1.87/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.87/2.05 inference(modus_ponens,[status(thm)],[5821, 5820])).
% 1.87/2.05 tff(5823,plain,
% 1.87/2.05 (~b(s(s(elem!1)), elem!1)),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[5822, 246, 5798, 3697, 5808])).
% 1.87/2.05 tff(5824,plain,
% 1.87/2.05 (s(s(elem!1)) = elem!1),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[156, 5823, 2232])).
% 1.87/2.05 tff(5825,plain,
% 1.87/2.05 (s(s(s(elem!1))) = s(elem!1)),
% 1.87/2.05 inference(monotonicity,[status(thm)],[5824])).
% 1.87/2.05 tff(5826,plain,
% 1.87/2.05 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[5825])).
% 1.87/2.05 tff(5827,plain,
% 1.87/2.05 (s(s(s(s(elem!1)))) = elem!1),
% 1.87/2.05 inference(transitivity,[status(thm)],[5826, 5824])).
% 1.87/2.05 tff(5828,plain,
% 1.87/2.05 (s(s(s(s(s(elem!1))))) = s(elem!1)),
% 1.87/2.05 inference(monotonicity,[status(thm)],[5827])).
% 1.87/2.05 tff(5829,plain,
% 1.87/2.05 ((s(s(s(s(s(elem!1))))) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[5828])).
% 1.87/2.05 tff(5830,plain,
% 1.87/2.05 ((~(s(s(s(s(s(elem!1))))) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[5829])).
% 1.87/2.05 tff(5831,plain,
% 1.87/2.05 (~(s(elem!1) = s(s(s(z))))),
% 1.87/2.05 inference(modus_ponens,[status(thm)],[1622, 5830])).
% 1.87/2.05 tff(5832,plain,
% 1.87/2.05 (~(s(s(s(s(z)))) = elem!1)),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[2399, 5831, 5816])).
% 1.87/2.05 tff(5833,plain,
% 1.87/2.05 ((s(s(s(s(s(elem!1))))) = elem!1) <=> (s(elem!1) = elem!1)),
% 1.87/2.05 inference(monotonicity,[status(thm)],[5828])).
% 1.87/2.05 tff(5834,plain,
% 1.87/2.05 ((s(s(s(s(s(elem!1))))) = elem!1) <=> (elem!1 = s(elem!1))),
% 1.87/2.05 inference(transitivity,[status(thm)],[5833, 2825])).
% 1.87/2.05 tff(5835,plain,
% 1.87/2.05 ((~(s(s(s(s(s(elem!1))))) = elem!1)) <=> (~(elem!1 = s(elem!1)))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[5834])).
% 1.87/2.05 tff(5836,plain,
% 1.87/2.05 (~(elem!1 = s(elem!1))),
% 1.87/2.05 inference(modus_ponens,[status(thm)],[69, 5835])).
% 1.87/2.05 tff(5837,plain,
% 1.87/2.05 (b(s(s(elem!1)), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[5824])).
% 1.87/2.05 tff(5838,plain,
% 1.87/2.05 ((~b(s(s(elem!1)), s(elem!1))) <=> (~b(elem!1, s(elem!1)))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[5837])).
% 1.87/2.05 tff(5839,plain,
% 1.87/2.05 (~b(elem!1, s(elem!1))),
% 1.87/2.05 inference(modus_ponens,[status(thm)],[5035, 5838])).
% 1.87/2.05 tff(5840,plain,
% 1.87/2.05 (r(elem!1, s(elem!1))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[2864, 5839, 5836])).
% 1.87/2.05 tff(5841,plain,
% 1.87/2.05 (s(elem!1) = s(s(s(s(s(elem!1)))))),
% 1.87/2.05 inference(symmetry,[status(thm)],[5828])).
% 1.87/2.05 tff(5842,plain,
% 1.87/2.05 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[5841])).
% 1.87/2.05 tff(5843,plain,
% 1.87/2.05 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 1.87/2.05 inference(symmetry,[status(thm)],[5842])).
% 1.87/2.05 tff(5844,plain,
% 1.87/2.05 ((~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[5843])).
% 1.87/2.05 tff(5845,plain,
% 1.87/2.05 (~(s(s(s(s(z)))) = s(elem!1))),
% 1.87/2.05 inference(modus_ponens,[status(thm)],[1501, 5844])).
% 1.87/2.05 tff(5846,plain,
% 1.87/2.05 (~r(z, s(z))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[292, 474, 267])).
% 1.87/2.05 tff(5847,plain,
% 1.87/2.05 (b(z, s(z))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[169, 5846])).
% 1.87/2.05 tff(5848,plain,
% 1.87/2.05 (r(z, s(s(elem!1))) <=> r(z, elem!1)),
% 1.87/2.05 inference(monotonicity,[status(thm)],[5824])).
% 1.87/2.05 tff(5849,plain,
% 1.87/2.05 (r(z, elem!1) <=> r(z, s(s(elem!1)))),
% 1.87/2.05 inference(symmetry,[status(thm)],[5848])).
% 1.87/2.05 tff(5850,plain,
% 1.87/2.05 (r(z, s(s(elem!1)))),
% 1.87/2.05 inference(modus_ponens,[status(thm)],[267, 5849])).
% 1.87/2.05 tff(5851,plain,
% 1.87/2.05 (r(s(s(elem!1)), s(s(s(s(s(elem!1)))))) <=> r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[5824])).
% 1.87/2.05 tff(5852,plain,
% 1.87/2.05 (r(elem!1, s(s(s(s(s(elem!1)))))) <=> r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.87/2.05 inference(symmetry,[status(thm)],[5851])).
% 1.87/2.05 tff(5853,plain,
% 1.87/2.05 (r(elem!1, s(s(s(s(s(elem!1)))))) <=> r(elem!1, s(elem!1))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[5828])).
% 1.87/2.05 tff(5854,plain,
% 1.87/2.05 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.87/2.05 inference(symmetry,[status(thm)],[5853])).
% 1.87/2.05 tff(5855,plain,
% 1.87/2.05 (r(elem!1, s(elem!1)) <=> r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.87/2.05 inference(transitivity,[status(thm)],[5854, 5852])).
% 1.87/2.05 tff(5856,plain,
% 1.87/2.05 (r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.87/2.05 inference(modus_ponens,[status(thm)],[5840, 5855])).
% 1.87/2.05 tff(5857,plain,
% 1.87/2.05 (~r(z, s(s(s(s(s(elem!1))))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[3314, 5856, 5850])).
% 1.87/2.05 tff(5858,plain,
% 1.87/2.05 (s(s(s(elem!1))) = s(elem!1)),
% 1.87/2.05 inference(monotonicity,[status(thm)],[2125])).
% 1.87/2.05 tff(5859,plain,
% 1.87/2.05 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[5858])).
% 1.87/2.05 tff(5860,plain,
% 1.87/2.05 (s(s(s(s(elem!1)))) = elem!1),
% 1.87/2.05 inference(transitivity,[status(thm)],[5859, 2125])).
% 1.87/2.05 tff(5861,plain,
% 1.87/2.05 (s(s(s(s(s(elem!1))))) = s(elem!1)),
% 1.87/2.05 inference(monotonicity,[status(thm)],[5860])).
% 1.87/2.05 tff(5862,plain,
% 1.87/2.05 (r(z, s(s(s(s(s(elem!1)))))) <=> r(z, s(elem!1))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[5861])).
% 1.87/2.05 tff(5863,plain,
% 1.87/2.05 (r(z, s(elem!1)) <=> r(z, s(s(s(s(s(elem!1))))))),
% 1.87/2.05 inference(symmetry,[status(thm)],[5862])).
% 1.87/2.05 tff(5864,assumption,(r(z, s(elem!1))), introduced(assumption)).
% 1.87/2.05 tff(5865,plain,
% 1.87/2.05 (r(z, s(s(s(s(s(elem!1))))))),
% 1.87/2.05 inference(modus_ponens,[status(thm)],[5864, 5863])).
% 1.87/2.05 tff(5866,assumption,(~r(z, s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.87/2.05 tff(5867,plain,
% 1.87/2.05 ($false),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[5866, 5865])).
% 1.87/2.05 tff(5868,plain,((~r(z, s(elem!1))) | r(z, s(s(s(s(s(elem!1)))))) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.05 tff(5869,plain,
% 1.87/2.05 (~r(z, s(elem!1))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[5868, 5857, 5824])).
% 1.87/2.05 tff(5870,plain,
% 1.87/2.05 (b(z, s(elem!1))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[2561, 5869])).
% 1.87/2.05 tff(5871,plain,
% 1.87/2.05 ((s(s(s(s(s(elem!1))))) = elem!1) <=> (s(elem!1) = elem!1)),
% 1.87/2.05 inference(transitivity,[status(thm)],[5834, 3423])).
% 1.87/2.05 tff(5872,plain,
% 1.87/2.05 ((~(s(s(s(s(s(elem!1))))) = elem!1)) <=> (~(s(elem!1) = elem!1))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[5871])).
% 1.87/2.05 tff(5873,plain,
% 1.87/2.05 (~(s(elem!1) = elem!1)),
% 1.87/2.05 inference(modus_ponens,[status(thm)],[69, 5872])).
% 1.87/2.05 tff(5874,plain,
% 1.87/2.05 (s(elem!1) = s(s(s(s(s(elem!1)))))),
% 1.87/2.05 inference(symmetry,[status(thm)],[5861])).
% 1.87/2.05 tff(5875,plain,
% 1.87/2.05 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[5874])).
% 1.87/2.05 tff(5876,plain,
% 1.87/2.05 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 1.87/2.05 inference(symmetry,[status(thm)],[5875])).
% 1.87/2.05 tff(5877,plain,
% 1.87/2.05 ((~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[5876])).
% 1.87/2.05 tff(5878,plain,
% 1.87/2.05 (~(s(s(s(s(z)))) = s(elem!1))),
% 1.87/2.05 inference(modus_ponens,[status(thm)],[1501, 5877])).
% 1.87/2.05 tff(5879,plain,
% 1.87/2.05 ((s(s(s(s(z)))) = elem!1) <=> (elem!1 = s(s(s(s(z)))))),
% 1.87/2.05 inference(symmetry,[status(thm)],[3067])).
% 1.87/2.05 tff(5880,plain,
% 1.87/2.05 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(elem!1 = s(s(s(s(z))))))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[5879])).
% 1.87/2.05 tff(5881,plain,
% 1.87/2.05 (~(elem!1 = s(s(s(s(z)))))),
% 1.87/2.05 inference(modus_ponens,[status(thm)],[3074, 5880])).
% 1.87/2.05 tff(5882,plain,
% 1.87/2.05 (r(z, s(s(elem!1))) <=> r(z, elem!1)),
% 1.87/2.05 inference(monotonicity,[status(thm)],[2125])).
% 1.87/2.05 tff(5883,plain,
% 1.87/2.05 (r(z, elem!1) <=> r(z, s(s(elem!1)))),
% 1.87/2.05 inference(symmetry,[status(thm)],[5882])).
% 1.87/2.05 tff(5884,plain,
% 1.87/2.05 (r(z, s(s(elem!1)))),
% 1.87/2.05 inference(modus_ponens,[status(thm)],[267, 5883])).
% 1.87/2.05 tff(5885,plain,
% 1.87/2.05 (r(s(s(elem!1)), s(s(s(s(s(elem!1)))))) <=> r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[2125])).
% 1.87/2.05 tff(5886,plain,
% 1.87/2.05 (r(elem!1, s(s(s(s(s(elem!1)))))) <=> r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.87/2.05 inference(symmetry,[status(thm)],[5885])).
% 1.87/2.05 tff(5887,plain,
% 1.87/2.05 (r(elem!1, s(s(s(s(s(elem!1)))))) <=> r(elem!1, s(elem!1))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[5861])).
% 1.87/2.05 tff(5888,plain,
% 1.87/2.05 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.87/2.05 inference(symmetry,[status(thm)],[5887])).
% 1.87/2.05 tff(5889,plain,
% 1.87/2.05 (r(elem!1, s(elem!1)) <=> r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.87/2.05 inference(transitivity,[status(thm)],[5888, 5886])).
% 1.87/2.05 tff(5890,plain,
% 1.87/2.05 (r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.87/2.05 inference(modus_ponens,[status(thm)],[601, 5889])).
% 1.87/2.05 tff(5891,plain,
% 1.87/2.05 (~r(z, s(s(s(s(s(elem!1))))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[3314, 5890, 5884])).
% 1.87/2.05 tff(5892,plain,
% 1.87/2.05 (~r(z, s(elem!1))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[5868, 5891, 2125])).
% 1.87/2.05 tff(5893,plain,
% 1.87/2.05 (b(z, s(elem!1))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[2561, 5892])).
% 1.87/2.05 tff(5894,plain,
% 1.87/2.05 ((s(s(s(s(s(elem!1))))) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[5861])).
% 1.87/2.05 tff(5895,plain,
% 1.87/2.05 ((~(s(s(s(s(s(elem!1))))) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[5894])).
% 1.87/2.05 tff(5896,plain,
% 1.87/2.05 (~(s(elem!1) = s(s(s(z))))),
% 1.87/2.05 inference(modus_ponens,[status(thm)],[1622, 5895])).
% 1.87/2.05 tff(5897,plain,
% 1.87/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(5898,plain,
% 1.87/2.05 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(5899,plain,
% 1.87/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z)))))))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[5898])).
% 1.87/2.05 tff(5900,plain,
% 1.87/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.87/2.05 inference(transitivity,[status(thm)],[5899, 5897])).
% 1.87/2.05 tff(5901,plain,
% 1.87/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.87/2.05 inference(quant_inst,[status(thm)],[])).
% 1.87/2.05 tff(5902,plain,
% 1.87/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z)))))),
% 1.87/2.05 inference(modus_ponens,[status(thm)],[5901, 5900])).
% 1.87/2.05 tff(5903,plain,
% 1.87/2.05 (~b(s(elem!1), s(s(s(z))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[5902, 246, 2002, 3697, 1200])).
% 1.87/2.05 tff(5904,plain,
% 1.87/2.05 (r(s(elem!1), s(s(s(z))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[1754, 5903, 5896])).
% 1.87/2.05 tff(5905,plain,
% 1.87/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(5906,plain,
% 1.87/2.05 (((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(5907,plain,
% 1.87/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[5906])).
% 1.87/2.05 tff(5908,plain,
% 1.87/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.87/2.05 inference(transitivity,[status(thm)],[5907, 5905])).
% 1.87/2.05 tff(5909,plain,
% 1.87/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.87/2.05 inference(quant_inst,[status(thm)],[])).
% 1.87/2.05 tff(5910,plain,
% 1.87/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.87/2.05 inference(modus_ponens,[status(thm)],[5909, 5908])).
% 1.87/2.05 tff(5911,plain,
% 1.87/2.05 (~r(s(s(s(s(z)))), s(elem!1))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[5910, 183, 2593, 5904])).
% 1.87/2.05 tff(5912,plain,
% 1.87/2.05 (b(s(s(s(s(z)))), s(elem!1))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[1728, 5911, 5878])).
% 1.87/2.05 tff(5913,assumption,(b(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 1.87/2.05 tff(5914,assumption,(b(s(s(s(s(z)))), s(elem!1))), introduced(assumption)).
% 1.87/2.05 tff(5915,plain,
% 1.87/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(5916,plain,
% 1.87/2.05 (((~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1)))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(5917,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 1.87/2.06 inference(monotonicity,[status(thm)],[5916])).
% 1.87/2.06 tff(5918,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.87/2.06 inference(transitivity,[status(thm)],[5917, 5915])).
% 1.87/2.06 tff(5919,plain,
% 1.87/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.87/2.06 inference(quant_inst,[status(thm)],[])).
% 1.87/2.06 tff(5920,plain,
% 1.87/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 1.87/2.06 inference(modus_ponens,[status(thm)],[5919, 5918])).
% 1.87/2.06 tff(5921,plain,
% 1.87/2.06 ($false),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[5920, 246, 2002, 3697, 1200, 5914, 5913])).
% 1.87/2.06 tff(5922,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.06 tff(5923,plain,
% 1.87/2.06 (~b(s(s(s(s(z)))), elem!1)),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[5922, 5912, 3697, 1200, 2002])).
% 1.87/2.06 tff(5924,plain,
% 1.87/2.06 (r(s(s(s(s(z)))), elem!1)),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[2442, 47, 3074, 5923])).
% 1.87/2.06 tff(5925,plain,
% 1.87/2.06 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.87/2.06 inference(monotonicity,[status(thm)],[5874])).
% 1.87/2.06 tff(5926,plain,
% 1.87/2.06 (b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 1.87/2.06 inference(symmetry,[status(thm)],[5925])).
% 1.87/2.06 tff(5927,plain,
% 1.87/2.06 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.87/2.06 inference(monotonicity,[status(thm)],[5874])).
% 1.87/2.06 tff(5928,plain,
% 1.87/2.06 ((~r(s(elem!1), s(s(s(s(z)))))) <=> (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))),
% 1.87/2.06 inference(monotonicity,[status(thm)],[5927])).
% 1.87/2.06 tff(5929,plain,
% 1.87/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(5930,plain,
% 1.87/2.06 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(z))))))) <=> ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(5931,plain,
% 1.87/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 1.87/2.06 inference(monotonicity,[status(thm)],[5930])).
% 1.87/2.06 tff(5932,plain,
% 1.87/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.87/2.06 inference(transitivity,[status(thm)],[5931, 5929])).
% 1.87/2.06 tff(5933,plain,
% 1.87/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.87/2.06 inference(quant_inst,[status(thm)],[])).
% 1.87/2.06 tff(5934,plain,
% 1.87/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 1.87/2.06 inference(modus_ponens,[status(thm)],[5933, 5932])).
% 1.87/2.06 tff(5935,plain,
% 1.87/2.06 (~r(s(elem!1), s(s(s(s(z)))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[5934, 183, 2593, 5904])).
% 1.87/2.06 tff(5936,plain,
% 1.87/2.06 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.87/2.06 inference(modus_ponens,[status(thm)],[5935, 5928])).
% 1.87/2.06 tff(5937,plain,
% 1.87/2.06 (b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[1897, 5936])).
% 1.87/2.06 tff(5938,plain,
% 1.87/2.06 (b(s(elem!1), s(s(s(s(z)))))),
% 1.87/2.06 inference(modus_ponens,[status(thm)],[5937, 5926])).
% 1.87/2.06 tff(5939,assumption,(b(z, s(elem!1))), introduced(assumption)).
% 1.87/2.06 tff(5940,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(5941,plain,
% 1.87/2.06 (((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(5942,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 1.87/2.06 inference(monotonicity,[status(thm)],[5941])).
% 1.87/2.06 tff(5943,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.87/2.06 inference(transitivity,[status(thm)],[5942, 5940])).
% 1.87/2.06 tff(5944,plain,
% 1.87/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(z)))))))),
% 1.87/2.06 inference(quant_inst,[status(thm)],[])).
% 1.87/2.06 tff(5945,plain,
% 1.87/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 1.87/2.06 inference(modus_ponens,[status(thm)],[5944, 5943])).
% 1.87/2.06 tff(5946,plain,
% 1.87/2.06 ((~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[5945, 246, 5912, 5939])).
% 1.87/2.06 tff(5947,plain,
% 1.87/2.06 (~b(z, s(s(s(s(z)))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[5946, 5938])).
% 1.87/2.06 tff(5948,plain,
% 1.87/2.06 ((z = s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[2645, 47, 5947])).
% 1.87/2.06 tff(5949,plain,
% 1.87/2.06 (r(z, s(s(s(s(z)))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[5948, 2635])).
% 1.87/2.06 tff(5950,plain,
% 1.87/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(5951,plain,
% 1.87/2.06 (((~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(5952,plain,
% 1.87/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z))))))))),
% 1.87/2.06 inference(monotonicity,[status(thm)],[5951])).
% 1.87/2.06 tff(5953,plain,
% 1.87/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))))),
% 1.87/2.06 inference(transitivity,[status(thm)],[5952, 5950])).
% 1.87/2.06 tff(5954,plain,
% 1.87/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))))),
% 1.87/2.06 inference(quant_inst,[status(thm)],[])).
% 1.87/2.06 tff(5955,plain,
% 1.87/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z))))))),
% 1.87/2.06 inference(modus_ponens,[status(thm)],[5954, 5953])).
% 1.87/2.06 tff(5956,plain,
% 1.87/2.06 ($false),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[5955, 183, 267, 5949, 5924])).
% 1.87/2.06 tff(5957,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, elem!1)) | (s(s(s(s(z)))) = elem!1) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(elem!1))) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.06 tff(5958,plain,
% 1.87/2.06 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[5957, 1200, 3074, 3697, 267, 2002, 5893, 2125])).
% 1.87/2.06 tff(5959,plain,
% 1.87/2.06 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[1702, 5958])).
% 1.87/2.06 tff(5960,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(5961,plain,
% 1.87/2.06 (((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(5962,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z))))))))),
% 1.87/2.06 inference(monotonicity,[status(thm)],[5961])).
% 1.87/2.06 tff(5963,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.87/2.06 inference(transitivity,[status(thm)],[5962, 5960])).
% 1.87/2.06 tff(5964,plain,
% 1.87/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.87/2.06 inference(quant_inst,[status(thm)],[])).
% 1.87/2.06 tff(5965,plain,
% 1.87/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z))))))),
% 1.87/2.06 inference(modus_ponens,[status(thm)],[5964, 5963])).
% 1.87/2.06 tff(5966,plain,
% 1.87/2.06 (~b(elem!1, s(s(s(s(z)))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[5965, 246, 2002, 3697, 5959])).
% 1.87/2.06 tff(5967,plain,
% 1.87/2.06 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z))))))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(5968,plain,
% 1.87/2.06 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z))))))),
% 1.87/2.06 inference(quant_inst,[status(thm)],[])).
% 1.87/2.06 tff(5969,plain,
% 1.87/2.06 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z)))))),
% 1.87/2.06 inference(modus_ponens,[status(thm)],[5968, 5967])).
% 1.87/2.06 tff(5970,plain,
% 1.87/2.06 ((elem!1 = s(s(s(s(z))))) | r(elem!1, s(s(s(s(z)))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[5969, 47, 5966])).
% 1.87/2.06 tff(5971,plain,
% 1.87/2.06 (r(elem!1, s(s(s(s(z)))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[5970, 5881])).
% 1.87/2.06 tff(5972,assumption,(r(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 1.87/2.06 tff(5973,assumption,(r(s(s(s(s(z)))), s(elem!1))), introduced(assumption)).
% 1.87/2.06 tff(5974,plain,
% 1.87/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(5975,plain,
% 1.87/2.06 (((~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(5976,plain,
% 1.87/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1)))))),
% 1.87/2.06 inference(monotonicity,[status(thm)],[5975])).
% 1.87/2.06 tff(5977,plain,
% 1.87/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.87/2.06 inference(transitivity,[status(thm)],[5976, 5974])).
% 1.87/2.06 tff(5978,plain,
% 1.87/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.87/2.06 inference(quant_inst,[status(thm)],[])).
% 1.87/2.06 tff(5979,plain,
% 1.87/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 1.87/2.06 inference(modus_ponens,[status(thm)],[5978, 5977])).
% 1.87/2.06 tff(5980,plain,
% 1.87/2.06 ($false),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[5979, 183, 601, 5973, 5972])).
% 1.87/2.06 tff(5981,plain,((~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.06 tff(5982,plain,
% 1.87/2.06 (~r(s(s(s(s(z)))), s(elem!1))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[5981, 5971, 601])).
% 1.87/2.06 tff(5983,plain,
% 1.87/2.06 (b(s(s(s(s(z)))), s(elem!1))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[1728, 5982, 5878])).
% 1.87/2.06 tff(5984,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z)))))))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(5985,plain,
% 1.87/2.06 (((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z)))))))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(5986,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z))))))))),
% 1.87/2.06 inference(monotonicity,[status(thm)],[5985])).
% 1.87/2.06 tff(5987,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z)))))))),
% 1.87/2.06 inference(transitivity,[status(thm)],[5986, 5984])).
% 1.87/2.06 tff(5988,plain,
% 1.87/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(z)))))))),
% 1.87/2.06 inference(quant_inst,[status(thm)],[])).
% 1.87/2.06 tff(5989,plain,
% 1.87/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z))))))),
% 1.87/2.06 inference(modus_ponens,[status(thm)],[5988, 5987])).
% 1.87/2.06 tff(5990,plain,
% 1.87/2.06 ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z))))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[5989, 246, 2002, 1200, 5893, 5959])).
% 1.87/2.06 tff(5991,plain,
% 1.87/2.06 (~b(z, s(s(s(s(z)))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[5990, 5983])).
% 1.87/2.06 tff(5992,plain,
% 1.87/2.06 ((z = s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[2645, 47, 5991])).
% 1.87/2.06 tff(5993,plain,
% 1.87/2.06 (r(z, s(s(s(s(z)))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[5992, 2635])).
% 1.87/2.06 tff(5994,plain,
% 1.87/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(5995,plain,
% 1.87/2.06 (((~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(5996,plain,
% 1.87/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))))),
% 1.87/2.06 inference(monotonicity,[status(thm)],[5995])).
% 1.87/2.06 tff(5997,plain,
% 1.87/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 1.87/2.07 inference(transitivity,[status(thm)],[5996, 5994])).
% 1.87/2.07 tff(5998,plain,
% 1.87/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~r(z, elem!1)))),
% 1.87/2.07 inference(quant_inst,[status(thm)],[])).
% 1.87/2.07 tff(5999,plain,
% 1.87/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))),
% 1.87/2.07 inference(modus_ponens,[status(thm)],[5998, 5997])).
% 1.87/2.07 tff(6000,plain,
% 1.87/2.07 ($false),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[5999, 183, 267, 474, 5971, 5993])).
% 1.87/2.07 tff(6001,plain,((~b(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~r(elem!1, s(elem!1))) | (s(s(s(s(z)))) = elem!1) | (~b(s(s(s(z))), elem!1)) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.07 tff(6002,plain,
% 1.87/2.07 (~b(s(elem!1), elem!1)),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[6001, 5798, 474, 267, 5840, 5832, 3697, 5824])).
% 1.87/2.07 tff(6003,plain,
% 1.87/2.07 (r(s(elem!1), elem!1)),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[5655, 6002, 5873])).
% 1.87/2.07 tff(6004,plain,
% 1.87/2.07 (~r(s(elem!1), z)),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[5533, 183, 267, 6003])).
% 1.87/2.07 tff(6005,plain,
% 1.87/2.07 (b(s(elem!1), z)),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[2581, 6004])).
% 1.87/2.07 tff(6006,assumption,(~(s(s(s(s(z)))) = s(elem!1))), introduced(assumption)).
% 1.87/2.07 tff(6007,plain,
% 1.87/2.07 (~b(elem!1, s(s(s(s(z)))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[5965, 246, 2002, 3697, 1833])).
% 1.87/2.07 tff(6008,plain,
% 1.87/2.07 ((elem!1 = s(s(s(s(z))))) | r(elem!1, s(s(s(s(z)))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[5969, 47, 6007])).
% 1.87/2.07 tff(6009,plain,
% 1.87/2.07 (r(elem!1, s(s(s(s(z)))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[6008, 5881])).
% 1.87/2.07 tff(6010,plain,
% 1.87/2.07 (~r(s(s(s(s(z)))), s(elem!1))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[5981, 6009, 601])).
% 1.87/2.07 tff(6011,plain,
% 1.87/2.07 (b(s(s(s(s(z)))), s(elem!1))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[1728, 6010, 6006])).
% 1.87/2.07 tff(6012,assumption,(b(s(elem!1), z)), introduced(assumption)).
% 1.87/2.07 tff(6013,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z)))))))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(6014,plain,
% 1.87/2.07 (((~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z)))))))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(6015,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z))))))))),
% 1.87/2.07 inference(monotonicity,[status(thm)],[6014])).
% 1.87/2.07 tff(6016,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z)))))))),
% 1.87/2.07 inference(transitivity,[status(thm)],[6015, 6013])).
% 1.87/2.07 tff(6017,plain,
% 1.87/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(z)))))))),
% 1.87/2.07 inference(quant_inst,[status(thm)],[])).
% 1.87/2.07 tff(6018,plain,
% 1.87/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z))))))),
% 1.87/2.07 inference(modus_ponens,[status(thm)],[6017, 6016])).
% 1.87/2.07 tff(6019,plain,
% 1.87/2.07 (~b(z, s(s(s(s(z)))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[6018, 246, 6012, 6011, 5939])).
% 1.87/2.07 tff(6020,plain,
% 1.87/2.07 ((z = s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[2645, 47, 6019])).
% 1.87/2.07 tff(6021,plain,
% 1.87/2.07 (r(z, s(s(s(s(z)))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[6020, 2635])).
% 1.87/2.07 tff(6022,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(6023,plain,
% 1.87/2.07 (((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(6024,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.87/2.07 inference(monotonicity,[status(thm)],[6023])).
% 1.87/2.07 tff(6025,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.87/2.07 inference(transitivity,[status(thm)],[6024, 6022])).
% 1.87/2.07 tff(6026,plain,
% 1.87/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.87/2.07 inference(quant_inst,[status(thm)],[])).
% 1.87/2.07 tff(6027,plain,
% 1.87/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.87/2.07 inference(modus_ponens,[status(thm)],[6026, 6025])).
% 1.87/2.07 tff(6028,plain,
% 1.87/2.07 (~b(s(s(s(s(z)))), elem!1)),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[6027, 246, 2002, 3697, 1833])).
% 1.87/2.07 tff(6029,plain,
% 1.87/2.07 (r(s(s(s(s(z)))), elem!1)),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[2442, 47, 3074, 6028])).
% 1.87/2.07 tff(6030,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), z)))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(6031,plain,
% 1.87/2.07 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(z))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), z)))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(6032,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), z))))),
% 1.87/2.07 inference(monotonicity,[status(thm)],[6031])).
% 1.87/2.07 tff(6033,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), z)))),
% 1.87/2.07 inference(transitivity,[status(thm)],[6032, 6030])).
% 1.87/2.07 tff(6034,plain,
% 1.87/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), z)))),
% 1.87/2.07 inference(quant_inst,[status(thm)],[])).
% 1.87/2.07 tff(6035,plain,
% 1.87/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), z))),
% 1.87/2.07 inference(modus_ponens,[status(thm)],[6034, 6033])).
% 1.87/2.07 tff(6036,plain,
% 1.87/2.07 (~b(s(s(s(s(z)))), z)),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[6035, 246, 236, 6012, 6011, 5939])).
% 1.87/2.07 tff(6037,assumption,(~b(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.87/2.07 tff(6038,assumption,(~r(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.87/2.07 tff(6039,plain,
% 1.87/2.07 ($false),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[2424, 47, 2421, 6038, 6037])).
% 1.87/2.07 tff(6040,plain,(b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 1.87/2.07 tff(6041,plain,
% 1.87/2.07 (r(s(s(s(s(z)))), z)),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[6040, 6036])).
% 1.87/2.07 tff(6042,plain,
% 1.87/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(6043,plain,
% 1.87/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.87/2.07 inference(quant_inst,[status(thm)],[])).
% 1.87/2.07 tff(6044,plain,
% 1.87/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 1.87/2.07 inference(modus_ponens,[status(thm)],[6043, 6042])).
% 1.87/2.07 tff(6045,plain,
% 1.87/2.07 ($false),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[6044, 183, 267, 6041, 6029, 6021])).
% 1.87/2.07 tff(6046,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (s(s(s(s(z)))) = s(elem!1)) | (~r(elem!1, s(elem!1))) | (s(s(s(s(z)))) = elem!1) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.07 tff(6047,plain,
% 1.87/2.07 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[6046, 6005, 267, 5870, 5847, 5845, 5840, 5832, 5798, 3697])).
% 1.87/2.07 tff(6048,plain,
% 1.87/2.07 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[1702, 6047])).
% 1.87/2.07 tff(6049,plain,
% 1.87/2.07 ((s(z) = s(elem!1)) <=> (s(z) = s(s(s(s(s(elem!1))))))),
% 1.87/2.07 inference(monotonicity,[status(thm)],[5874])).
% 1.87/2.07 tff(6050,plain,
% 1.87/2.07 ((s(z) = s(elem!1)) <=> (s(s(s(s(s(elem!1))))) = s(z))),
% 1.87/2.07 inference(transitivity,[status(thm)],[6049, 317])).
% 1.87/2.07 tff(6051,plain,
% 1.87/2.07 ((s(s(s(s(s(elem!1))))) = s(z)) <=> (s(z) = s(elem!1))),
% 1.87/2.07 inference(symmetry,[status(thm)],[6050])).
% 1.87/2.07 tff(6052,plain,
% 1.87/2.07 ((~(s(s(s(s(s(elem!1))))) = s(z))) <=> (~(s(z) = s(elem!1)))),
% 1.87/2.07 inference(monotonicity,[status(thm)],[6051])).
% 1.87/2.07 tff(6053,plain,
% 1.87/2.07 (~(s(z) = s(elem!1))),
% 1.87/2.07 inference(modus_ponens,[status(thm)],[331, 6052])).
% 1.87/2.07 tff(6054,plain,
% 1.87/2.07 (~r(s(z), z)),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[5432, 267, 217])).
% 1.87/2.07 tff(6055,plain,
% 1.87/2.07 (b(s(z), z)),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[1069, 6054])).
% 1.87/2.07 tff(6056,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(6057,plain,
% 1.87/2.07 (((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(6058,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1)))))),
% 1.87/2.07 inference(monotonicity,[status(thm)],[6057])).
% 1.87/2.07 tff(6059,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))))),
% 1.87/2.07 inference(transitivity,[status(thm)],[6058, 6056])).
% 1.87/2.07 tff(6060,plain,
% 1.87/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 1.87/2.07 inference(quant_inst,[status(thm)],[])).
% 1.87/2.07 tff(6061,plain,
% 1.87/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1)))),
% 1.87/2.07 inference(modus_ponens,[status(thm)],[6060, 6059])).
% 1.87/2.07 tff(6062,plain,
% 1.87/2.07 (~b(s(z), s(elem!1))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[6061, 246, 6055, 236, 5535])).
% 1.87/2.07 tff(6063,plain,
% 1.87/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), elem!1)))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(6064,plain,
% 1.87/2.07 (((~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1)))) <=> ((~r(s(z), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), elem!1)))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(6065,plain,
% 1.87/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), elem!1))))),
% 1.87/2.07 inference(monotonicity,[status(thm)],[6064])).
% 1.87/2.07 tff(6066,plain,
% 1.87/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), elem!1)))),
% 1.87/2.07 inference(transitivity,[status(thm)],[6065, 6063])).
% 1.87/2.07 tff(6067,plain,
% 1.87/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))))),
% 1.87/2.07 inference(quant_inst,[status(thm)],[])).
% 1.87/2.07 tff(6068,plain,
% 1.87/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), elem!1))),
% 1.87/2.07 inference(modus_ponens,[status(thm)],[6067, 6066])).
% 1.87/2.07 tff(6069,plain,
% 1.87/2.07 (~r(s(z), s(elem!1))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[6068, 183, 217, 367])).
% 1.87/2.07 tff(6070,plain,
% 1.87/2.07 ((s(z) = s(elem!1)) | b(s(z), s(elem!1))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[2973, 47, 6069])).
% 1.87/2.07 tff(6071,plain,
% 1.87/2.07 ($false),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[6070, 6062, 6053])).
% 1.87/2.07 tff(6072,plain,((~r(s(elem!1), elem!1)) | (~b(z, s(z))) | (~(s(s(elem!1)) = elem!1)) | (~r(z, elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.07 tff(6073,plain,
% 1.87/2.07 (~r(s(z), elem!1)),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[6072, 6003, 267, 5824, 5847])).
% 1.87/2.07 tff(6074,plain,
% 1.87/2.07 (b(s(z), elem!1)),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[1034, 6073, 2277])).
% 1.87/2.07 tff(6075,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(6076,plain,
% 1.87/2.07 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(6077,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))))),
% 1.87/2.08 inference(monotonicity,[status(thm)],[6076])).
% 1.87/2.08 tff(6078,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 1.87/2.08 inference(transitivity,[status(thm)],[6077, 6075])).
% 1.87/2.08 tff(6079,plain,
% 1.87/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 1.87/2.08 inference(quant_inst,[status(thm)],[])).
% 1.87/2.08 tff(6080,plain,
% 1.87/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))),
% 1.87/2.08 inference(modus_ponens,[status(thm)],[6079, 6078])).
% 1.87/2.08 tff(6081,plain,
% 1.87/2.08 (~b(s(z), s(s(s(z))))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[6080, 246, 6074, 5798, 3697])).
% 1.87/2.08 tff(6082,plain,
% 1.87/2.08 (r(s(z), s(s(s(z))))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[1291, 6081])).
% 1.87/2.08 tff(6083,plain,
% 1.87/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(6084,plain,
% 1.87/2.08 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(6085,plain,
% 1.87/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))))),
% 1.87/2.08 inference(monotonicity,[status(thm)],[6084])).
% 1.87/2.08 tff(6086,plain,
% 1.87/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.87/2.08 inference(transitivity,[status(thm)],[6085, 6083])).
% 1.87/2.08 tff(6087,plain,
% 1.87/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.87/2.08 inference(quant_inst,[status(thm)],[])).
% 1.87/2.08 tff(6088,plain,
% 1.87/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))),
% 1.87/2.08 inference(modus_ponens,[status(thm)],[6087, 6086])).
% 1.87/2.08 tff(6089,plain,
% 1.87/2.08 (~r(s(z), s(s(s(s(z)))))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[6088, 183, 6082, 6048])).
% 1.87/2.08 tff(6090,plain,
% 1.87/2.08 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z))))))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(6091,plain,
% 1.87/2.08 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z))))))),
% 1.87/2.08 inference(quant_inst,[status(thm)],[])).
% 1.87/2.08 tff(6092,plain,
% 1.87/2.08 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 1.87/2.08 inference(modus_ponens,[status(thm)],[6091, 6090])).
% 1.87/2.08 tff(6093,plain,
% 1.87/2.08 ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z)))))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[6092, 47, 6089])).
% 1.87/2.08 tff(6094,plain,
% 1.87/2.08 (b(s(z), s(s(s(s(z)))))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[6093, 5790])).
% 1.87/2.08 tff(6095,assumption,(r(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.87/2.08 tff(6096,assumption,(r(s(z), s(s(s(z))))), introduced(assumption)).
% 1.87/2.08 tff(6097,plain,
% 1.87/2.08 ($false),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[3272, 183, 6096, 2593, 6095])).
% 1.87/2.08 tff(6098,plain,((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.08 tff(6099,plain,
% 1.87/2.08 (~r(s(s(s(s(z)))), s(z))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[6098, 6048, 6082])).
% 1.87/2.08 tff(6100,assumption,(~b(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.87/2.08 tff(6101,assumption,(~r(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.87/2.08 tff(6102,plain,
% 1.87/2.08 ($false),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[2411, 47, 1713, 6101, 6100])).
% 1.87/2.08 tff(6103,plain,(b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.08 tff(6104,plain,
% 1.87/2.08 (b(s(s(s(s(z)))), s(z))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[6103, 6099])).
% 1.87/2.08 tff(6105,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(6106,plain,
% 1.87/2.08 (((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(6107,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))))),
% 1.87/2.08 inference(monotonicity,[status(thm)],[6106])).
% 1.87/2.08 tff(6108,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.87/2.08 inference(transitivity,[status(thm)],[6107, 6105])).
% 1.87/2.08 tff(6109,plain,
% 1.87/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.87/2.08 inference(quant_inst,[status(thm)],[])).
% 1.87/2.08 tff(6110,plain,
% 1.87/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))),
% 1.87/2.08 inference(modus_ponens,[status(thm)],[6109, 6108])).
% 1.87/2.08 tff(6111,plain,
% 1.87/2.08 (~b(s(s(s(s(z)))), z)),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[6110, 246, 5847, 6104, 6094])).
% 1.87/2.08 tff(6112,plain,
% 1.87/2.08 (r(s(s(s(s(z)))), z)),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[6040, 6111])).
% 1.87/2.08 tff(6113,plain,
% 1.87/2.08 (~r(elem!1, z)),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[1163, 1114, 474])).
% 1.87/2.08 tff(6114,plain,
% 1.87/2.08 (b(elem!1, z)),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[1143, 6113, 1438])).
% 1.87/2.08 tff(6115,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(6116,plain,
% 1.87/2.08 (((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(6117,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))))),
% 1.87/2.08 inference(monotonicity,[status(thm)],[6116])).
% 1.87/2.08 tff(6118,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 1.87/2.08 inference(transitivity,[status(thm)],[6117, 6115])).
% 1.87/2.08 tff(6119,plain,
% 1.87/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))),
% 1.87/2.08 inference(quant_inst,[status(thm)],[])).
% 1.87/2.08 tff(6120,plain,
% 1.87/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))),
% 1.87/2.08 inference(modus_ponens,[status(thm)],[6119, 6118])).
% 1.87/2.08 tff(6121,plain,
% 1.87/2.08 (~b(s(s(s(z))), z)),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[6120, 246, 6114, 1044, 236, 2002, 3697])).
% 1.87/2.08 tff(6122,plain,
% 1.87/2.08 (r(s(s(s(z))), z)),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[995, 6121])).
% 1.87/2.08 tff(6123,plain,
% 1.87/2.08 (~b(s(z), s(s(s(z))))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[6080, 246, 1044, 2002, 3697])).
% 1.87/2.08 tff(6124,plain,
% 1.87/2.08 (r(s(z), s(s(s(z))))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[1291, 6123])).
% 1.87/2.08 tff(6125,plain,
% 1.87/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(6126,plain,
% 1.87/2.08 (((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(6127,plain,
% 1.87/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z))))),
% 1.87/2.08 inference(monotonicity,[status(thm)],[6126])).
% 1.87/2.08 tff(6128,plain,
% 1.87/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.87/2.08 inference(transitivity,[status(thm)],[6127, 6125])).
% 1.87/2.08 tff(6129,plain,
% 1.87/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 1.87/2.08 inference(quant_inst,[status(thm)],[])).
% 1.87/2.08 tff(6130,plain,
% 1.87/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z))),
% 1.87/2.08 inference(modus_ponens,[status(thm)],[6129, 6128])).
% 1.87/2.08 tff(6131,plain,
% 1.87/2.08 ($false),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[6130, 183, 1114, 6124, 6122])).
% 1.87/2.08 tff(6132,plain,((~r(s(z), z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (elem!1 = z) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.08 tff(6133,plain,
% 1.87/2.08 (~r(s(z), z)),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[6132, 6074, 5847, 5798, 3697, 5401, 474])).
% 1.87/2.08 tff(6134,plain,
% 1.87/2.08 (b(s(z), z)),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[1069, 6133])).
% 1.87/2.08 tff(6135,plain,
% 1.87/2.08 (~b(elem!1, z)),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[1064, 6134, 6074, 5847])).
% 1.87/2.08 tff(6136,plain,
% 1.87/2.08 (r(elem!1, z)),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[1143, 6135, 5401])).
% 1.87/2.08 tff(6137,plain,
% 1.87/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(6138,plain,
% 1.87/2.08 (((~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(6139,plain,
% 1.87/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z))))),
% 1.87/2.08 inference(monotonicity,[status(thm)],[6138])).
% 1.87/2.08 tff(6140,plain,
% 1.87/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 1.87/2.08 inference(transitivity,[status(thm)],[6139, 6137])).
% 1.87/2.08 tff(6141,plain,
% 1.87/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.87/2.08 inference(quant_inst,[status(thm)],[])).
% 1.87/2.08 tff(6142,plain,
% 1.87/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z))),
% 1.87/2.08 inference(modus_ponens,[status(thm)],[6141, 6140])).
% 1.87/2.08 tff(6143,plain,
% 1.87/2.08 (~r(s(s(s(s(z)))), elem!1)),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[6142, 183, 6136, 6112])).
% 1.87/2.08 tff(6144,plain,
% 1.87/2.08 (b(s(s(s(s(z)))), elem!1)),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[2442, 47, 5832, 6143])).
% 1.87/2.08 tff(6145,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(6146,plain,
% 1.87/2.08 (((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(6147,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.87/2.08 inference(monotonicity,[status(thm)],[6146])).
% 1.87/2.08 tff(6148,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.87/2.08 inference(transitivity,[status(thm)],[6147, 6145])).
% 1.87/2.08 tff(6149,plain,
% 1.87/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.87/2.08 inference(quant_inst,[status(thm)],[])).
% 1.87/2.08 tff(6150,plain,
% 1.87/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))),
% 1.87/2.08 inference(modus_ponens,[status(thm)],[6149, 6148])).
% 1.87/2.08 tff(6151,plain,
% 1.87/2.08 ($false),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[6150, 246, 6074, 5798, 3697, 6104, 6144])).
% 1.87/2.08 tff(6152,plain,((~r(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (s(z) = elem!1) | (s(s(s(s(s(elem!1))))) = elem!1) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), elem!1) | (elem!1 = s(s(s(z)))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.08 tff(6153,plain,
% 1.87/2.08 (~r(s(s(s(z))), s(z))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[6152, 5786, 5775, 5365, 5778, 69, 5035, 2232, 5764, 2133])).
% 1.87/2.08 tff(6154,plain,
% 1.87/2.08 (b(s(s(s(z))), s(z))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[52, 6153])).
% 1.87/2.08 tff(6155,plain,
% 1.87/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(6156,plain,
% 1.87/2.08 (((~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(6157,plain,
% 1.87/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))))),
% 1.87/2.08 inference(monotonicity,[status(thm)],[6156])).
% 1.87/2.08 tff(6158,plain,
% 1.87/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.87/2.08 inference(transitivity,[status(thm)],[6157, 6155])).
% 1.87/2.08 tff(6159,plain,
% 1.87/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(z, elem!1)))),
% 1.87/2.08 inference(quant_inst,[status(thm)],[])).
% 1.87/2.08 tff(6160,plain,
% 1.87/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 1.87/2.08 inference(modus_ponens,[status(thm)],[6159, 6158])).
% 1.87/2.08 tff(6161,plain,
% 1.87/2.08 ($false),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[6160, 183, 267, 474, 413, 429])).
% 1.87/2.08 tff(6162,plain,((~r(z, s(s(s(z))))) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.08 tff(6163,plain,
% 1.87/2.09 (~r(z, s(s(s(z))))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[6162, 413, 267, 474])).
% 1.87/2.09 tff(6164,plain,
% 1.87/2.09 ($false),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[2221, 47, 4030, 2214, 5476])).
% 1.87/2.09 tff(6165,plain,(b(z, s(s(s(z)))) | r(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.09 tff(6166,plain,
% 1.87/2.09 (b(z, s(s(s(z))))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[6165, 6163])).
% 1.87/2.09 tff(6167,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(6168,plain,
% 1.87/2.09 (((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(6169,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[6168])).
% 1.87/2.09 tff(6170,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.87/2.09 inference(transitivity,[status(thm)],[6169, 6167])).
% 1.87/2.09 tff(6171,plain,
% 1.87/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 1.87/2.09 inference(quant_inst,[status(thm)],[])).
% 1.87/2.09 tff(6172,plain,
% 1.87/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[6171, 6170])).
% 1.87/2.09 tff(6173,plain,
% 1.87/2.09 ($false),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[6172, 246, 1056, 236, 2003, 4651])).
% 1.87/2.09 tff(6174,plain,((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.09 tff(6175,plain,
% 1.87/2.09 (~b(s(z), z)),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[6174, 6166, 2003, 5847])).
% 1.87/2.09 tff(6176,plain,
% 1.87/2.09 (r(s(z), z)),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[1069, 6175])).
% 1.87/2.09 tff(6177,plain,
% 1.87/2.09 (~r(s(z), elem!1)),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[5432, 6176, 267])).
% 1.87/2.09 tff(6178,plain,
% 1.87/2.09 (b(s(z), elem!1)),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[1034, 6177, 2277])).
% 1.87/2.09 tff(6179,plain,
% 1.87/2.09 (~r(elem!1, z)),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[1163, 6176, 474])).
% 1.87/2.09 tff(6180,plain,
% 1.87/2.09 (b(elem!1, z)),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[1143, 6179, 5401])).
% 1.87/2.09 tff(6181,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(6182,plain,
% 1.87/2.09 (((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(6183,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[6182])).
% 1.87/2.09 tff(6184,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.87/2.09 inference(transitivity,[status(thm)],[6183, 6181])).
% 1.87/2.09 tff(6185,plain,
% 1.87/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 1.87/2.09 inference(quant_inst,[status(thm)],[])).
% 1.87/2.09 tff(6186,plain,
% 1.87/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[6185, 6184])).
% 1.87/2.09 tff(6187,plain,
% 1.87/2.09 (~b(s(z), s(s(s(z))))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[6186, 246, 6180, 6178, 5847, 3697, 2003])).
% 1.87/2.09 tff(6188,plain,
% 1.87/2.09 (r(s(z), s(s(s(z))))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[1291, 6187])).
% 1.87/2.09 tff(6189,plain,
% 1.87/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(6190,plain,
% 1.87/2.09 (((~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(6191,plain,
% 1.87/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[6190])).
% 1.87/2.09 tff(6192,plain,
% 1.87/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.87/2.09 inference(transitivity,[status(thm)],[6191, 6189])).
% 1.87/2.09 tff(6193,plain,
% 1.87/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(z))))),
% 1.87/2.09 inference(quant_inst,[status(thm)],[])).
% 1.87/2.09 tff(6194,plain,
% 1.87/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[6193, 6192])).
% 1.87/2.09 tff(6195,plain,
% 1.87/2.09 ($false),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[6194, 183, 474, 413, 6188])).
% 1.87/2.09 tff(6196,plain,((~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))) | (s(z) = elem!1) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.09 tff(6197,plain,
% 1.87/2.09 (~r(elem!1, s(s(s(z))))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[6196, 6154, 5764, 5775, 5778, 5365])).
% 1.87/2.09 tff(6198,plain,
% 1.87/2.09 (b(elem!1, s(s(s(z))))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[470, 6197, 5786])).
% 1.87/2.09 tff(6199,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(6200,plain,
% 1.87/2.09 (((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(6201,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[6200])).
% 1.87/2.09 tff(6202,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.87/2.09 inference(transitivity,[status(thm)],[6201, 6199])).
% 1.87/2.09 tff(6203,plain,
% 1.87/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 1.87/2.09 inference(quant_inst,[status(thm)],[])).
% 1.87/2.09 tff(6204,plain,
% 1.87/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[6203, 6202])).
% 1.87/2.09 tff(6205,plain,
% 1.87/2.09 ($false),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[6204, 246, 1044, 2002, 3697, 2003])).
% 1.87/2.09 tff(6206,plain,((~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.09 tff(6207,plain,
% 1.87/2.09 (~b(s(z), elem!1)),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[6206, 6198, 5764, 6154])).
% 1.87/2.09 tff(6208,plain,
% 1.87/2.09 (r(s(z), elem!1)),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[1034, 6207, 5778])).
% 1.87/2.09 tff(6209,plain,
% 1.87/2.09 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[5581, 6208, 5365, 5777])).
% 1.87/2.09 tff(6210,plain,
% 1.87/2.09 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[86, 6209, 69])).
% 1.87/2.09 tff(6211,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(6212,plain,
% 1.87/2.09 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(6213,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(z))), s(z)))))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[6212])).
% 1.87/2.09 tff(6214,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 1.87/2.09 inference(transitivity,[status(thm)],[6213, 6211])).
% 1.87/2.09 tff(6215,plain,
% 1.87/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.87/2.09 inference(quant_inst,[status(thm)],[])).
% 1.87/2.09 tff(6216,plain,
% 1.87/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(z))), s(z)))),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[6215, 6214])).
% 1.87/2.09 tff(6217,plain,
% 1.87/2.09 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[6216, 246, 6198, 5764, 6154, 6210])).
% 1.87/2.09 tff(6218,plain,
% 1.87/2.09 (r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[1626, 6217])).
% 1.87/2.09 tff(6219,plain,
% 1.87/2.09 (~r(s(z), z)),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[5432, 6208, 5365])).
% 1.87/2.09 tff(6220,plain,
% 1.87/2.09 (b(s(z), z)),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[1069, 6219])).
% 1.87/2.09 tff(6221,plain,
% 1.87/2.09 (~b(z, s(s(s(z))))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[6174, 6220, 6154, 5777])).
% 1.87/2.09 tff(6222,plain,
% 1.87/2.09 (r(z, s(s(s(z))))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[6165, 6221])).
% 1.87/2.09 tff(6223,plain,
% 1.87/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(6224,plain,
% 1.87/2.09 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(6225,plain,
% 1.87/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), z))))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[6224])).
% 1.87/2.09 tff(6226,plain,
% 1.87/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 1.87/2.09 inference(transitivity,[status(thm)],[6225, 6223])).
% 1.87/2.09 tff(6227,plain,
% 1.87/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 1.87/2.09 inference(quant_inst,[status(thm)],[])).
% 1.87/2.09 tff(6228,plain,
% 1.87/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), z))),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[6227, 6226])).
% 1.87/2.09 tff(6229,plain,
% 1.87/2.09 (~r(s(s(s(s(s(elem!1))))), z)),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[6228, 183, 6222, 6218])).
% 1.87/2.09 tff(6230,plain,
% 1.87/2.09 (b(s(s(s(s(s(elem!1))))), z)),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[1601, 6229])).
% 1.87/2.09 tff(6231,plain,
% 1.87/2.09 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[5578, 246, 6220, 5777, 6230])).
% 1.87/2.09 tff(6232,plain,
% 1.87/2.09 (r(s(s(s(s(s(elem!1))))), s(z))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[2311, 47, 331, 6231])).
% 1.87/2.09 tff(6233,plain,
% 1.87/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(6234,plain,
% 1.87/2.09 (((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(elem!1, s(s(s(s(s(elem!1)))))))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(6235,plain,
% 1.87/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(elem!1, s(s(s(s(s(elem!1)))))))))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[6234])).
% 1.87/2.10 tff(6236,plain,
% 1.87/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.87/2.10 inference(transitivity,[status(thm)],[6235, 6233])).
% 1.87/2.10 tff(6237,plain,
% 1.87/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.87/2.10 inference(quant_inst,[status(thm)],[])).
% 1.87/2.10 tff(6238,plain,
% 1.87/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(elem!1, s(s(s(s(s(elem!1)))))))),
% 1.87/2.10 inference(modus_ponens,[status(thm)],[6237, 6236])).
% 1.87/2.10 tff(6239,plain,
% 1.87/2.10 (~r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[6238, 183, 5775, 6232])).
% 1.87/2.10 tff(6240,plain,
% 1.87/2.10 (b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[5125, 6239, 5452])).
% 1.87/2.10 tff(6241,plain,
% 1.87/2.10 ((s(s(s(s(s(elem!1))))) = s(z)) <=> (s(z) = s(s(s(s(s(elem!1))))))),
% 1.87/2.10 inference(symmetry,[status(thm)],[317])).
% 1.87/2.10 tff(6242,plain,
% 1.87/2.10 ((~(s(s(s(s(s(elem!1))))) = s(z))) <=> (~(s(z) = s(s(s(s(s(elem!1)))))))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[6241])).
% 1.87/2.10 tff(6243,plain,
% 1.87/2.10 (~(s(z) = s(s(s(s(s(elem!1))))))),
% 1.87/2.10 inference(modus_ponens,[status(thm)],[331, 6242])).
% 1.87/2.10 tff(6244,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(z), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(z), s(s(s(s(s(elem!1))))))))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(6245,plain,
% 1.87/2.10 (((~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(z), s(s(s(s(s(elem!1))))))))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(6246,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(z), s(s(s(s(s(elem!1)))))))))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[6245])).
% 1.87/2.10 tff(6247,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(z), s(s(s(s(s(elem!1))))))))),
% 1.87/2.10 inference(transitivity,[status(thm)],[6246, 6244])).
% 1.87/2.10 tff(6248,plain,
% 1.87/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(elem!1))))))))),
% 1.87/2.10 inference(quant_inst,[status(thm)],[])).
% 1.87/2.10 tff(6249,plain,
% 1.87/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(z), s(s(s(s(s(elem!1)))))))),
% 1.87/2.10 inference(modus_ponens,[status(thm)],[6248, 6247])).
% 1.87/2.10 tff(6250,plain,
% 1.87/2.10 (~b(s(z), s(s(s(s(s(elem!1))))))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[6249, 246, 6220, 5777, 6230])).
% 1.87/2.10 tff(6251,plain,
% 1.87/2.10 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(elem!1)))))) | b(s(z), s(s(s(s(s(elem!1)))))) | r(s(z), s(s(s(s(s(elem!1)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(elem!1)))))) | b(s(z), s(s(s(s(s(elem!1)))))) | r(s(z), s(s(s(s(s(elem!1)))))))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(6252,plain,
% 1.87/2.10 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(elem!1)))))) | b(s(z), s(s(s(s(s(elem!1)))))) | r(s(z), s(s(s(s(s(elem!1)))))))),
% 1.87/2.10 inference(quant_inst,[status(thm)],[])).
% 1.87/2.10 tff(6253,plain,
% 1.87/2.10 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(elem!1)))))) | b(s(z), s(s(s(s(s(elem!1)))))) | r(s(z), s(s(s(s(s(elem!1))))))),
% 1.87/2.10 inference(modus_ponens,[status(thm)],[6252, 6251])).
% 1.87/2.10 tff(6254,plain,
% 1.87/2.10 ((s(z) = s(s(s(s(s(elem!1)))))) | r(s(z), s(s(s(s(s(elem!1))))))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[6253, 47, 6250])).
% 1.87/2.10 tff(6255,plain,
% 1.87/2.10 (r(s(z), s(s(s(s(s(elem!1))))))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[6254, 6243])).
% 1.87/2.10 tff(6256,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(6257,plain,
% 1.87/2.10 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(6258,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[6257])).
% 1.87/2.10 tff(6259,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.87/2.10 inference(transitivity,[status(thm)],[6258, 6256])).
% 1.87/2.10 tff(6260,plain,
% 1.87/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.87/2.10 inference(quant_inst,[status(thm)],[])).
% 1.87/2.10 tff(6261,plain,
% 1.87/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 1.87/2.10 inference(modus_ponens,[status(thm)],[6260, 6259])).
% 1.87/2.10 tff(6262,plain,
% 1.87/2.10 (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[6261, 246, 6198, 5764, 6210])).
% 1.87/2.10 tff(6263,plain,
% 1.87/2.10 ((s(s(s(z))) = s(s(s(s(s(elem!1)))))) | r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[3127, 47, 6262])).
% 1.87/2.10 tff(6264,plain,
% 1.87/2.10 (r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[6263, 3117])).
% 1.87/2.10 tff(6265,plain,
% 1.87/2.10 (~b(s(s(s(z))), z)),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[2098, 6220, 6154, 5777])).
% 1.87/2.10 tff(6266,plain,
% 1.87/2.10 (r(s(s(s(z))), z)),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[995, 6265])).
% 1.87/2.10 tff(6267,plain,
% 1.87/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(6268,plain,
% 1.87/2.10 (((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(6269,plain,
% 1.87/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(s(s(elem!1)))))))))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[6268])).
% 1.87/2.10 tff(6270,plain,
% 1.87/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 1.87/2.10 inference(transitivity,[status(thm)],[6269, 6267])).
% 1.87/2.10 tff(6271,plain,
% 1.87/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 1.87/2.10 inference(quant_inst,[status(thm)],[])).
% 1.87/2.10 tff(6272,plain,
% 1.87/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(s(s(elem!1)))))))),
% 1.87/2.10 inference(modus_ponens,[status(thm)],[6271, 6270])).
% 1.87/2.10 tff(6273,plain,
% 1.87/2.10 (~r(s(z), s(s(s(z))))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[6272, 183, 6266, 6264, 6255])).
% 1.87/2.10 tff(6274,plain,
% 1.87/2.10 (b(s(z), s(s(s(z))))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[1291, 6273])).
% 1.87/2.10 tff(6275,plain,
% 1.87/2.10 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[5804, 5778])).
% 1.87/2.10 tff(6276,assumption,(s(s(s(elem!1))) = s(s(s(s(z))))), introduced(assumption)).
% 1.87/2.10 tff(6277,plain,
% 1.87/2.10 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.87/2.10 inference(symmetry,[status(thm)],[6276])).
% 1.87/2.10 tff(6278,plain,
% 1.87/2.10 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(elem!1))))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[6277])).
% 1.87/2.10 tff(6279,plain,
% 1.87/2.10 (s(s(s(z))) = s(s(elem!1))),
% 1.87/2.10 inference(transitivity,[status(thm)],[1492, 6278, 103])).
% 1.87/2.10 tff(6280,plain,
% 1.87/2.10 ($false),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[119, 6279])).
% 1.87/2.10 tff(6281,plain,((~(s(s(s(elem!1))) = s(s(s(s(z)))))) | (s(s(s(z))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.10 tff(6282,plain,
% 1.87/2.10 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[6281, 6275])).
% 1.87/2.10 tff(6283,plain,
% 1.87/2.10 (elem!1 = s(s(s(elem!1)))),
% 1.87/2.10 inference(transitivity,[status(thm)],[3154, 348, 351])).
% 1.87/2.10 tff(6284,plain,
% 1.87/2.10 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[6283])).
% 1.87/2.10 tff(6285,plain,
% 1.87/2.10 (b(s(s(s(elem!1))), s(s(s(z))))),
% 1.87/2.10 inference(modus_ponens,[status(thm)],[2002, 6284])).
% 1.87/2.10 tff(6286,plain,
% 1.87/2.10 (r(s(s(s(s(s(elem!1))))), s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[344])).
% 1.87/2.10 tff(6287,assumption,(r(s(s(s(s(s(elem!1))))), s(s(s(z))))), introduced(assumption)).
% 1.87/2.10 tff(6288,plain,
% 1.87/2.10 (r(s(s(elem!1)), s(s(s(z))))),
% 1.87/2.10 inference(modus_ponens,[status(thm)],[6287, 6286])).
% 1.87/2.10 tff(6289,plain,
% 1.87/2.10 (~b(z, s(s(s(z))))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[6174, 1056, 2003, 236])).
% 1.87/2.10 tff(6290,plain,
% 1.87/2.10 (r(z, s(s(s(z))))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[6165, 6289])).
% 1.87/2.10 tff(6291,plain,
% 1.87/2.10 (b(s(s(s(s(s(elem!1))))), z) <=> b(s(s(elem!1)), z)),
% 1.87/2.10 inference(monotonicity,[status(thm)],[344])).
% 1.87/2.10 tff(6292,plain,
% 1.87/2.10 (~r(s(s(s(s(s(elem!1))))), z)),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[6228, 183, 6290, 6287])).
% 1.87/2.10 tff(6293,plain,
% 1.87/2.10 (b(s(s(s(s(s(elem!1))))), z)),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[1601, 6292])).
% 1.87/2.10 tff(6294,plain,
% 1.87/2.10 (b(s(s(elem!1)), z)),
% 1.87/2.10 inference(modus_ponens,[status(thm)],[6293, 6291])).
% 1.87/2.10 tff(6295,plain,
% 1.87/2.10 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 1.87/2.10 inference(symmetry,[status(thm)],[344])).
% 1.87/2.10 tff(6296,plain,
% 1.87/2.10 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[6295])).
% 1.87/2.10 tff(6297,plain,
% 1.87/2.10 (b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.87/2.10 inference(symmetry,[status(thm)],[6296])).
% 1.87/2.10 tff(6298,plain,
% 1.87/2.10 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[6295])).
% 1.87/2.10 tff(6299,plain,
% 1.87/2.10 ((~r(s(s(s(s(z)))), s(s(elem!1)))) <=> (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[6298])).
% 1.87/2.10 tff(6300,plain,
% 1.87/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(6301,plain,
% 1.87/2.10 (((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(6302,plain,
% 1.87/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[6301])).
% 1.87/2.10 tff(6303,plain,
% 1.87/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.87/2.10 inference(transitivity,[status(thm)],[6302, 6300])).
% 1.87/2.10 tff(6304,plain,
% 1.87/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.87/2.10 inference(quant_inst,[status(thm)],[])).
% 1.87/2.10 tff(6305,plain,
% 1.87/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 1.87/2.10 inference(modus_ponens,[status(thm)],[6304, 6303])).
% 1.87/2.10 tff(6306,plain,
% 1.87/2.10 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[6305, 183, 173, 3886, 2593])).
% 1.87/2.10 tff(6307,plain,
% 1.87/2.10 (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.87/2.10 inference(modus_ponens,[status(thm)],[6306, 6299])).
% 1.87/2.10 tff(6308,plain,
% 1.87/2.10 (b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[1506, 6307])).
% 1.87/2.10 tff(6309,plain,
% 1.87/2.10 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.87/2.10 inference(modus_ponens,[status(thm)],[6308, 6297])).
% 1.87/2.10 tff(6310,plain,
% 1.87/2.10 (~r(s(s(s(s(z)))), z)),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[2599, 183, 429, 2593])).
% 1.87/2.10 tff(6311,plain,
% 1.87/2.10 (b(s(s(s(s(z)))), z)),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[6040, 6310])).
% 1.87/2.10 tff(6312,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(6313,plain,
% 1.87/2.10 (((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(6314,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), z))))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[6313])).
% 1.87/2.10 tff(6315,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)))),
% 1.87/2.10 inference(transitivity,[status(thm)],[6314, 6312])).
% 1.87/2.10 tff(6316,plain,
% 1.87/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.87/2.10 inference(quant_inst,[status(thm)],[])).
% 1.87/2.10 tff(6317,plain,
% 1.87/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), z))),
% 1.87/2.10 inference(modus_ponens,[status(thm)],[6316, 6315])).
% 1.87/2.10 tff(6318,plain,
% 1.87/2.10 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[6317, 246, 1056, 1100, 236, 6311])).
% 1.87/2.10 tff(6319,plain,
% 1.87/2.10 ($false),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[6318, 6309])).
% 1.87/2.10 tff(6320,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.10 tff(6321,plain,
% 1.87/2.10 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[6320, 6294, 1056, 344, 236, 6290, 173, 6288])).
% 1.87/2.10 tff(6322,plain,
% 1.87/2.10 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[1702, 6321])).
% 1.87/2.10 tff(6323,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(6324,plain,
% 1.87/2.10 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(6325,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[6324])).
% 1.87/2.10 tff(6326,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.87/2.11 inference(transitivity,[status(thm)],[6325, 6323])).
% 1.87/2.11 tff(6327,plain,
% 1.87/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.87/2.11 inference(quant_inst,[status(thm)],[])).
% 1.87/2.11 tff(6328,plain,
% 1.87/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[6327, 6326])).
% 1.87/2.11 tff(6329,plain,
% 1.87/2.11 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[6328, 246, 2401, 2003, 6322, 6285])).
% 1.87/2.11 tff(6330,assumption,(~(s(s(s(elem!1))) = s(s(s(s(z)))))), introduced(assumption)).
% 1.87/2.11 tff(6331,plain,
% 1.87/2.11 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(6332,plain,
% 1.87/2.11 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 1.87/2.11 inference(quant_inst,[status(thm)],[])).
% 1.87/2.11 tff(6333,plain,
% 1.87/2.11 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[6332, 6331])).
% 1.87/2.11 tff(6334,plain,
% 1.87/2.11 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[6333, 47, 6330, 6329])).
% 1.87/2.11 tff(6335,plain,
% 1.87/2.11 (r(elem!1, s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[6283])).
% 1.87/2.11 tff(6336,plain,
% 1.87/2.11 (r(s(s(s(elem!1))), s(z))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[474, 6335])).
% 1.87/2.11 tff(6337,plain,
% 1.87/2.11 (~b(s(s(s(s(z)))), s(z))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[2407, 246, 1056, 2401, 2003, 6322])).
% 1.87/2.11 tff(6338,plain,
% 1.87/2.11 (r(s(s(s(s(z)))), s(z))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[6103, 6337])).
% 1.87/2.11 tff(6339,plain,
% 1.87/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(6340,plain,
% 1.87/2.11 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(6341,plain,
% 1.87/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z)))))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[6340])).
% 1.87/2.11 tff(6342,plain,
% 1.87/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.87/2.11 inference(transitivity,[status(thm)],[6341, 6339])).
% 1.87/2.11 tff(6343,plain,
% 1.87/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.87/2.11 inference(quant_inst,[status(thm)],[])).
% 1.87/2.11 tff(6344,plain,
% 1.87/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z)))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[6343, 6342])).
% 1.87/2.11 tff(6345,plain,
% 1.87/2.11 ($false),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[6344, 183, 6338, 6336, 6334])).
% 1.87/2.11 tff(6346,plain,((~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.11 tff(6347,plain,
% 1.87/2.11 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[6346, 6282, 6274, 6154, 6220, 5777, 2133, 6198, 5775, 6218])).
% 1.87/2.11 tff(6348,plain,
% 1.87/2.11 (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[3815, 6347])).
% 1.87/2.11 tff(6349,plain,
% 1.87/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(6350,plain,
% 1.87/2.11 (((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(6351,plain,
% 1.87/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(z)))))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[6350])).
% 1.87/2.11 tff(6352,plain,
% 1.87/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 1.87/2.11 inference(transitivity,[status(thm)],[6351, 6349])).
% 1.87/2.11 tff(6353,plain,
% 1.87/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.87/2.11 inference(quant_inst,[status(thm)],[])).
% 1.87/2.11 tff(6354,plain,
% 1.87/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(z)))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[6353, 6352])).
% 1.87/2.11 tff(6355,plain,
% 1.87/2.11 (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[6354, 183, 2133, 6232])).
% 1.87/2.11 tff(6356,plain,
% 1.87/2.11 ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[1547, 47, 6355])).
% 1.87/2.11 tff(6357,plain,
% 1.87/2.11 (b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[6356, 6348])).
% 1.87/2.11 tff(6358,plain,
% 1.87/2.11 (~b(s(s(elem!1)), elem!1)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[4853, 6357, 6210, 6240])).
% 1.87/2.11 tff(6359,plain,
% 1.87/2.11 (s(s(elem!1)) = elem!1),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[156, 6358, 2232])).
% 1.87/2.11 tff(6360,plain,
% 1.87/2.11 (s(s(s(elem!1))) = s(elem!1)),
% 1.87/2.11 inference(monotonicity,[status(thm)],[6359])).
% 1.87/2.11 tff(6361,plain,
% 1.87/2.11 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[6360])).
% 1.87/2.11 tff(6362,plain,
% 1.87/2.11 (s(s(s(s(elem!1)))) = elem!1),
% 1.87/2.11 inference(transitivity,[status(thm)],[6361, 6359])).
% 1.87/2.11 tff(6363,plain,
% 1.87/2.11 (s(s(s(s(s(elem!1))))) = s(elem!1)),
% 1.87/2.11 inference(monotonicity,[status(thm)],[6362])).
% 1.87/2.11 tff(6364,plain,
% 1.87/2.11 (b(elem!1, s(s(s(s(s(elem!1)))))) <=> b(elem!1, s(elem!1))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[6363])).
% 1.87/2.11 tff(6365,plain,
% 1.87/2.11 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.87/2.11 inference(symmetry,[status(thm)],[6364])).
% 1.87/2.11 tff(6366,plain,
% 1.87/2.11 ((~b(elem!1, s(elem!1))) <=> (~b(elem!1, s(s(s(s(s(elem!1)))))))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[6365])).
% 1.87/2.11 tff(6367,plain,
% 1.87/2.11 (b(s(s(elem!1)), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[6359])).
% 1.87/2.11 tff(6368,plain,
% 1.87/2.11 ((~b(s(s(elem!1)), s(elem!1))) <=> (~b(elem!1, s(elem!1)))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[6367])).
% 1.87/2.11 tff(6369,plain,
% 1.87/2.11 (~b(elem!1, s(elem!1))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[5035, 6368])).
% 1.87/2.11 tff(6370,plain,
% 1.87/2.11 (~b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[6369, 6366])).
% 1.87/2.11 tff(6371,plain,
% 1.87/2.11 ($false),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[6240, 6370])).
% 1.87/2.11 tff(6372,plain,(b(elem!1, s(z)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), elem!1) | (s(s(s(s(s(elem!1))))) = elem!1) | b(s(s(elem!1)), s(z)) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.87/2.11 tff(6373,plain,
% 1.87/2.11 (b(elem!1, s(z))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[6372, 5035, 2232, 69, 2124, 55])).
% 1.87/2.11 tff(6374,plain,
% 1.87/2.11 (~(s(s(elem!1)) = elem!1)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[2130, 6373, 2124])).
% 1.87/2.11 tff(6375,plain,
% 1.87/2.11 (b(s(s(elem!1)), elem!1)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[156, 6374, 2232])).
% 1.87/2.11 tff(6376,plain,
% 1.87/2.11 (~r(elem!1, s(z))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[292, 170, 5365])).
% 1.87/2.11 tff(6377,plain,
% 1.87/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z))))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(6378,plain,
% 1.87/2.11 (((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z)))) <=> ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z))))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(6379,plain,
% 1.87/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z)))))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[6378])).
% 1.87/2.11 tff(6380,plain,
% 1.87/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z))))),
% 1.87/2.11 inference(transitivity,[status(thm)],[6379, 6377])).
% 1.87/2.11 tff(6381,plain,
% 1.87/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z))))),
% 1.87/2.11 inference(quant_inst,[status(thm)],[])).
% 1.87/2.11 tff(6382,plain,
% 1.87/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z)))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[6381, 6380])).
% 1.87/2.11 tff(6383,plain,
% 1.87/2.11 ($false),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[6382, 183, 267, 217, 171])).
% 1.87/2.11 tff(6384,plain,((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.11 tff(6385,plain,
% 1.87/2.11 (~r(s(z), elem!1)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[6384, 170, 5365])).
% 1.87/2.11 tff(6386,assumption,(~r(elem!1, s(z))), introduced(assumption)).
% 1.87/2.11 tff(6387,plain,
% 1.87/2.11 (b(elem!1, s(z))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[214, 2339, 6386])).
% 1.87/2.11 tff(6388,assumption,(~r(s(z), elem!1)), introduced(assumption)).
% 1.87/2.11 tff(6389,plain,
% 1.87/2.11 (b(s(z), elem!1)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[1034, 2277, 6388])).
% 1.87/2.11 tff(6390,plain,
% 1.87/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(6391,plain,
% 1.87/2.11 (((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(6392,plain,
% 1.87/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z)))))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[6391])).
% 1.87/2.11 tff(6393,plain,
% 1.87/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 1.87/2.11 inference(transitivity,[status(thm)],[6392, 6390])).
% 1.87/2.11 tff(6394,plain,
% 1.87/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), 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)))))),
% 1.87/2.11 inference(quant_inst,[status(thm)],[])).
% 1.87/2.11 tff(6395,plain,
% 1.87/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z)))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[6394, 6393])).
% 1.87/2.11 tff(6396,plain,
% 1.87/2.11 ($false),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[6395, 246, 6389, 2362, 6387, 235])).
% 1.87/2.11 tff(6397,plain,((s(z) = elem!1) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | r(elem!1, s(z)) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.87/2.11 tff(6398,plain,
% 1.87/2.11 (~b(s(z), s(s(elem!1)))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[6397, 6385, 2277, 2362, 6376])).
% 1.87/2.11 tff(6399,plain,
% 1.87/2.11 (r(s(z), s(s(elem!1)))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[233, 6398])).
% 1.87/2.11 tff(6400,plain,
% 1.87/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1)))))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(6401,plain,
% 1.87/2.11 (((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z)))) <=> ((~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1)))))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(6402,plain,
% 1.87/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1))))))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[6401])).
% 1.87/2.11 tff(6403,plain,
% 1.87/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1)))))),
% 1.87/2.11 inference(transitivity,[status(thm)],[6402, 6400])).
% 1.87/2.11 tff(6404,plain,
% 1.87/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))))),
% 1.87/2.11 inference(quant_inst,[status(thm)],[])).
% 1.87/2.11 tff(6405,plain,
% 1.87/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1))))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[6404, 6403])).
% 1.87/2.11 tff(6406,plain,
% 1.87/2.11 ($false),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[6405, 183, 171, 266, 1113])).
% 1.87/2.11 tff(6407,plain,((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.11 tff(6408,plain,
% 1.87/2.11 (~r(z, s(s(elem!1)))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[6407, 6399, 170])).
% 1.87/2.11 tff(6409,plain,
% 1.87/2.11 (b(z, s(s(elem!1)))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[264, 6408])).
% 1.87/2.11 tff(6410,plain,
% 1.87/2.11 (~r(s(s(elem!1)), s(z))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[191, 170, 172])).
% 1.87/2.11 tff(6411,plain,
% 1.87/2.11 (b(s(s(elem!1)), s(z))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[197, 6410])).
% 1.87/2.11 tff(6412,plain,
% 1.87/2.11 (~r(elem!1, s(z))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[292, 170, 267])).
% 1.87/2.11 tff(6413,plain,
% 1.87/2.11 (b(elem!1, s(z))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[214, 6412, 3])).
% 1.87/2.11 tff(6414,plain,
% 1.87/2.11 (r(s(z), elem!1)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[1034, 10, 1445])).
% 1.87/2.11 tff(6415,plain,
% 1.87/2.11 (~r(z, elem!1)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[6384, 6414, 170])).
% 1.87/2.11 tff(6416,plain,
% 1.87/2.11 (z = elem!1),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[60, 6415, 55])).
% 1.87/2.11 tff(6417,plain,
% 1.87/2.11 (b(z, s(z)) <=> b(elem!1, s(z))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[6416])).
% 1.87/2.11 tff(6418,plain,
% 1.87/2.11 (b(elem!1, s(z)) <=> b(z, s(z))),
% 1.87/2.11 inference(symmetry,[status(thm)],[6417])).
% 1.87/2.11 tff(6419,plain,
% 1.87/2.11 (b(elem!1, s(z))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[214, 3, 6386])).
% 1.87/2.11 tff(6420,plain,
% 1.87/2.11 (b(z, s(z))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[6419, 6418])).
% 1.87/2.11 tff(6421,plain,
% 1.87/2.11 ($false),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[54, 6420])).
% 1.87/2.11 tff(6422,plain,((elem!1 = s(z)) | b(z, s(z)) | b(z, elem!1) | b(s(z), elem!1) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.11 tff(6423,plain,
% 1.87/2.11 (b(s(z), elem!1)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[6422, 6412, 55, 3, 54])).
% 1.87/2.11 tff(6424,plain,
% 1.87/2.11 ($false),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[3799, 6423, 6413, 2362, 6411])).
% 1.87/2.11 tff(6425,plain,(b(z, s(z)) | (~b(s(s(elem!1)), elem!1)) | b(z, elem!1) | (elem!1 = s(z)) | (~r(s(s(elem!1)), z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.11 tff(6426,plain,
% 1.87/2.11 (~r(s(s(elem!1)), z)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[6425, 54, 55, 5365, 2339, 2362])).
% 1.87/2.11 tff(6427,plain,
% 1.87/2.11 (b(s(s(elem!1)), z)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[523, 6426])).
% 1.87/2.11 tff(6428,plain,
% 1.87/2.11 (b(s(z), elem!1)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[1034, 6385, 2277])).
% 1.87/2.11 tff(6429,plain,
% 1.87/2.11 (~r(z, s(s(elem!1)))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[6407, 1113, 171])).
% 1.87/2.11 tff(6430,plain,
% 1.87/2.11 (b(z, s(s(elem!1)))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[264, 6429])).
% 1.87/2.11 tff(6431,plain,
% 1.87/2.11 (r(z, s(s(s(z))))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[267, 2225])).
% 1.87/2.11 tff(6432,plain,
% 1.87/2.11 ($false),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[4030, 6431])).
% 1.87/2.11 tff(6433,plain,((~(s(s(s(z))) = elem!1)) | r(z, s(s(s(z)))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.11 tff(6434,plain,
% 1.87/2.11 (~(s(s(s(z))) = elem!1)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[6433, 4030, 267])).
% 1.87/2.11 tff(6435,plain,
% 1.87/2.11 (r(s(s(s(z))), elem!1)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[647, 6434, 1])).
% 1.87/2.11 tff(6436,plain,
% 1.87/2.11 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[5485, 6435, 267])).
% 1.87/2.11 tff(6437,plain,
% 1.87/2.11 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[86, 6436, 69])).
% 1.87/2.11 tff(6438,plain,
% 1.87/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(6439,plain,
% 1.87/2.11 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(6440,plain,
% 1.87/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(elem!1))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[6439])).
% 1.87/2.11 tff(6441,plain,
% 1.87/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(elem!1))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.87/2.12 inference(transitivity,[status(thm)],[6440, 6438])).
% 1.87/2.12 tff(6442,plain,
% 1.87/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 1.87/2.12 inference(quant_inst,[status(thm)],[])).
% 1.87/2.12 tff(6443,plain,
% 1.87/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[6442, 6441])).
% 1.87/2.12 tff(6444,plain,
% 1.87/2.12 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[6443, 246, 1044, 2001, 6437])).
% 1.87/2.12 tff(6445,assumption,(~b(s(s(s(s(s(elem!1))))), s(z))), introduced(assumption)).
% 1.87/2.12 tff(6446,plain,
% 1.87/2.12 ($false),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[2311, 47, 331, 4097, 6445])).
% 1.87/2.12 tff(6447,plain,(b(s(s(s(s(s(elem!1))))), s(z)) | r(s(s(s(s(s(elem!1))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.12 tff(6448,plain,
% 1.87/2.12 (r(s(s(s(s(s(elem!1))))), s(z))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[6447, 6444])).
% 1.87/2.12 tff(6449,plain,
% 1.87/2.12 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[4092, 6448, 173, 171, 6430])).
% 1.87/2.12 tff(6450,plain,
% 1.87/2.12 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 1.87/2.12 inference(symmetry,[status(thm)],[6449])).
% 1.87/2.12 tff(6451,plain,
% 1.87/2.12 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.87/2.12 inference(monotonicity,[status(thm)],[6450])).
% 1.87/2.12 tff(6452,plain,
% 1.87/2.12 (b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.87/2.12 inference(symmetry,[status(thm)],[6451])).
% 1.87/2.12 tff(6453,plain,
% 1.87/2.12 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.87/2.12 inference(monotonicity,[status(thm)],[6450])).
% 1.87/2.12 tff(6454,plain,
% 1.87/2.12 ((~r(s(s(s(s(z)))), s(s(elem!1)))) <=> (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))),
% 1.87/2.12 inference(monotonicity,[status(thm)],[6453])).
% 1.87/2.12 tff(6455,plain,
% 1.87/2.12 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[5568, 1, 2362])).
% 1.87/2.12 tff(6456,plain,
% 1.87/2.12 (b(z, s(s(s(z))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[6165, 4143])).
% 1.87/2.12 tff(6457,plain,
% 1.87/2.12 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[4248, 183, 173, 430])).
% 1.87/2.12 tff(6458,plain,
% 1.87/2.12 (b(s(s(s(z))), s(s(elem!1)))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[689, 6457, 119])).
% 1.87/2.12 tff(6459,plain,
% 1.87/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.87/2.12 inference(rewrite,[status(thm)],[])).
% 1.87/2.12 tff(6460,plain,
% 1.87/2.12 (((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, elem!1)) | (~r(s(s(s(z))), z))) <=> ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.87/2.12 inference(rewrite,[status(thm)],[])).
% 1.87/2.12 tff(6461,plain,
% 1.87/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))))),
% 1.87/2.12 inference(monotonicity,[status(thm)],[6460])).
% 1.87/2.12 tff(6462,plain,
% 1.87/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.87/2.12 inference(transitivity,[status(thm)],[6461, 6459])).
% 1.87/2.12 tff(6463,plain,
% 1.87/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)))),
% 1.87/2.12 inference(quant_inst,[status(thm)],[])).
% 1.87/2.12 tff(6464,plain,
% 1.87/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[6463, 6462])).
% 1.87/2.12 tff(6465,plain,
% 1.87/2.12 (~r(s(s(s(z))), z)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[6464, 183, 267, 171, 430])).
% 1.87/2.12 tff(6466,plain,
% 1.87/2.12 (b(s(s(s(z))), z)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[995, 6465])).
% 1.87/2.12 tff(6467,plain,
% 1.87/2.12 ($false),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[4659, 6466, 6458, 6456, 1100])).
% 1.87/2.12 tff(6468,plain,((~r(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), z)) | (s(s(s(z))) = s(s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.12 tff(6469,plain,
% 1.87/2.12 (~r(s(s(s(z))), s(z))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[6468, 1100, 6455, 267, 171, 173])).
% 1.87/2.12 tff(6470,plain,
% 1.87/2.12 (b(s(s(s(z))), s(z))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[52, 6469])).
% 1.87/2.12 tff(6471,plain,
% 1.87/2.12 (b(z, s(s(s(z))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[6165, 4030])).
% 1.87/2.12 tff(6472,plain,
% 1.87/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))))),
% 1.87/2.12 inference(rewrite,[status(thm)],[])).
% 1.87/2.12 tff(6473,plain,
% 1.87/2.12 (((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z)))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))))),
% 1.87/2.12 inference(rewrite,[status(thm)],[])).
% 1.87/2.12 tff(6474,plain,
% 1.87/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z)))))),
% 1.87/2.12 inference(monotonicity,[status(thm)],[6473])).
% 1.87/2.12 tff(6475,plain,
% 1.87/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))))),
% 1.87/2.12 inference(transitivity,[status(thm)],[6474, 6472])).
% 1.87/2.12 tff(6476,plain,
% 1.87/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))))),
% 1.87/2.12 inference(quant_inst,[status(thm)],[])).
% 1.87/2.12 tff(6477,plain,
% 1.87/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z)))),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[6476, 6475])).
% 1.87/2.12 tff(6478,plain,
% 1.87/2.12 ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[6477, 246, 2362, 2001, 6430, 6470])).
% 1.87/2.12 tff(6479,plain,
% 1.87/2.12 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[6478, 6471])).
% 1.87/2.12 tff(6480,plain,
% 1.87/2.12 (r(s(s(s(z))), s(s(elem!1)))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[689, 6479, 6455])).
% 1.87/2.12 tff(6481,plain,
% 1.87/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.87/2.12 inference(rewrite,[status(thm)],[])).
% 1.87/2.12 tff(6482,plain,
% 1.87/2.12 (((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.87/2.12 inference(rewrite,[status(thm)],[])).
% 1.87/2.12 tff(6483,plain,
% 1.87/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1))))))),
% 1.87/2.12 inference(monotonicity,[status(thm)],[6482])).
% 1.87/2.12 tff(6484,plain,
% 1.87/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.87/2.12 inference(transitivity,[status(thm)],[6483, 6481])).
% 1.87/2.12 tff(6485,plain,
% 1.87/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))))),
% 1.87/2.12 inference(quant_inst,[status(thm)],[])).
% 1.87/2.12 tff(6486,plain,
% 1.87/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1))))),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[6485, 6484])).
% 1.87/2.12 tff(6487,plain,
% 1.87/2.12 (~r(s(z), s(s(s(z))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[6486, 183, 1113, 6480])).
% 1.87/2.12 tff(6488,plain,
% 1.87/2.12 (b(s(z), s(s(s(z))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[1291, 6487])).
% 1.87/2.12 tff(6489,plain,
% 1.87/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.87/2.12 inference(rewrite,[status(thm)],[])).
% 1.87/2.12 tff(6490,plain,
% 1.87/2.12 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.87/2.12 inference(rewrite,[status(thm)],[])).
% 1.87/2.12 tff(6491,plain,
% 1.87/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.87/2.12 inference(monotonicity,[status(thm)],[6490])).
% 1.87/2.12 tff(6492,plain,
% 1.87/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.87/2.12 inference(transitivity,[status(thm)],[6491, 6489])).
% 1.87/2.12 tff(6493,plain,
% 1.87/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.87/2.12 inference(quant_inst,[status(thm)],[])).
% 1.87/2.12 tff(6494,plain,
% 1.87/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[6493, 6492])).
% 1.87/2.12 tff(6495,plain,
% 1.87/2.12 (~b(s(s(s(s(z)))), s(z))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[6494, 246, 1044, 2401, 2003, 1833])).
% 1.87/2.12 tff(6496,plain,
% 1.87/2.12 (r(s(s(s(s(z)))), s(z))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[6103, 6495])).
% 1.87/2.12 tff(6497,plain,
% 1.87/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.87/2.12 inference(rewrite,[status(thm)],[])).
% 1.87/2.12 tff(6498,plain,
% 1.87/2.12 (((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.87/2.12 inference(rewrite,[status(thm)],[])).
% 1.87/2.12 tff(6499,plain,
% 1.87/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))))),
% 1.87/2.12 inference(monotonicity,[status(thm)],[6498])).
% 1.87/2.12 tff(6500,plain,
% 1.87/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.87/2.12 inference(transitivity,[status(thm)],[6499, 6497])).
% 1.87/2.12 tff(6501,plain,
% 1.87/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 1.87/2.12 inference(quant_inst,[status(thm)],[])).
% 1.87/2.12 tff(6502,plain,
% 1.87/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[6501, 6500])).
% 1.87/2.12 tff(6503,plain,
% 1.87/2.12 (~r(s(s(s(s(z)))), z)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[6502, 183, 267, 171, 6496])).
% 1.87/2.12 tff(6504,plain,
% 1.87/2.12 (b(s(s(s(s(z)))), z)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[6040, 6503])).
% 1.87/2.12 tff(6505,plain,
% 1.87/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)))),
% 1.87/2.12 inference(rewrite,[status(thm)],[])).
% 1.87/2.12 tff(6506,plain,
% 1.87/2.12 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)))),
% 1.87/2.12 inference(rewrite,[status(thm)],[])).
% 1.87/2.12 tff(6507,plain,
% 1.87/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), z))))),
% 1.87/2.12 inference(monotonicity,[status(thm)],[6506])).
% 1.87/2.12 tff(6508,plain,
% 1.87/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)))),
% 1.87/2.12 inference(transitivity,[status(thm)],[6507, 6505])).
% 1.87/2.12 tff(6509,plain,
% 1.87/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.87/2.12 inference(quant_inst,[status(thm)],[])).
% 1.87/2.12 tff(6510,plain,
% 1.87/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), z))),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[6509, 6508])).
% 1.87/2.12 tff(6511,plain,
% 1.87/2.12 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[6510, 246, 2362, 1100, 1099, 6504])).
% 1.87/2.12 tff(6512,plain,
% 1.87/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.97/2.12 inference(rewrite,[status(thm)],[])).
% 1.97/2.12 tff(6513,plain,
% 1.97/2.12 (((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.97/2.12 inference(rewrite,[status(thm)],[])).
% 1.97/2.12 tff(6514,plain,
% 1.97/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.97/2.12 inference(monotonicity,[status(thm)],[6513])).
% 1.97/2.12 tff(6515,plain,
% 1.97/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.97/2.12 inference(transitivity,[status(thm)],[6514, 6512])).
% 1.97/2.12 tff(6516,plain,
% 1.97/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.97/2.12 inference(quant_inst,[status(thm)],[])).
% 1.97/2.12 tff(6517,plain,
% 1.97/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 1.97/2.12 inference(modus_ponens,[status(thm)],[6516, 6515])).
% 1.97/2.12 tff(6518,plain,
% 1.97/2.12 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[6517, 183, 173, 6496])).
% 1.97/2.12 tff(6519,plain,
% 1.97/2.12 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(elem!1))) | b(s(s(s(s(z)))), s(s(elem!1))) | r(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(elem!1))) | b(s(s(s(s(z)))), s(s(elem!1))) | r(s(s(s(s(z)))), s(s(elem!1))))),
% 1.97/2.12 inference(rewrite,[status(thm)],[])).
% 1.97/2.12 tff(6520,plain,
% 1.97/2.12 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(elem!1))) | b(s(s(s(s(z)))), s(s(elem!1))) | r(s(s(s(s(z)))), s(s(elem!1))))),
% 1.97/2.12 inference(quant_inst,[status(thm)],[])).
% 1.97/2.12 tff(6521,plain,
% 1.97/2.12 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(elem!1))) | b(s(s(s(s(z)))), s(s(elem!1))) | r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.97/2.12 inference(modus_ponens,[status(thm)],[6520, 6519])).
% 1.97/2.12 tff(6522,plain,
% 1.97/2.12 ((s(s(s(s(z)))) = s(s(elem!1))) | b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[6521, 47, 6518])).
% 1.97/2.12 tff(6523,plain,
% 1.97/2.12 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[6522, 6511])).
% 1.97/2.12 tff(6524,plain,
% 1.97/2.12 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 1.97/2.12 inference(monotonicity,[status(thm)],[6523])).
% 1.97/2.12 tff(6525,plain,
% 1.97/2.12 (s(s(s(z))) = s(elem!1)),
% 1.97/2.12 inference(transitivity,[status(thm)],[1492, 6524, 92])).
% 1.97/2.12 tff(6526,plain,
% 1.97/2.12 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(elem!1)), s(elem!1))),
% 1.97/2.12 inference(monotonicity,[status(thm)],[6525])).
% 1.97/2.12 tff(6527,plain,
% 1.97/2.12 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.97/2.12 inference(symmetry,[status(thm)],[6526])).
% 1.97/2.12 tff(6528,plain,
% 1.97/2.12 ((~b(s(s(elem!1)), s(elem!1))) <=> (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.97/2.12 inference(monotonicity,[status(thm)],[6527])).
% 1.97/2.12 tff(6529,plain,
% 1.97/2.12 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.97/2.12 inference(modus_ponens,[status(thm)],[5035, 6528])).
% 1.97/2.12 tff(6530,plain,
% 1.97/2.12 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[6523])).
% 1.97/2.13 tff(6531,plain,
% 1.97/2.13 (b(s(s(elem!1)), s(s(s(z))))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[1833, 6530])).
% 1.97/2.13 tff(6532,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[6531, 6529])).
% 1.97/2.13 tff(6533,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | b(s(s(elem!1)), s(elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(6534,plain,
% 1.97/2.13 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[6533, 6488, 2362, 1100, 6430, 267, 171, 173, 1044, 5035, 6470])).
% 1.97/2.13 tff(6535,plain,
% 1.97/2.13 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1702, 6534])).
% 1.97/2.13 tff(6536,plain,
% 1.97/2.13 (~(s(s(elem!1)) = s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[421, 6455])).
% 1.97/2.13 tff(6537,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(6538,plain,
% 1.97/2.13 (((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(6539,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[6538])).
% 1.97/2.13 tff(6540,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.97/2.13 inference(transitivity,[status(thm)],[6539, 6537])).
% 1.97/2.13 tff(6541,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(elem!1)))))),
% 1.97/2.13 inference(quant_inst,[status(thm)],[])).
% 1.97/2.13 tff(6542,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[6541, 6540])).
% 1.97/2.13 tff(6543,plain,
% 1.97/2.13 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[6542, 246, 1044, 2362, 6430, 6470, 6471])).
% 1.97/2.13 tff(6544,plain,
% 1.97/2.13 (r(s(s(elem!1)), s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[454, 6543, 6536])).
% 1.97/2.13 tff(6545,plain,
% 1.97/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(6546,plain,
% 1.97/2.13 (((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(6547,plain,
% 1.97/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[6546])).
% 1.97/2.13 tff(6548,plain,
% 1.97/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.97/2.13 inference(transitivity,[status(thm)],[6547, 6545])).
% 1.97/2.13 tff(6549,plain,
% 1.97/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.97/2.13 inference(quant_inst,[status(thm)],[])).
% 1.97/2.13 tff(6550,plain,
% 1.97/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[6549, 6548])).
% 1.97/2.13 tff(6551,plain,
% 1.97/2.13 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[6550, 183, 6544, 6535])).
% 1.97/2.13 tff(6552,plain,
% 1.97/2.13 (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[6551, 6454])).
% 1.97/2.13 tff(6553,plain,
% 1.97/2.13 (b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1506, 6552])).
% 1.97/2.13 tff(6554,plain,
% 1.97/2.13 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[6553, 6452])).
% 1.97/2.13 tff(6555,plain,
% 1.97/2.13 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(elem!1)))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[6449])).
% 1.97/2.13 tff(6556,plain,
% 1.97/2.13 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.97/2.13 inference(symmetry,[status(thm)],[6555])).
% 1.97/2.13 tff(6557,plain,
% 1.97/2.13 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.97/2.13 inference(transitivity,[status(thm)],[108, 6556, 325])).
% 1.97/2.13 tff(6558,plain,
% 1.97/2.13 (inj_0(s(elem!1)) = inj_0(s(s(s(s(elem!1)))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[6557])).
% 1.97/2.13 tff(6559,plain,
% 1.97/2.13 (elem!1 = s(s(s(elem!1)))),
% 1.97/2.13 inference(transitivity,[status(thm)],[3154, 6558, 351])).
% 1.97/2.13 tff(6560,plain,
% 1.97/2.13 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[6559])).
% 1.97/2.13 tff(6561,plain,
% 1.97/2.13 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(elem!1))),
% 1.97/2.13 inference(symmetry,[status(thm)],[6558])).
% 1.97/2.13 tff(6562,plain,
% 1.97/2.13 (s(s(s(elem!1))) = elem!1),
% 1.97/2.13 inference(transitivity,[status(thm)],[352, 6561, 343])).
% 1.97/2.13 tff(6563,plain,
% 1.97/2.13 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(z)))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[6562])).
% 1.97/2.13 tff(6564,plain,
% 1.97/2.13 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.97/2.13 inference(transitivity,[status(thm)],[6563, 3067])).
% 1.97/2.13 tff(6565,plain,
% 1.97/2.13 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[6564])).
% 1.97/2.13 tff(6566,plain,
% 1.97/2.13 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[6281, 6455])).
% 1.97/2.13 tff(6567,plain,
% 1.97/2.13 (~(s(s(s(s(z)))) = elem!1)),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[6566, 6565])).
% 1.97/2.13 tff(6568,plain,
% 1.97/2.13 (~b(elem!1, s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2011, 6470, 2001, 1044])).
% 1.97/2.13 tff(6569,plain,
% 1.97/2.13 (~(elem!1 = s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[3013, 6434])).
% 1.97/2.13 tff(6570,plain,
% 1.97/2.13 (r(elem!1, s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[470, 6569, 6568])).
% 1.97/2.13 tff(6571,plain,
% 1.97/2.13 (~r(s(s(s(s(z)))), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2618, 183, 6570, 6535])).
% 1.97/2.13 tff(6572,plain,
% 1.97/2.13 ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2442, 47, 6571])).
% 1.97/2.13 tff(6573,plain,
% 1.97/2.13 (b(s(s(s(s(z)))), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[6572, 6567])).
% 1.97/2.13 tff(6574,plain,
% 1.97/2.13 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[6573, 6560])).
% 1.97/2.13 tff(6575,plain,
% 1.97/2.13 (b(elem!1, s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[6559])).
% 1.97/2.13 tff(6576,plain,
% 1.97/2.13 (b(s(s(s(elem!1))), s(z))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[2001, 6575])).
% 1.97/2.13 tff(6577,plain,
% 1.97/2.13 (b(s(z), elem!1) <=> b(s(z), s(s(s(elem!1))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[6559])).
% 1.97/2.13 tff(6578,plain,
% 1.97/2.13 (b(s(z), s(s(s(elem!1))))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[1044, 6577])).
% 1.97/2.13 tff(6579,plain,
% 1.97/2.13 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[6559])).
% 1.97/2.13 tff(6580,plain,
% 1.97/2.13 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[2362, 6579])).
% 1.97/2.13 tff(6581,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(6582,plain,
% 1.97/2.13 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(6583,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[6582])).
% 1.97/2.13 tff(6584,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.97/2.13 inference(transitivity,[status(thm)],[6583, 6581])).
% 1.97/2.13 tff(6585,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.97/2.13 inference(quant_inst,[status(thm)],[])).
% 1.97/2.13 tff(6586,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[6585, 6584])).
% 1.97/2.13 tff(6587,plain,
% 1.97/2.13 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[6586, 246, 6580, 6578, 6576, 6574])).
% 1.97/2.13 tff(6588,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[6587, 6554])).
% 1.97/2.13 tff(6589,plain,(r(z, s(s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (s(s(s(s(s(elem!1))))) = elem!1) | (~r(z, elem!1)) | b(s(s(s(z))), elem!1) | (~b(s(s(elem!1)), z)) | b(s(s(elem!1)), s(elem!1)) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(6590,plain,
% 1.97/2.13 (r(z, s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[6589, 6428, 2362, 2001, 173, 170, 69, 5365, 1, 6427, 5035, 6399])).
% 1.97/2.13 tff(6591,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[5419, 183, 267, 634, 429])).
% 1.97/2.13 tff(6592,plain,((~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(6593,plain,
% 1.97/2.13 (~r(s(s(s(z))), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[6592, 6590, 5365])).
% 1.97/2.13 tff(6594,plain,
% 1.97/2.13 (s(s(s(z))) = elem!1),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[647, 6593, 1])).
% 1.97/2.13 tff(6595,plain,
% 1.97/2.13 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[5623, 6594])).
% 1.97/2.13 tff(6596,plain,
% 1.97/2.13 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[4092, 6595, 173, 170, 6409])).
% 1.97/2.13 tff(6597,plain,
% 1.97/2.13 (b(s(s(s(s(s(elem!1))))), s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[6447, 6596])).
% 1.97/2.13 tff(6598,plain,
% 1.97/2.13 (~r(s(s(s(z))), s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[6468, 6427, 6455, 5365, 170, 173])).
% 1.97/2.13 tff(6599,plain,
% 1.97/2.13 (b(s(s(s(z))), s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[52, 6598])).
% 1.97/2.13 tff(6600,plain,
% 1.97/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(6601,plain,
% 1.97/2.13 (((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(6602,plain,
% 1.97/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[6601])).
% 1.97/2.13 tff(6603,plain,
% 1.97/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.97/2.13 inference(transitivity,[status(thm)],[6602, 6600])).
% 1.97/2.13 tff(6604,plain,
% 1.97/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z))))),
% 1.97/2.13 inference(quant_inst,[status(thm)],[])).
% 1.97/2.13 tff(6605,plain,
% 1.97/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[6604, 6603])).
% 1.97/2.13 tff(6606,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[6605, 183, 171, 6096, 429])).
% 1.97/2.13 tff(6607,plain,((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(6608,plain,
% 1.97/2.13 (~r(s(z), s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[6607, 170, 6590])).
% 1.97/2.13 tff(6609,plain,
% 1.97/2.13 (b(s(z), s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1291, 6608])).
% 1.97/2.13 tff(6610,plain,
% 1.97/2.13 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[6533, 6609, 2362, 6427, 6409, 5365, 170, 173, 6428, 5035, 6599])).
% 1.97/2.13 tff(6611,plain,
% 1.97/2.13 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1702, 6610])).
% 1.97/2.13 tff(6612,plain,
% 1.97/2.13 (r(s(elem!1), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[5548, 6594, 6611])).
% 1.97/2.13 tff(6613,plain,
% 1.97/2.13 (s(s(s(s(z)))) = s(elem!1)),
% 1.97/2.13 inference(monotonicity,[status(thm)],[6594])).
% 1.97/2.13 tff(6614,plain,
% 1.97/2.13 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(elem!1) = s(s(s(s(s(elem!1))))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[6613])).
% 1.97/2.13 tff(6615,plain,
% 1.97/2.13 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(elem!1))),
% 1.97/2.13 inference(transitivity,[status(thm)],[6614, 1800])).
% 1.97/2.13 tff(6616,plain,
% 1.97/2.13 ((~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(s(elem!1))))) = s(elem!1)))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[6615])).
% 1.97/2.13 tff(6617,plain,
% 1.97/2.13 (~(s(s(s(s(s(elem!1))))) = s(elem!1))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[1501, 6616])).
% 1.97/2.13 tff(6618,plain,
% 1.97/2.13 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[5543, 6617, 5365, 6612])).
% 1.97/2.13 tff(6619,plain,
% 1.97/2.13 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[86, 6618, 69])).
% 1.97/2.13 tff(6620,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[6443, 246, 6428, 2001, 6619, 6597])).
% 1.97/2.13 tff(6621,plain,(b(z, s(z)) | (~b(elem!1, s(z))) | (s(s(s(s(s(elem!1))))) = elem!1) | (~r(s(s(elem!1)), s(z))) | b(s(s(s(z))), elem!1) | (~b(s(s(elem!1)), elem!1)) | b(s(s(elem!1)), s(elem!1)) | (s(z) = elem!1) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(6622,plain,
% 1.97/2.13 (b(z, s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[6621, 1, 69, 2133, 6373, 6375, 5035, 5374, 55])).
% 1.97/2.13 tff(6623,plain,
% 1.97/2.13 (~r(s(s(s(z))), s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2713, 1445, 634, 2232])).
% 1.97/2.13 tff(6624,plain,
% 1.97/2.13 (b(s(s(s(z))), s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[52, 6623])).
% 1.97/2.13 tff(6625,plain,
% 1.97/2.13 (r(s(z), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1034, 1445, 2277])).
% 1.97/2.13 tff(6626,plain,
% 1.97/2.13 (~r(s(z), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[5432, 6625, 267])).
% 1.97/2.13 tff(6627,plain,
% 1.97/2.13 (b(s(z), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1069, 6626])).
% 1.97/2.13 tff(6628,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[6174, 6627, 6624, 5477, 236])).
% 1.97/2.13 tff(6629,plain,(b(s(z), elem!1) | (~b(z, s(z))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | r(s(s(elem!1)), elem!1) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(6630,plain,
% 1.97/2.13 (b(s(z), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[6629, 6435, 267, 2232, 236, 5374])).
% 1.97/2.13 tff(6631,plain,
% 1.97/2.13 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[6443, 246, 6630, 2001, 6437])).
% 1.97/2.13 tff(6632,plain,
% 1.97/2.13 (r(s(s(s(s(s(elem!1))))), s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[6447, 6631])).
% 1.97/2.13 tff(6633,plain,
% 1.97/2.13 (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[6354, 183, 2133, 6632])).
% 1.97/2.13 tff(6634,plain,
% 1.97/2.13 (~(s(s(elem!1)) = elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2130, 2001, 2124])).
% 1.97/2.13 tff(6635,plain,
% 1.97/2.13 (b(s(s(elem!1)), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[156, 6634, 2232])).
% 1.97/2.13 tff(6636,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(6637,plain,
% 1.97/2.13 (((~b(s(z), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(6638,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[6637])).
% 1.97/2.13 tff(6639,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.97/2.13 inference(transitivity,[status(thm)],[6638, 6636])).
% 1.97/2.13 tff(6640,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.97/2.13 inference(quant_inst,[status(thm)],[])).
% 1.97/2.13 tff(6641,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[6640, 6639])).
% 1.97/2.14 tff(6642,plain,
% 1.97/2.14 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[6641, 246, 6630, 6635, 2001, 6437])).
% 1.97/2.14 tff(6643,plain,
% 1.97/2.14 ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[1547, 47, 6642])).
% 1.97/2.14 tff(6644,plain,
% 1.97/2.14 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[6643, 6633])).
% 1.97/2.14 tff(6645,plain,
% 1.97/2.14 (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[6644])).
% 1.97/2.14 tff(6646,plain,
% 1.97/2.14 (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))),
% 1.97/2.14 inference(symmetry,[status(thm)],[6645])).
% 1.97/2.14 tff(6647,plain,
% 1.97/2.14 (b(s(s(s(s(s(s(elem!1)))))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[6646])).
% 1.97/2.14 tff(6648,plain,
% 1.97/2.14 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.97/2.14 inference(symmetry,[status(thm)],[6647])).
% 1.97/2.14 tff(6649,plain,
% 1.97/2.14 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[6644])).
% 1.97/2.14 tff(6650,plain,
% 1.97/2.14 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.97/2.14 inference(transitivity,[status(thm)],[108, 6649, 325])).
% 1.97/2.14 tff(6651,plain,
% 1.97/2.14 (inj_0(s(elem!1)) = inj_0(s(s(s(s(elem!1)))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[6650])).
% 1.97/2.14 tff(6652,plain,
% 1.97/2.14 (elem!1 = s(s(s(elem!1)))),
% 1.97/2.14 inference(transitivity,[status(thm)],[3154, 6651, 351])).
% 1.97/2.14 tff(6653,plain,
% 1.97/2.14 (b(elem!1, s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[6652])).
% 1.97/2.14 tff(6654,plain,
% 1.97/2.14 (b(s(s(s(elem!1))), s(z))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[2001, 6653])).
% 1.97/2.14 tff(6655,plain,
% 1.97/2.14 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[6654, 6648])).
% 1.97/2.14 tff(6656,plain,
% 1.97/2.14 (b(s(z), s(s(s(s(s(s(elem!1))))))) <=> b(s(z), s(s(s(elem!1))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[6646])).
% 1.97/2.14 tff(6657,plain,
% 1.97/2.14 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.97/2.14 inference(symmetry,[status(thm)],[6656])).
% 1.97/2.14 tff(6658,plain,
% 1.97/2.14 (b(s(z), elem!1) <=> b(s(z), s(s(s(elem!1))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[6652])).
% 1.97/2.14 tff(6659,plain,
% 1.97/2.14 (b(s(z), s(s(s(elem!1))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[6630, 6658])).
% 1.97/2.14 tff(6660,plain,
% 1.97/2.14 (b(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[6659, 6657])).
% 1.97/2.14 tff(6661,plain,
% 1.97/2.14 (~r(s(s(s(z))), z)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[5411, 183, 267, 6435])).
% 1.97/2.14 tff(6662,plain,
% 1.97/2.14 (b(s(s(s(z))), z)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[995, 6661])).
% 1.97/2.14 tff(6663,plain,
% 1.97/2.14 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[5568, 1, 6635])).
% 1.97/2.14 tff(6664,plain,
% 1.97/2.14 (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(elem!1))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[6646])).
% 1.97/2.14 tff(6665,plain,
% 1.97/2.14 (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(s(s(elem!1)))))))),
% 1.97/2.14 inference(symmetry,[status(thm)],[6664])).
% 1.97/2.14 tff(6666,plain,
% 1.97/2.14 (b(s(s(s(s(s(elem!1))))), elem!1) <=> b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[6652])).
% 1.97/2.14 tff(6667,plain,
% 1.97/2.14 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[6437, 6666])).
% 1.97/2.14 tff(6668,plain,
% 1.97/2.14 (b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1)))))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[6667, 6665])).
% 1.97/2.14 tff(6669,assumption,(b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 1.97/2.14 tff(6670,assumption,(b(s(z), s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 1.97/2.14 tff(6671,plain,
% 1.97/2.14 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[3812])).
% 1.97/2.14 tff(6672,plain,
% 1.97/2.14 (r(s(s(s(z))), s(s(s(s(s(elem!1)))))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[3813])).
% 1.97/2.14 tff(6673,plain,
% 1.97/2.14 ((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) <=> (~r(s(s(s(z))), s(s(elem!1))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[6672])).
% 1.97/2.14 tff(6674,plain,
% 1.97/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(6675,plain,
% 1.97/2.14 (((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(6676,plain,
% 1.97/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z)))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[6675])).
% 1.97/2.14 tff(6677,plain,
% 1.97/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 1.97/2.14 inference(transitivity,[status(thm)],[6676, 6674])).
% 1.97/2.14 tff(6678,plain,
% 1.97/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(6679,plain,
% 1.97/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z)))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[6678, 6677])).
% 1.97/2.14 tff(6680,plain,
% 1.97/2.14 (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[6679, 183, 430, 4064])).
% 1.97/2.14 tff(6681,plain,
% 1.97/2.14 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[6680, 6673])).
% 1.97/2.14 tff(6682,plain,
% 1.97/2.14 (b(s(s(s(z))), s(s(elem!1)))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[689, 6681, 119])).
% 1.97/2.14 tff(6683,plain,
% 1.97/2.14 (b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[6682, 6671])).
% 1.97/2.14 tff(6684,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1)))))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(6685,plain,
% 1.97/2.14 (((~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1)))))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(6686,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1))))))))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[6685])).
% 1.97/2.14 tff(6687,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1)))))))))),
% 1.97/2.14 inference(transitivity,[status(thm)],[6686, 6684])).
% 1.97/2.14 tff(6688,plain,
% 1.97/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(6689,plain,
% 1.97/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1))))))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[6688, 6687])).
% 1.97/2.14 tff(6690,plain,
% 1.97/2.14 (~b(s(z), s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[6689, 246, 236, 4651, 6683, 6670, 6669])).
% 1.97/2.14 tff(6691,plain,
% 1.97/2.14 (r(s(z), s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[1291, 6690])).
% 1.97/2.14 tff(6692,plain,
% 1.97/2.14 (~b(elem!1, s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[4259, 430, 2124, 2232, 2001, 119])).
% 1.97/2.14 tff(6693,plain,
% 1.97/2.14 (r(elem!1, s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[470, 6692, 1675])).
% 1.97/2.14 tff(6694,plain,
% 1.97/2.14 (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[3812])).
% 1.97/2.14 tff(6695,plain,
% 1.97/2.14 (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))),
% 1.97/2.14 inference(symmetry,[status(thm)],[6694])).
% 1.97/2.14 tff(6696,plain,
% 1.97/2.14 (b(s(s(s(s(s(s(elem!1)))))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[6695])).
% 1.97/2.14 tff(6697,plain,
% 1.97/2.14 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.97/2.14 inference(symmetry,[status(thm)],[6696])).
% 1.97/2.14 tff(6698,plain,
% 1.97/2.14 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[3812])).
% 1.97/2.14 tff(6699,plain,
% 1.97/2.14 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.97/2.14 inference(transitivity,[status(thm)],[108, 6698, 325])).
% 1.97/2.14 tff(6700,plain,
% 1.97/2.14 (inj_0(s(elem!1)) = inj_0(s(s(s(s(elem!1)))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[6699])).
% 1.97/2.14 tff(6701,plain,
% 1.97/2.14 (elem!1 = s(s(s(elem!1)))),
% 1.97/2.14 inference(transitivity,[status(thm)],[3154, 6700, 351])).
% 1.97/2.14 tff(6702,plain,
% 1.97/2.14 (b(elem!1, s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[6701])).
% 1.97/2.14 tff(6703,plain,
% 1.97/2.14 (b(s(s(s(elem!1))), s(z))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[2001, 6702])).
% 1.97/2.14 tff(6704,plain,
% 1.97/2.14 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[6703, 6697])).
% 1.97/2.14 tff(6705,plain,
% 1.97/2.14 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[6281, 119])).
% 1.97/2.14 tff(6706,assumption,(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))), introduced(assumption)).
% 1.97/2.14 tff(6707,plain,
% 1.97/2.14 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.97/2.14 inference(transitivity,[status(thm)],[6694, 6706])).
% 1.97/2.14 tff(6708,plain,
% 1.97/2.14 ($false),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[6330, 6707])).
% 1.97/2.14 tff(6709,plain,((~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z)))))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~(s(s(elem!1)) = s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.14 tff(6710,plain,
% 1.97/2.14 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z)))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[6709, 3812, 6705])).
% 1.97/2.14 tff(6711,plain,
% 1.97/2.14 (~b(s(s(elem!1)), z)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[4659, 6682, 4651, 2090])).
% 1.97/2.14 tff(6712,plain,
% 1.97/2.14 (r(s(s(elem!1)), z)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[523, 6711])).
% 1.97/2.14 tff(6713,plain,
% 1.97/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(6714,plain,
% 1.97/2.14 (((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(6715,plain,
% 1.97/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[6714])).
% 1.97/2.14 tff(6716,plain,
% 1.97/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))),
% 1.97/2.14 inference(transitivity,[status(thm)],[6715, 6713])).
% 1.97/2.14 tff(6717,plain,
% 1.97/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(6718,plain,
% 1.97/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[6717, 6716])).
% 1.97/2.14 tff(6719,plain,
% 1.97/2.14 ($false),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[6718, 183, 173, 1114, 172])).
% 1.97/2.14 tff(6720,plain,((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.14 tff(6721,plain,
% 1.97/2.14 (~r(s(z), z)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[6720, 6712, 2133])).
% 1.97/2.14 tff(6722,plain,
% 1.97/2.14 (b(s(z), z)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[1069, 6721])).
% 1.97/2.14 tff(6723,assumption,(b(s(s(s(s(s(s(elem!1)))))), s(z))), introduced(assumption)).
% 1.97/2.14 tff(6724,plain,
% 1.97/2.14 (~r(s(s(s(s(z)))), s(z))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[6098, 2593, 6096])).
% 1.97/2.14 tff(6725,plain,
% 1.97/2.14 (b(s(s(s(s(z)))), s(z))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[6103, 6724])).
% 1.97/2.14 tff(6726,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), 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)))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(6727,plain,
% 1.97/2.14 (((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(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), z)) | (~b(z, 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)))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(6728,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), 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))))))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[6727])).
% 1.97/2.14 tff(6729,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), 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)))))))),
% 1.97/2.14 inference(transitivity,[status(thm)],[6728, 6726])).
% 1.97/2.14 tff(6730,plain,
% 1.97/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(6731,plain,
% 1.97/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(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))))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[6730, 6729])).
% 1.97/2.14 tff(6732,plain,
% 1.97/2.14 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[6731, 246, 1056, 236, 6725, 6723])).
% 1.97/2.14 tff(6733,plain,
% 1.97/2.14 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(elem!1))),
% 1.97/2.14 inference(symmetry,[status(thm)],[6700])).
% 1.97/2.14 tff(6734,plain,
% 1.97/2.14 (s(s(s(s(s(s(elem!1)))))) = elem!1),
% 1.97/2.14 inference(transitivity,[status(thm)],[6695, 352, 6733, 343])).
% 1.97/2.14 tff(6735,plain,
% 1.97/2.14 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[6734])).
% 1.97/2.14 tff(6736,plain,
% 1.97/2.14 (r(elem!1, s(s(s(z)))) <=> r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.97/2.14 inference(symmetry,[status(thm)],[6735])).
% 1.97/2.14 tff(6737,plain,
% 1.97/2.14 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[413, 6736])).
% 1.97/2.14 tff(6738,plain,
% 1.97/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~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(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~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(s(z)))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(6739,plain,
% 1.97/2.14 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~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(s(z)))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(6740,plain,
% 1.97/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~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(s(z))))))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[6739])).
% 1.97/2.14 tff(6741,plain,
% 1.97/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~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(s(z)))))))),
% 1.97/2.14 inference(transitivity,[status(thm)],[6740, 6738])).
% 1.97/2.14 tff(6742,plain,
% 1.97/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(6743,plain,
% 1.97/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~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(s(z))))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[6742, 6741])).
% 1.97/2.14 tff(6744,plain,
% 1.97/2.14 ((~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(s(z))))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[6743, 183, 2593])).
% 1.97/2.14 tff(6745,plain,
% 1.97/2.14 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[6744, 6737])).
% 1.97/2.14 tff(6746,assumption,(~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z)))))), introduced(assumption)).
% 1.97/2.14 tff(6747,plain,
% 1.97/2.14 (((~![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))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(6748,plain,
% 1.97/2.14 ((~![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))))))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(6749,plain,
% 1.97/2.14 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[6748, 6747])).
% 1.97/2.14 tff(6750,plain,
% 1.97/2.14 ($false),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[6749, 47, 6746, 6745, 6732])).
% 1.97/2.14 tff(6751,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(elem!1, s(s(s(z))))) | (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.14 tff(6752,plain,
% 1.97/2.14 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[6751, 6722, 6710, 236, 6704, 6693, 3812, 6691])).
% 1.97/2.14 tff(6753,plain,
% 1.97/2.14 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[1702, 6752])).
% 1.97/2.15 tff(6754,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(6755,plain,
% 1.97/2.15 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(6756,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[6755])).
% 1.97/2.15 tff(6757,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.97/2.15 inference(transitivity,[status(thm)],[6756, 6754])).
% 1.97/2.15 tff(6758,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(6759,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[6758, 6757])).
% 1.97/2.15 tff(6760,plain,
% 1.97/2.15 (~b(s(s(s(s(z)))), z)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[6759, 246, 236, 4651, 2090, 6753])).
% 1.97/2.15 tff(6761,plain,
% 1.97/2.15 (r(s(s(s(s(z)))), z)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[6040, 6760])).
% 1.97/2.15 tff(6762,plain,
% 1.97/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(6763,plain,
% 1.97/2.15 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(6764,plain,
% 1.97/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z)))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[6763])).
% 1.97/2.15 tff(6765,plain,
% 1.97/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 1.97/2.15 inference(transitivity,[status(thm)],[6764, 6762])).
% 1.97/2.15 tff(6766,plain,
% 1.97/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(6767,plain,
% 1.97/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z)))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[6766, 6765])).
% 1.97/2.15 tff(6768,plain,
% 1.97/2.15 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[6767, 183, 430, 4064])).
% 1.97/2.15 tff(6769,plain,
% 1.97/2.15 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[1626, 6768])).
% 1.97/2.15 tff(6770,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(6771,plain,
% 1.97/2.15 (((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1)))))))) <=> ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(6772,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[6771])).
% 1.97/2.15 tff(6773,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.97/2.15 inference(transitivity,[status(thm)],[6772, 6770])).
% 1.97/2.15 tff(6774,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(6775,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[6774, 6773])).
% 1.97/2.15 tff(6776,plain,
% 1.97/2.15 (~b(z, s(s(s(s(s(elem!1))))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[6775, 246, 4651, 2090, 6769])).
% 1.97/2.15 tff(6777,plain,
% 1.97/2.15 (r(z, s(s(s(s(s(elem!1))))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[2487, 47, 5706, 6776])).
% 1.97/2.15 tff(6778,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(6779,plain,
% 1.97/2.15 (((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(6780,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[6779])).
% 1.97/2.15 tff(6781,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 1.97/2.15 inference(transitivity,[status(thm)],[6780, 6778])).
% 1.97/2.15 tff(6782,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(6783,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[6782, 6781])).
% 1.97/2.15 tff(6784,plain,
% 1.97/2.15 (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[6783, 246, 4651, 2090, 6753, 6769])).
% 1.97/2.15 tff(6785,plain,
% 1.97/2.15 (r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[1506, 6784])).
% 1.97/2.15 tff(6786,plain,
% 1.97/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(6787,plain,
% 1.97/2.15 (((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(6788,plain,
% 1.97/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[6787])).
% 1.97/2.15 tff(6789,plain,
% 1.97/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 1.97/2.15 inference(transitivity,[status(thm)],[6788, 6786])).
% 1.97/2.15 tff(6790,plain,
% 1.97/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), z)))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(6791,plain,
% 1.97/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[6790, 6789])).
% 1.97/2.15 tff(6792,plain,
% 1.97/2.15 ($false),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[6791, 183, 6785, 6777, 6761])).
% 1.97/2.15 tff(6793,plain,((~r(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1)))))))) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (elem!1 = s(s(s(z)))) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), elem!1) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.15 tff(6794,plain,
% 1.97/2.15 (~r(s(s(s(z))), s(z))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[6793, 6471, 6662, 236, 6644, 6660, 6668, 6663, 6632, 6569, 2124, 2232, 2001])).
% 1.97/2.15 tff(6795,plain,
% 1.97/2.15 (b(s(s(s(z))), s(z))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[52, 6794])).
% 1.97/2.15 tff(6796,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(6797,plain,
% 1.97/2.15 (((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(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(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(6798,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z)))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[6797])).
% 1.97/2.15 tff(6799,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 1.97/2.15 inference(transitivity,[status(thm)],[6798, 6796])).
% 1.97/2.15 tff(6800,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(6801,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[6800, 6799])).
% 1.97/2.15 tff(6802,plain,
% 1.97/2.15 ($false),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[6801, 246, 236, 6795, 6662, 6660, 6655])).
% 1.97/2.15 tff(6803,plain,(r(z, s(s(s(z)))) | (~b(z, s(z))) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), elem!1) | (~b(elem!1, s(z))) | (~r(z, elem!1)) | (s(s(s(s(s(elem!1))))) = elem!1) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.15 tff(6804,plain,
% 1.97/2.15 (r(z, s(s(s(z))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[6803, 6622, 2124, 2232, 6373, 5365, 69, 1])).
% 1.97/2.15 tff(6805,plain,
% 1.97/2.15 (~r(s(s(s(z))), elem!1)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[6592, 6804, 5365])).
% 1.97/2.15 tff(6806,plain,
% 1.97/2.15 (s(s(s(z))) = elem!1),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[647, 6805, 1])).
% 1.97/2.15 tff(6807,plain,
% 1.97/2.15 (s(s(s(s(z)))) = s(elem!1)),
% 1.97/2.15 inference(monotonicity,[status(thm)],[6806])).
% 1.97/2.15 tff(6808,plain,
% 1.97/2.15 (s(elem!1) = s(s(s(s(z))))),
% 1.97/2.15 inference(symmetry,[status(thm)],[6807])).
% 1.97/2.15 tff(6809,plain,
% 1.97/2.15 (r(s(elem!1), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[6808])).
% 1.97/2.15 tff(6810,plain,
% 1.97/2.15 (r(s(s(s(s(z)))), s(z)) <=> r(s(elem!1), s(z))),
% 1.97/2.15 inference(symmetry,[status(thm)],[6809])).
% 1.97/2.15 tff(6811,plain,
% 1.97/2.15 (b(s(s(s(s(z)))), s(z)) <=> b(s(elem!1), s(z))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[6807])).
% 1.97/2.15 tff(6812,plain,
% 1.97/2.15 (b(s(elem!1), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 1.97/2.15 inference(symmetry,[status(thm)],[6811])).
% 1.97/2.15 tff(6813,plain,
% 1.97/2.15 ((~b(s(elem!1), s(z))) <=> (~b(s(s(s(s(z)))), s(z)))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[6812])).
% 1.97/2.15 tff(6814,plain,
% 1.97/2.15 ((s(s(s(s(z)))) = elem!1) <=> (s(elem!1) = elem!1)),
% 1.97/2.16 inference(monotonicity,[status(thm)],[6807])).
% 1.97/2.16 tff(6815,plain,
% 1.97/2.16 ((s(s(s(s(z)))) = elem!1) <=> (elem!1 = s(elem!1))),
% 1.97/2.16 inference(transitivity,[status(thm)],[6814, 2825])).
% 1.97/2.16 tff(6816,plain,
% 1.97/2.16 ((s(s(s(s(z)))) = elem!1) <=> (s(elem!1) = elem!1)),
% 1.97/2.16 inference(transitivity,[status(thm)],[6815, 3423])).
% 1.97/2.16 tff(6817,plain,
% 1.97/2.16 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(s(elem!1) = elem!1))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[6816])).
% 1.97/2.16 tff(6818,plain,
% 1.97/2.16 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.97/2.16 inference(monotonicity,[status(thm)],[6806])).
% 1.97/2.16 tff(6819,plain,
% 1.97/2.16 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[6818])).
% 1.97/2.16 tff(6820,plain,
% 1.97/2.16 (~(s(s(s(s(z)))) = elem!1)),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[1697, 6819])).
% 1.97/2.16 tff(6821,plain,
% 1.97/2.16 (~(s(elem!1) = elem!1)),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[6820, 6817])).
% 1.97/2.16 tff(6822,plain,
% 1.97/2.16 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(elem!1) = s(s(s(s(s(elem!1))))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[6807])).
% 1.97/2.16 tff(6823,plain,
% 1.97/2.16 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(elem!1))),
% 1.97/2.16 inference(transitivity,[status(thm)],[6822, 1800])).
% 1.97/2.16 tff(6824,plain,
% 1.97/2.16 ((~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(s(elem!1))))) = s(elem!1)))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[6823])).
% 1.97/2.16 tff(6825,plain,
% 1.97/2.16 (~(s(s(s(s(s(elem!1))))) = s(elem!1))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[1501, 6824])).
% 1.97/2.16 tff(6826,plain,
% 1.97/2.16 (elem!1 = s(s(s(z)))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[1677, 6806])).
% 1.97/2.16 tff(6827,plain,
% 1.97/2.16 ((~b(s(s(s(z))), s(z))) <=> (~b(elem!1, s(z)))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[2294])).
% 1.97/2.16 tff(6828,plain,
% 1.97/2.16 (~b(elem!1, s(z))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[2, 6827])).
% 1.97/2.16 tff(6829,plain,
% 1.97/2.16 ($false),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[2001, 6828])).
% 1.97/2.16 tff(6830,plain,((~(elem!1 = s(s(s(z))))) | (~b(elem!1, s(z))) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.16 tff(6831,plain,
% 1.97/2.16 (b(s(s(s(z))), s(z))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[6830, 6826, 6373])).
% 1.97/2.16 tff(6832,plain,
% 1.97/2.16 (~(elem!1 = s(s(elem!1)))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[5450, 6374])).
% 1.97/2.16 tff(6833,plain,
% 1.97/2.16 ((s(z) = elem!1) <=> (s(z) = s(s(elem!1)))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[2392])).
% 1.97/2.16 tff(6834,plain,
% 1.97/2.16 ((s(z) = elem!1) <=> (s(s(elem!1)) = s(z))),
% 1.97/2.16 inference(transitivity,[status(thm)],[6833, 225])).
% 1.97/2.16 tff(6835,plain,
% 1.97/2.16 ((s(s(elem!1)) = s(z)) <=> (s(z) = elem!1)),
% 1.97/2.16 inference(symmetry,[status(thm)],[6834])).
% 1.97/2.16 tff(6836,plain,
% 1.97/2.16 ((~(s(s(elem!1)) = s(z))) <=> (~(s(z) = elem!1))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[6835])).
% 1.97/2.16 tff(6837,plain,
% 1.97/2.16 (~(s(z) = elem!1)),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[113, 6836])).
% 1.97/2.16 tff(6838,plain,
% 1.97/2.16 (s(s(elem!1)) = elem!1),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[5450, 2392])).
% 1.97/2.16 tff(6839,plain,
% 1.97/2.16 (~(s(s(s(z))) = elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[5385, 6838])).
% 1.97/2.16 tff(6840,plain,
% 1.97/2.16 (r(s(s(s(z))), elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[647, 6839, 1])).
% 1.97/2.16 tff(6841,plain,
% 1.97/2.16 (s(s(elem!1)) = elem!1),
% 1.97/2.16 inference(symmetry,[status(thm)],[2392])).
% 1.97/2.16 tff(6842,plain,
% 1.97/2.16 (r(s(s(elem!1)), elem!1) <=> r(elem!1, elem!1)),
% 1.97/2.16 inference(monotonicity,[status(thm)],[6841])).
% 1.97/2.16 tff(6843,plain,
% 1.97/2.16 (r(elem!1, elem!1) <=> r(s(s(elem!1)), elem!1)),
% 1.97/2.16 inference(symmetry,[status(thm)],[6842])).
% 1.97/2.16 tff(6844,plain,
% 1.97/2.16 ((~r(elem!1, elem!1)) <=> (~r(s(s(elem!1)), elem!1))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[6843])).
% 1.97/2.16 tff(6845,plain,
% 1.97/2.16 (^[X: $i] : refl((~r(X, X)) <=> (~r(X, X)))),
% 1.97/2.16 inference(bind,[status(th)],[])).
% 1.97/2.16 tff(6846,plain,
% 1.97/2.16 (![X: $i] : (~r(X, X)) <=> ![X: $i] : (~r(X, X))),
% 1.97/2.16 inference(quant_intro,[status(thm)],[6845])).
% 1.97/2.16 tff(6847,plain,
% 1.97/2.16 (![X: $i] : (~r(X, X)) <=> ![X: $i] : (~r(X, X))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(6848,axiom,(![X: $i] : (~r(X, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ri')).
% 1.97/2.16 tff(6849,plain,
% 1.97/2.16 (![X: $i] : (~r(X, X))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[6848, 6847])).
% 1.97/2.16 tff(6850,plain,(
% 1.97/2.16 ![X: $i] : (~r(X, X))),
% 1.97/2.16 inference(skolemize,[status(sab)],[6849])).
% 1.97/2.16 tff(6851,plain,
% 1.97/2.16 (![X: $i] : (~r(X, X))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[6850, 6846])).
% 1.97/2.16 tff(6852,plain,
% 1.97/2.16 ((~![X: $i] : (~r(X, X))) | (~r(elem!1, elem!1))),
% 1.97/2.16 inference(quant_inst,[status(thm)],[])).
% 1.97/2.16 tff(6853,plain,
% 1.97/2.16 (~r(elem!1, elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[6852, 6851])).
% 1.97/2.16 tff(6854,plain,
% 1.97/2.16 (~r(s(s(elem!1)), elem!1)),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[6853, 6844])).
% 1.97/2.16 tff(6855,plain,
% 1.97/2.16 (~b(z, s(z))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[6629, 6854, 267, 1445, 6840, 6837])).
% 1.97/2.16 tff(6856,plain,
% 1.97/2.16 (r(s(z), elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[1034, 6837, 1445])).
% 1.97/2.16 tff(6857,plain,
% 1.97/2.16 (~r(z, s(z))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[6384, 6856, 267])).
% 1.97/2.16 tff(6858,plain,
% 1.97/2.16 ($false),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[169, 6857, 6855])).
% 1.97/2.16 tff(6859,plain,((~(elem!1 = s(s(elem!1)))) | (~r(z, elem!1)) | b(s(z), elem!1) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.16 tff(6860,plain,
% 1.97/2.16 (~(elem!1 = s(s(elem!1)))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[6859, 1445, 1, 267])).
% 1.97/2.16 tff(6861,plain,
% 1.97/2.16 (~r(z, s(z))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[6384, 6625, 267])).
% 1.97/2.16 tff(6862,plain,
% 1.97/2.16 (b(z, s(z))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[169, 6861])).
% 1.97/2.16 tff(6863,plain,
% 1.97/2.16 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[5581, 6862, 267, 6625])).
% 1.97/2.16 tff(6864,plain,
% 1.97/2.16 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[86, 6863, 69])).
% 1.97/2.16 tff(6865,plain,
% 1.97/2.16 (elem!1 = s(s(elem!1))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[2125, 134])).
% 1.97/2.16 tff(6866,plain,
% 1.97/2.16 ($false),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[1204, 6865])).
% 1.97/2.16 tff(6867,plain,((~(s(s(elem!1)) = elem!1)) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.16 tff(6868,plain,
% 1.97/2.16 (~(s(s(elem!1)) = elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[6867, 6860])).
% 1.97/2.16 tff(6869,plain,
% 1.97/2.16 (b(s(s(elem!1)), elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[156, 6868, 2232])).
% 1.97/2.16 tff(6870,plain,
% 1.97/2.16 (~r(s(s(s(z))), elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[6629, 6862, 267, 2232, 1445, 2277])).
% 1.97/2.16 tff(6871,plain,
% 1.97/2.16 (s(s(s(z))) = elem!1),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[647, 6870, 1])).
% 1.97/2.16 tff(6872,plain,
% 1.97/2.16 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[5623, 6871])).
% 1.97/2.16 tff(6873,plain,
% 1.97/2.16 (elem!1 = s(s(s(z)))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[1677, 6871])).
% 1.97/2.16 tff(6874,plain,
% 1.97/2.16 (b(elem!1, s(z))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[2297, 6873, 2003])).
% 1.97/2.16 tff(6875,assumption,(b(s(s(s(s(s(elem!1))))), s(z))), introduced(assumption)).
% 1.97/2.16 tff(6876,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(6877,plain,
% 1.97/2.16 (((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(6878,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[6877])).
% 1.97/2.16 tff(6879,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.97/2.16 inference(transitivity,[status(thm)],[6878, 6876])).
% 1.97/2.16 tff(6880,plain,
% 1.97/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.97/2.16 inference(quant_inst,[status(thm)],[])).
% 1.97/2.16 tff(6881,plain,
% 1.97/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[6880, 6879])).
% 1.97/2.16 tff(6882,plain,
% 1.97/2.16 ($false),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[6881, 246, 1056, 2001, 236, 714, 6875])).
% 1.97/2.16 tff(6883,plain,((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.16 tff(6884,plain,
% 1.97/2.16 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[6883, 6627, 6874, 6862, 6864])).
% 1.97/2.16 tff(6885,plain,
% 1.97/2.16 (r(s(s(s(s(s(elem!1))))), s(z))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[2311, 47, 331, 6884])).
% 1.97/2.16 tff(6886,plain,
% 1.97/2.16 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[4079, 183, 173, 6885])).
% 1.97/2.16 tff(6887,plain,
% 1.97/2.16 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[1557, 6886, 6872])).
% 1.97/2.16 tff(6888,plain,
% 1.97/2.16 (~b(elem!1, s(s(elem!1)))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[4983, 6887, 6869, 6864])).
% 1.97/2.16 tff(6889,plain,
% 1.97/2.16 (r(elem!1, s(s(elem!1)))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[1268, 6888, 6860])).
% 1.97/2.16 tff(6890,plain,
% 1.97/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(6891,plain,
% 1.97/2.16 (((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1))) <=> ((~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(6892,plain,
% 1.97/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[6891])).
% 1.97/2.16 tff(6893,plain,
% 1.97/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 1.97/2.16 inference(transitivity,[status(thm)],[6892, 6890])).
% 1.97/2.16 tff(6894,plain,
% 1.97/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)))),
% 1.97/2.16 inference(quant_inst,[status(thm)],[])).
% 1.97/2.16 tff(6895,plain,
% 1.97/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[6894, 6893])).
% 1.97/2.16 tff(6896,plain,
% 1.97/2.16 ($false),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[6895, 183, 6625, 6889, 1113])).
% 1.97/2.16 tff(6897,plain,(b(s(z), elem!1) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | b(s(s(s(z))), elem!1) | (s(s(s(s(s(elem!1))))) = elem!1) | (~r(z, elem!1)) | r(s(s(elem!1)), elem!1) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.16 tff(6898,plain,
% 1.97/2.16 (~r(s(z), s(s(elem!1)))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[6897, 1445, 173, 1, 2003, 69, 267, 2232, 5374])).
% 1.97/2.16 tff(6899,plain,
% 1.97/2.16 (b(s(z), s(s(elem!1)))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[233, 6898])).
% 1.97/2.16 tff(6900,plain,
% 1.97/2.16 (r(s(z), elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[1034, 1445, 5374])).
% 1.97/2.16 tff(6901,plain,
% 1.97/2.16 (~r(s(z), z)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[5432, 6900, 267])).
% 1.97/2.16 tff(6902,plain,
% 1.97/2.16 (b(s(z), z)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[1069, 6901])).
% 1.97/2.16 tff(6903,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(6904,plain,
% 1.97/2.16 (((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(6905,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z)))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[6904])).
% 1.97/2.16 tff(6906,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 1.97/2.16 inference(transitivity,[status(thm)],[6905, 6903])).
% 1.97/2.16 tff(6907,plain,
% 1.97/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))),
% 1.97/2.16 inference(quant_inst,[status(thm)],[])).
% 1.97/2.16 tff(6908,plain,
% 1.97/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z)))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[6907, 6906])).
% 1.97/2.16 tff(6909,plain,
% 1.97/2.16 (~b(z, s(s(elem!1)))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[6908, 246, 6902, 2362, 2001, 236, 6899])).
% 1.97/2.16 tff(6910,plain,
% 1.97/2.16 (r(z, s(s(elem!1)))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[264, 6909])).
% 1.97/2.16 tff(6911,plain,
% 1.97/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(6912,plain,
% 1.97/2.16 (((~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(6913,plain,
% 1.97/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[6912])).
% 1.97/2.16 tff(6914,plain,
% 1.97/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 1.97/2.16 inference(transitivity,[status(thm)],[6913, 6911])).
% 1.97/2.16 tff(6915,plain,
% 1.97/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)))),
% 1.97/2.16 inference(quant_inst,[status(thm)],[])).
% 1.97/2.16 tff(6916,plain,
% 1.97/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[6915, 6914])).
% 1.97/2.16 tff(6917,plain,
% 1.97/2.16 ($false),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[6916, 183, 267, 602, 266])).
% 1.97/2.16 tff(6918,plain,((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.16 tff(6919,plain,
% 1.97/2.16 (~r(elem!1, s(s(elem!1)))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[6918, 6910, 267])).
% 1.97/2.16 tff(6920,plain,
% 1.97/2.16 (b(elem!1, s(s(elem!1)))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[1268, 6919, 1204])).
% 1.97/2.16 tff(6921,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(6922,plain,
% 1.97/2.16 (((~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z)))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(6923,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z)))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[6922])).
% 1.97/2.16 tff(6924,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 1.97/2.16 inference(transitivity,[status(thm)],[6923, 6921])).
% 1.97/2.16 tff(6925,plain,
% 1.97/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 1.97/2.16 inference(quant_inst,[status(thm)],[])).
% 1.97/2.16 tff(6926,plain,
% 1.97/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z)))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[6925, 6924])).
% 1.97/2.16 tff(6927,plain,
% 1.97/2.16 ($false),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[6926, 246, 2362, 2001, 6920, 6899])).
% 1.97/2.16 tff(6928,plain,(b(s(z), elem!1) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (elem!1 = s(s(elem!1))) | (~r(z, elem!1)) | (~b(z, s(z))) | (~r(s(s(elem!1)), s(z))) | b(s(s(s(z))), elem!1) | (~b(s(s(s(z))), s(z))) | (s(s(s(s(s(elem!1))))) = elem!1) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.16 tff(6929,plain,
% 1.97/2.16 (b(s(z), elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[6928, 6622, 6373, 6832, 5365, 6375, 2133, 1, 6831, 69, 2232])).
% 1.97/2.16 tff(6930,plain,
% 1.97/2.16 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[5623, 6806])).
% 1.97/2.16 tff(6931,plain,
% 1.97/2.16 (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[3815, 6930])).
% 1.97/2.16 tff(6932,plain,
% 1.97/2.16 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[6443, 246, 1044, 2001, 714])).
% 1.97/2.16 tff(6933,plain,
% 1.97/2.16 (r(s(s(s(s(s(elem!1))))), s(z))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[6447, 6932])).
% 1.97/2.16 tff(6934,plain,
% 1.97/2.16 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[6641, 246, 1044, 2362, 2001, 714])).
% 1.97/2.16 tff(6935,plain,
% 1.97/2.16 (r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[1547, 47, 6934, 4476])).
% 1.97/2.16 tff(6936,plain,
% 1.97/2.16 ($false),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[6354, 183, 173, 6935, 6933])).
% 1.97/2.16 tff(6937,plain,((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), s(z))) | (s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.16 tff(6938,plain,
% 1.97/2.16 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[6937, 6931, 2133, 6929, 6375, 6373])).
% 1.97/2.16 tff(6939,plain,
% 1.97/2.16 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[86, 6938, 69])).
% 1.97/2.16 tff(6940,plain,
% 1.97/2.16 (~r(s(elem!1), elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[5543, 6939, 5365, 6825])).
% 1.97/2.17 tff(6941,plain,
% 1.97/2.17 (b(s(elem!1), elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[5655, 6940, 6821])).
% 1.97/2.17 tff(6942,plain,
% 1.97/2.17 (~(s(s(elem!1)) = s(elem!1))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[5640, 6374])).
% 1.97/2.17 tff(6943,assumption,(s(elem!1) = s(s(elem!1))), introduced(assumption)).
% 1.97/2.17 tff(6944,plain,
% 1.97/2.17 (s(s(elem!1)) = s(elem!1)),
% 1.97/2.17 inference(symmetry,[status(thm)],[6943])).
% 1.97/2.17 tff(6945,plain,
% 1.97/2.17 ($false),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[5642, 6944])).
% 1.97/2.17 tff(6946,plain,((~(s(elem!1) = s(s(elem!1)))) | (s(s(elem!1)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(6947,plain,
% 1.97/2.17 (~(s(elem!1) = s(s(elem!1)))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[6946, 6942])).
% 1.97/2.17 tff(6948,plain,
% 1.97/2.17 (r(s(elem!1), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[5379])).
% 1.97/2.17 tff(6949,plain,
% 1.97/2.17 (r(s(s(s(s(z)))), s(z)) <=> r(s(elem!1), s(z))),
% 1.97/2.17 inference(symmetry,[status(thm)],[6948])).
% 1.97/2.17 tff(6950,plain,
% 1.97/2.17 (b(s(s(s(s(z)))), s(z)) <=> b(s(elem!1), s(z))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[5378])).
% 1.97/2.17 tff(6951,plain,
% 1.97/2.17 (b(s(elem!1), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 1.97/2.17 inference(symmetry,[status(thm)],[6950])).
% 1.97/2.17 tff(6952,plain,
% 1.97/2.17 ((~b(s(elem!1), s(z))) <=> (~b(s(s(s(s(z)))), s(z)))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[6951])).
% 1.97/2.17 tff(6953,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(6954,plain,
% 1.97/2.17 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(6955,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z)))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[6954])).
% 1.97/2.17 tff(6956,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.97/2.17 inference(transitivity,[status(thm)],[6955, 6953])).
% 1.97/2.17 tff(6957,plain,
% 1.97/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.97/2.17 inference(quant_inst,[status(thm)],[])).
% 1.97/2.17 tff(6958,plain,
% 1.97/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z)))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[6957, 6956])).
% 1.97/2.17 tff(6959,plain,
% 1.97/2.17 (~b(s(elem!1), s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[6958, 246, 1044, 2001, 1200])).
% 1.97/2.17 tff(6960,plain,
% 1.97/2.17 (~b(s(s(s(s(z)))), s(z))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[6959, 6952])).
% 1.97/2.17 tff(6961,plain,
% 1.97/2.17 (r(s(s(s(s(z)))), s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[6103, 6960])).
% 1.97/2.17 tff(6962,plain,
% 1.97/2.17 (r(s(elem!1), s(z))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[6961, 6949])).
% 1.97/2.17 tff(6963,assumption,(~(s(elem!1) = s(s(elem!1)))), introduced(assumption)).
% 1.97/2.17 tff(6964,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(6965,plain,
% 1.97/2.17 (((~b(s(z), elem!1)) | (~b(s(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(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(6966,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[6965])).
% 1.97/2.17 tff(6967,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)))),
% 1.97/2.17 inference(transitivity,[status(thm)],[6966, 6964])).
% 1.97/2.17 tff(6968,plain,
% 1.97/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(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)))))),
% 1.97/2.17 inference(quant_inst,[status(thm)],[])).
% 1.97/2.17 tff(6969,plain,
% 1.97/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[6968, 6967])).
% 1.97/2.17 tff(6970,plain,
% 1.97/2.17 (~b(s(elem!1), s(s(elem!1)))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[6969, 246, 1044, 2362, 2001, 1200])).
% 1.97/2.17 tff(6971,plain,
% 1.97/2.17 (r(s(elem!1), s(s(elem!1)))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[5561, 47, 6970, 6963])).
% 1.97/2.17 tff(6972,plain,
% 1.97/2.17 (~b(s(z), s(s(elem!1)))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[6395, 246, 1044, 2362, 2001])).
% 1.97/2.17 tff(6973,plain,
% 1.97/2.17 (r(s(z), s(s(elem!1)))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[233, 6972])).
% 1.97/2.17 tff(6974,plain,
% 1.97/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(6975,plain,
% 1.97/2.17 (((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(6976,plain,
% 1.97/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[6975])).
% 1.97/2.17 tff(6977,plain,
% 1.97/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.97/2.17 inference(transitivity,[status(thm)],[6976, 6974])).
% 1.97/2.17 tff(6978,plain,
% 1.97/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))),
% 1.97/2.17 inference(quant_inst,[status(thm)],[])).
% 1.97/2.17 tff(6979,plain,
% 1.97/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1))))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[6978, 6977])).
% 1.97/2.17 tff(6980,plain,
% 1.97/2.17 ($false),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[6979, 183, 1114, 6973, 6971, 6962])).
% 1.97/2.17 tff(6981,plain,((~b(s(elem!1), elem!1)) | (~r(s(z), z)) | (~(s(s(s(z))) = elem!1)) | (s(elem!1) = s(s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(6982,plain,
% 1.97/2.17 (~r(s(z), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[6981, 6941, 6806, 6947, 6929, 6375, 6373])).
% 1.97/2.17 tff(6983,plain,
% 1.97/2.17 (b(s(z), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[1069, 6982])).
% 1.97/2.17 tff(6984,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(6985,plain,
% 1.97/2.17 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(6986,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z)))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[6985])).
% 1.97/2.17 tff(6987,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.97/2.17 inference(transitivity,[status(thm)],[6986, 6984])).
% 1.97/2.17 tff(6988,plain,
% 1.97/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.97/2.17 inference(quant_inst,[status(thm)],[])).
% 1.97/2.17 tff(6989,plain,
% 1.97/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z)))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[6988, 6987])).
% 1.97/2.17 tff(6990,plain,
% 1.97/2.17 (~b(s(elem!1), s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[6989, 246, 6983, 6929, 6373, 6941])).
% 1.97/2.17 tff(6991,plain,
% 1.97/2.17 (~b(s(s(s(s(z)))), s(z))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[6990, 6813])).
% 1.97/2.17 tff(6992,plain,
% 1.97/2.17 (r(s(s(s(s(z)))), s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[6103, 6991])).
% 1.97/2.17 tff(6993,plain,
% 1.97/2.17 (r(s(elem!1), s(z))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[6992, 6810])).
% 1.97/2.17 tff(6994,plain,
% 1.97/2.17 (~r(s(s(elem!1)), elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[1681, 1555, 82, 1, 55, 1055])).
% 1.97/2.17 tff(6995,plain,
% 1.97/2.17 ((s(s(elem!1)) = elem!1) <=> (s(s(elem!1)) = z)),
% 1.97/2.17 inference(symmetry,[status(thm)],[148])).
% 1.97/2.17 tff(6996,plain,
% 1.97/2.17 (~b(s(s(elem!1)), elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[4228, 88, 1054])).
% 1.97/2.17 tff(6997,plain,
% 1.97/2.17 (s(s(elem!1)) = elem!1),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[156, 6996, 2232])).
% 1.97/2.17 tff(6998,plain,
% 1.97/2.17 (s(s(elem!1)) = z),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[6997, 6995])).
% 1.97/2.17 tff(6999,plain,
% 1.97/2.17 ($false),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[139, 6998])).
% 1.97/2.17 tff(7000,plain,((~(z = elem!1)) | r(s(s(elem!1)), elem!1) | b(s(s(elem!1)), z)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(7001,plain,
% 1.97/2.17 (~(z = elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7000, 6994, 1054])).
% 1.97/2.17 tff(7002,plain,
% 1.97/2.17 (r(z, elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[60, 7001, 55])).
% 1.97/2.17 tff(7003,plain,
% 1.97/2.17 ((s(s(s(s(s(elem!1))))) = s(s(elem!1))) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 1.97/2.17 inference(monotonicity,[status(thm)],[2125])).
% 1.97/2.17 tff(7004,plain,
% 1.97/2.17 ((s(s(s(s(s(elem!1))))) = elem!1) <=> (s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 1.97/2.17 inference(symmetry,[status(thm)],[7003])).
% 1.97/2.17 tff(7005,plain,
% 1.97/2.17 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[5485, 5387, 267])).
% 1.97/2.17 tff(7006,plain,
% 1.97/2.17 (s(s(s(s(s(elem!1))))) = elem!1),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[86, 7005, 82])).
% 1.97/2.17 tff(7007,plain,
% 1.97/2.17 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[7006, 7004])).
% 1.97/2.17 tff(7008,plain,
% 1.97/2.17 ($false),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[1555, 7007])).
% 1.97/2.17 tff(7009,plain,((~(s(s(elem!1)) = elem!1)) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | b(s(s(s(s(s(elem!1))))), elem!1) | (~r(z, elem!1)) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(7010,plain,
% 1.97/2.17 (~(s(s(elem!1)) = elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7009, 1555, 82, 7002, 1])).
% 1.97/2.17 tff(7011,plain,
% 1.97/2.17 (b(s(s(elem!1)), elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[156, 7010, 6994])).
% 1.97/2.17 tff(7012,plain,
% 1.97/2.17 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[5568, 7011, 1])).
% 1.97/2.17 tff(7013,plain,
% 1.97/2.17 (~(s(z) = elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[121, 7012])).
% 1.97/2.17 tff(7014,plain,
% 1.97/2.17 (~(elem!1 = s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[2279, 7013])).
% 1.97/2.17 tff(7015,plain,
% 1.97/2.17 (b(z, s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[6425, 7014, 55, 7011, 1055, 7002])).
% 1.97/2.17 tff(7016,assumption,(~r(elem!1, z)), introduced(assumption)).
% 1.97/2.17 tff(7017,plain,
% 1.97/2.17 (r(s(s(elem!1)), z) <=> r(elem!1, z)),
% 1.97/2.17 inference(monotonicity,[status(thm)],[2125])).
% 1.97/2.17 tff(7018,plain,
% 1.97/2.17 (r(elem!1, z) <=> r(s(s(elem!1)), z)),
% 1.97/2.17 inference(symmetry,[status(thm)],[7017])).
% 1.97/2.17 tff(7019,plain,
% 1.97/2.17 ((~r(elem!1, z)) <=> (~r(s(s(elem!1)), z))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[7018])).
% 1.97/2.17 tff(7020,plain,
% 1.97/2.17 (~r(s(s(elem!1)), z)),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[7016, 7019])).
% 1.97/2.17 tff(7021,plain,
% 1.97/2.17 ($false),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[172, 7020])).
% 1.97/2.17 tff(7022,plain,((~(s(s(elem!1)) = elem!1)) | (~r(s(s(elem!1)), z)) | r(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(7023,plain,
% 1.97/2.17 (~(s(s(elem!1)) = elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7022, 7016, 1055])).
% 1.97/2.17 tff(7024,plain,
% 1.97/2.17 (b(s(s(elem!1)), elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[156, 7023, 2232])).
% 1.97/2.17 tff(7025,plain,
% 1.97/2.17 (~(z = elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[4228, 7024, 1054])).
% 1.97/2.17 tff(7026,plain,
% 1.97/2.17 (r(z, elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[60, 7025, 55])).
% 1.97/2.17 tff(7027,plain,
% 1.97/2.17 (~(elem!1 = z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[1041, 7025])).
% 1.97/2.17 tff(7028,plain,
% 1.97/2.17 (b(elem!1, z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[1143, 7027, 7016])).
% 1.97/2.17 tff(7029,plain,
% 1.97/2.17 (elem!1 = s(s(s(z)))),
% 1.97/2.17 inference(symmetry,[status(thm)],[1673])).
% 1.97/2.17 tff(7030,assumption,(s(s(s(s(s(elem!1))))) = elem!1), introduced(assumption)).
% 1.97/2.17 tff(7031,plain,
% 1.97/2.17 (s(s(s(s(s(elem!1))))) = s(s(s(z)))),
% 1.97/2.17 inference(transitivity,[status(thm)],[7030, 7029])).
% 1.97/2.17 tff(7032,plain,
% 1.97/2.17 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(z))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[7031])).
% 1.97/2.17 tff(7033,plain,
% 1.97/2.17 (s(s(s(s(elem!1)))) = s(s(z))),
% 1.97/2.17 inference(transitivity,[status(thm)],[326, 7032, 24])).
% 1.97/2.17 tff(7034,plain,
% 1.97/2.17 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(z)))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[7033])).
% 1.97/2.17 tff(7035,plain,
% 1.97/2.17 (inj_0(s(s(z))) = inj_0(s(s(s(s(elem!1)))))),
% 1.97/2.17 inference(symmetry,[status(thm)],[7034])).
% 1.97/2.17 tff(7036,plain,
% 1.97/2.17 (s(z) = s(s(s(elem!1)))),
% 1.97/2.17 inference(transitivity,[status(thm)],[1523, 7035, 351])).
% 1.97/2.17 tff(7037,plain,
% 1.97/2.17 (inj_0(s(z)) = inj_0(s(s(s(elem!1))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[7036])).
% 1.97/2.17 tff(7038,plain,
% 1.97/2.17 (inj_0(s(s(s(elem!1)))) = inj_0(s(z))),
% 1.97/2.17 inference(symmetry,[status(thm)],[7037])).
% 1.97/2.17 tff(7039,plain,
% 1.97/2.17 (s(s(elem!1)) = z),
% 1.97/2.17 inference(transitivity,[status(thm)],[104, 7038, 20])).
% 1.97/2.17 tff(7040,plain,
% 1.97/2.17 ($false),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[139, 7039])).
% 1.97/2.17 tff(7041,plain,((~(s(s(s(s(s(elem!1))))) = elem!1)) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(7042,plain,
% 1.97/2.17 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7041, 1673])).
% 1.97/2.17 tff(7043,plain,
% 1.97/2.17 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[86, 7042, 82])).
% 1.97/2.17 tff(7044,plain,
% 1.97/2.17 (~r(s(s(s(s(s(elem!1))))), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[5470, 183, 267, 7043])).
% 1.97/2.17 tff(7045,plain,
% 1.97/2.17 (b(s(s(s(s(s(elem!1))))), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[1601, 7044])).
% 1.97/2.17 tff(7046,plain,
% 1.97/2.17 ((s(z) = s(s(s(z)))) <=> (s(z) = elem!1)),
% 1.97/2.17 inference(monotonicity,[status(thm)],[1673])).
% 1.97/2.17 tff(7047,plain,
% 1.97/2.17 ((~(s(z) = s(s(s(z))))) <=> (~(s(z) = elem!1))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[7046])).
% 1.97/2.17 tff(7048,plain,
% 1.97/2.17 (~(s(z) = elem!1)),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[767, 7047])).
% 1.97/2.17 tff(7049,plain,
% 1.97/2.17 ((s(z) = s(s(s(z)))) <=> (elem!1 = s(z))),
% 1.97/2.17 inference(transitivity,[status(thm)],[7046, 5])).
% 1.97/2.17 tff(7050,plain,
% 1.97/2.17 ((~(s(z) = s(s(s(z))))) <=> (~(elem!1 = s(z)))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[7049])).
% 1.97/2.17 tff(7051,plain,
% 1.97/2.17 (~(elem!1 = s(z))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[767, 7050])).
% 1.97/2.17 tff(7052,plain,
% 1.97/2.17 (b(s(s(elem!1)), z) | (~b(elem!1, z)) | (~r(z, elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[1097, 113])).
% 1.97/2.17 tff(7053,plain,
% 1.97/2.17 (~b(z, s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7052, 201, 1054, 1044, 267, 1051])).
% 1.97/2.17 tff(7054,plain,
% 1.97/2.17 (r(z, s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[169, 7053])).
% 1.97/2.17 tff(7055,plain,
% 1.97/2.17 (r(elem!1, s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[214, 4175, 3])).
% 1.97/2.17 tff(7056,plain,
% 1.97/2.17 ($false),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[292, 7055, 7054, 267])).
% 1.97/2.17 tff(7057,plain,((~b(s(s(elem!1)), s(z))) | (~r(z, elem!1)) | (elem!1 = s(z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | b(s(s(elem!1)), z) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(7058,plain,
% 1.97/2.17 (~b(s(s(elem!1)), s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7057, 1044, 3, 2362, 267, 1054, 1051])).
% 1.97/2.17 tff(7059,plain,
% 1.97/2.17 (r(s(s(elem!1)), s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[197, 7058])).
% 1.97/2.17 tff(7060,plain,
% 1.97/2.17 (~r(z, s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[191, 7059, 1055])).
% 1.97/2.17 tff(7061,plain,
% 1.97/2.17 (b(z, s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[169, 7060])).
% 1.97/2.17 tff(7062,plain,
% 1.97/2.17 (~r(s(z), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[6720, 7059, 1055])).
% 1.97/2.17 tff(7063,plain,
% 1.97/2.17 (b(s(z), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[1069, 7062])).
% 1.97/2.17 tff(7064,plain,
% 1.97/2.17 ($false),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[1064, 7063, 7061, 1051, 1044])).
% 1.97/2.17 tff(7065,plain,((~b(s(z), elem!1)) | (~b(elem!1, z)) | (elem!1 = s(z)) | (~b(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | b(s(s(elem!1)), z)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(7066,plain,
% 1.97/2.17 (~b(s(z), elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7065, 7051, 1051, 2362, 267, 1054])).
% 1.97/2.17 tff(7067,plain,
% 1.97/2.17 (r(s(z), elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[1034, 7066, 7048])).
% 1.97/2.17 tff(7068,plain,
% 1.97/2.17 (~r(z, s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[6384, 7067, 267])).
% 1.97/2.17 tff(7069,plain,
% 1.97/2.17 (b(z, s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[169, 7068])).
% 1.97/2.17 tff(7070,plain,
% 1.97/2.17 (~r(s(z), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[5432, 7067, 267])).
% 1.97/2.17 tff(7071,plain,
% 1.97/2.17 (b(s(z), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[1069, 7070])).
% 1.97/2.17 tff(7072,plain,
% 1.97/2.17 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[5578, 246, 7071, 7069, 7045])).
% 1.97/2.17 tff(7073,plain,
% 1.97/2.17 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[2307, 183, 7067, 7043])).
% 1.97/2.17 tff(7074,plain,
% 1.97/2.17 ($false),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[2311, 47, 331, 7073, 7072])).
% 1.97/2.17 tff(7075,plain,((~(s(s(s(z))) = elem!1)) | (~r(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | b(s(s(elem!1)), z) | b(s(s(s(s(s(elem!1))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(7076,plain,
% 1.97/2.17 (~(s(s(s(z))) = elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7075, 7026, 7028, 7024, 1054, 82])).
% 1.97/2.17 tff(7077,plain,
% 1.97/2.17 (r(s(s(s(z))), elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[647, 7076, 1])).
% 1.97/2.17 tff(7078,plain,
% 1.97/2.17 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[5485, 7077, 7026])).
% 1.97/2.17 tff(7079,plain,
% 1.97/2.17 (s(s(s(s(s(elem!1))))) = elem!1),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[86, 7078, 82])).
% 1.97/2.17 tff(7080,plain,
% 1.97/2.17 ((s(s(s(s(s(elem!1))))) = s(z)) <=> (elem!1 = s(z))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[7030])).
% 1.97/2.17 tff(7081,plain,
% 1.97/2.17 ((s(s(s(s(s(elem!1))))) = s(z)) <=> (s(z) = elem!1)),
% 1.97/2.17 inference(transitivity,[status(thm)],[7080, 4])).
% 1.97/2.17 tff(7082,plain,
% 1.97/2.17 ((s(s(s(s(s(elem!1))))) = s(z)) <=> (elem!1 = s(z))),
% 1.97/2.17 inference(transitivity,[status(thm)],[7081, 5])).
% 1.97/2.17 tff(7083,plain,
% 1.97/2.17 ((~(s(s(s(s(s(elem!1))))) = s(z))) <=> (~(elem!1 = s(z)))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[7082])).
% 1.97/2.17 tff(7084,plain,
% 1.97/2.17 (~(elem!1 = s(z))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[331, 7083])).
% 1.97/2.17 tff(7085,plain,
% 1.97/2.17 ((~(s(s(s(s(s(elem!1))))) = s(z))) <=> (~(s(z) = elem!1))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[7081])).
% 1.97/2.17 tff(7086,plain,
% 1.97/2.17 (~(s(z) = elem!1)),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[331, 7085])).
% 1.97/2.17 tff(7087,plain,
% 1.97/2.17 (b(s(z), elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[1034, 7086, 6388])).
% 1.97/2.17 tff(7088,plain,
% 1.97/2.17 ($false),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7065, 7087, 7084, 1051, 2362, 267, 1054])).
% 1.97/2.17 tff(7089,plain,((~(s(s(s(s(s(elem!1))))) = elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | b(s(s(elem!1)), z) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(7090,plain,
% 1.97/2.17 (r(s(z), elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7089, 7079, 7024, 7026, 1054, 7028])).
% 1.97/2.17 tff(7091,plain,
% 1.97/2.17 (~r(s(z), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[5432, 7090, 7026])).
% 1.97/2.17 tff(7092,plain,
% 1.97/2.17 (b(s(z), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[1069, 7091])).
% 1.97/2.17 tff(7093,plain,
% 1.97/2.17 (~r(s(s(s(z))), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[5411, 183, 7026, 7077])).
% 1.97/2.17 tff(7094,plain,
% 1.97/2.17 (b(s(s(s(z))), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[995, 7093])).
% 1.97/2.17 tff(7095,plain,
% 1.97/2.17 (~r(z, s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[6384, 7090, 7026])).
% 1.97/2.17 tff(7096,plain,
% 1.97/2.17 (b(z, s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[169, 7095])).
% 1.97/2.17 tff(7097,plain,
% 1.97/2.17 (~r(s(s(s(z))), s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[3017, 7090, 7077])).
% 1.97/2.17 tff(7098,plain,
% 1.97/2.17 (b(s(s(s(z))), s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[52, 7097])).
% 1.97/2.17 tff(7099,plain,
% 1.97/2.17 ($false),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[2098, 7098, 7096, 7094, 7092])).
% 1.97/2.17 tff(7100,plain,(r(elem!1, z) | b(s(s(elem!1)), z) | b(s(s(s(s(s(elem!1))))), elem!1) | b(s(s(s(z))), elem!1) | b(z, elem!1) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(7101,plain,
% 1.97/2.17 (r(elem!1, z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7100, 6994, 82, 1, 55, 1054])).
% 1.97/2.17 tff(7102,plain,
% 1.97/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(7103,plain,
% 1.97/2.17 (((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(7104,plain,
% 1.97/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[7103])).
% 1.97/2.17 tff(7105,plain,
% 1.97/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))),
% 1.97/2.17 inference(transitivity,[status(thm)],[7104, 7102])).
% 1.97/2.17 tff(7106,plain,
% 1.97/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))))),
% 1.97/2.17 inference(quant_inst,[status(thm)],[])).
% 1.97/2.17 tff(7107,plain,
% 1.97/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[7106, 7105])).
% 1.97/2.17 tff(7108,plain,
% 1.97/2.17 (~r(elem!1, s(s(elem!1)))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7107, 183, 7101, 1055])).
% 1.97/2.17 tff(7109,plain,
% 1.97/2.17 (~(elem!1 = s(s(elem!1)))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[5450, 7010])).
% 1.97/2.17 tff(7110,plain,
% 1.97/2.17 (b(elem!1, s(s(elem!1)))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[1268, 7109, 7108])).
% 1.97/2.18 tff(7111,plain,
% 1.97/2.18 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[5610, 7011, 7110, 7015, 7002, 1])).
% 1.97/2.18 tff(7112,plain,
% 1.97/2.18 (s(s(s(s(s(elem!1))))) = elem!1),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[86, 7111, 82])).
% 1.97/2.18 tff(7113,plain,
% 1.97/2.18 (~(s(s(s(z))) = elem!1)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7041, 7112])).
% 1.97/2.18 tff(7114,plain,
% 1.97/2.18 (r(s(s(s(z))), elem!1)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[647, 7113, 1])).
% 1.97/2.18 tff(7115,plain,
% 1.97/2.18 (b(s(z), elem!1)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[6629, 7114, 7002, 7015, 6994, 7013])).
% 1.97/2.18 tff(7116,plain,
% 1.97/2.18 (~(elem!1 = s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[3013, 7113])).
% 1.97/2.18 tff(7117,plain,
% 1.97/2.18 (~r(s(s(s(z))), z)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[5411, 183, 7002, 7114])).
% 1.97/2.18 tff(7118,plain,
% 1.97/2.18 (b(s(s(s(z))), z)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[995, 7117])).
% 1.97/2.18 tff(7119,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(7120,plain,
% 1.97/2.18 (((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(7121,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z)))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[7120])).
% 1.97/2.18 tff(7122,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 1.97/2.18 inference(transitivity,[status(thm)],[7121, 7119])).
% 1.97/2.18 tff(7123,plain,
% 1.97/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(7124,plain,
% 1.97/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z)))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[7123, 7122])).
% 1.97/2.18 tff(7125,plain,
% 1.97/2.18 (~b(s(s(elem!1)), s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7124, 246, 7115, 7011, 7110])).
% 1.97/2.18 tff(7126,plain,
% 1.97/2.18 (r(s(s(elem!1)), s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[197, 7125])).
% 1.97/2.18 tff(7127,plain,
% 1.97/2.18 (~r(s(z), z)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[6720, 7126, 1055])).
% 1.97/2.18 tff(7128,plain,
% 1.97/2.18 (b(s(z), z)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[1069, 7127])).
% 1.97/2.18 tff(7129,plain,
% 1.97/2.18 (~b(s(s(s(z))), s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[2098, 7128, 7118, 7015])).
% 1.97/2.18 tff(7130,plain,
% 1.97/2.18 (r(s(s(s(z))), s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[52, 7129])).
% 1.97/2.18 tff(7131,plain,
% 1.97/2.18 (b(elem!1, s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[2282, 7130, 7114, 6994])).
% 1.97/2.18 tff(7132,plain,
% 1.97/2.18 (~b(elem!1, s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[4259, 7130, 6994, 7012, 7125, 7131])).
% 1.97/2.18 tff(7133,plain,
% 1.97/2.18 (r(elem!1, s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[470, 7132, 7116])).
% 1.97/2.18 tff(7134,plain,
% 1.97/2.18 (~b(s(z), s(s(elem!1)))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[5589, 246, 7115, 7011, 7110])).
% 1.97/2.18 tff(7135,plain,
% 1.97/2.18 (r(s(z), s(s(elem!1)))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[233, 7134])).
% 1.97/2.18 tff(7136,plain,
% 1.97/2.18 (~r(z, s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[5419, 183, 7002, 7114])).
% 1.97/2.18 tff(7137,plain,
% 1.97/2.18 (b(z, s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[2221, 47, 7136, 5476])).
% 1.97/2.18 tff(7138,plain,
% 1.97/2.18 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[4248, 183, 7126, 7130])).
% 1.97/2.18 tff(7139,plain,
% 1.97/2.18 (b(s(s(s(z))), s(s(elem!1)))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[689, 7138, 7012])).
% 1.97/2.18 tff(7140,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(7141,plain,
% 1.97/2.18 (((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z)))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(7142,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z)))))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[7141])).
% 1.97/2.18 tff(7143,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))))),
% 1.97/2.18 inference(transitivity,[status(thm)],[7142, 7140])).
% 1.97/2.18 tff(7144,plain,
% 1.97/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(7145,plain,
% 1.97/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z)))))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[7144, 7143])).
% 1.97/2.18 tff(7146,plain,
% 1.97/2.18 (~b(s(z), s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7145, 246, 7115, 7011, 7015, 7139, 7137])).
% 1.97/2.18 tff(7147,plain,
% 1.97/2.18 (r(s(z), s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[1291, 7146])).
% 1.97/2.18 tff(7148,plain,
% 1.97/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(7149,plain,
% 1.97/2.18 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(7150,plain,
% 1.97/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[7149])).
% 1.97/2.18 tff(7151,plain,
% 1.97/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.97/2.18 inference(transitivity,[status(thm)],[7150, 7148])).
% 1.97/2.18 tff(7152,plain,
% 1.97/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(7153,plain,
% 1.97/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[7152, 7151])).
% 1.97/2.18 tff(7154,plain,
% 1.97/2.18 (~r(s(s(s(s(z)))), s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7153, 183, 1113, 6096, 2593])).
% 1.97/2.18 tff(7155,plain,
% 1.97/2.18 (b(s(s(s(s(z)))), s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[2411, 47, 1713, 7154])).
% 1.97/2.18 tff(7156,plain,
% 1.97/2.18 (b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[7030])).
% 1.97/2.18 tff(7157,plain,
% 1.97/2.18 (elem!1 = s(s(s(s(s(elem!1)))))),
% 1.97/2.18 inference(symmetry,[status(thm)],[7030])).
% 1.97/2.18 tff(7158,plain,
% 1.97/2.18 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[7157])).
% 1.97/2.18 tff(7159,plain,
% 1.97/2.18 ((~r(elem!1, s(s(s(s(z)))))) <=> (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[7158])).
% 1.97/2.18 tff(7160,plain,
% 1.97/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(7161,plain,
% 1.97/2.18 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(7162,plain,
% 1.97/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[7161])).
% 1.97/2.18 tff(7163,plain,
% 1.97/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.97/2.18 inference(transitivity,[status(thm)],[7162, 7160])).
% 1.97/2.18 tff(7164,plain,
% 1.97/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(7165,plain,
% 1.97/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[7164, 7163])).
% 1.97/2.18 tff(7166,plain,
% 1.97/2.18 (~r(elem!1, s(s(s(s(z)))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7165, 183, 413, 2593])).
% 1.97/2.18 tff(7167,plain,
% 1.97/2.18 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[7166, 7159])).
% 1.97/2.18 tff(7168,plain,
% 1.97/2.18 (b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[1897, 7167])).
% 1.97/2.18 tff(7169,plain,
% 1.97/2.18 (b(elem!1, s(s(s(s(z)))))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[7168, 7156])).
% 1.97/2.18 tff(7170,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(7171,plain,
% 1.97/2.18 (((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(7172,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z))))))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[7171])).
% 1.97/2.18 tff(7173,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.97/2.18 inference(transitivity,[status(thm)],[7172, 7170])).
% 1.97/2.18 tff(7174,plain,
% 1.97/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(7175,plain,
% 1.97/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z))))))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[7174, 7173])).
% 1.97/2.18 tff(7176,plain,
% 1.97/2.18 ($false),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7175, 246, 1044, 2001, 7169, 7155])).
% 1.97/2.18 tff(7177,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~(s(s(s(s(s(elem!1))))) = elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.18 tff(7178,plain,
% 1.97/2.18 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7177, 7147, 7131, 7112, 7135, 7133, 7115])).
% 1.97/2.18 tff(7179,plain,
% 1.97/2.18 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[1702, 7178])).
% 1.97/2.18 tff(7180,plain,
% 1.97/2.18 (~(s(s(elem!1)) = s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[421, 7012])).
% 1.97/2.18 tff(7181,plain,
% 1.97/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(7182,plain,
% 1.97/2.18 (((~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z)))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(7183,plain,
% 1.97/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[7182])).
% 1.97/2.18 tff(7184,plain,
% 1.97/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.97/2.18 inference(transitivity,[status(thm)],[7183, 7181])).
% 1.97/2.18 tff(7185,plain,
% 1.97/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(7186,plain,
% 1.97/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[7185, 7184])).
% 1.97/2.19 tff(7187,plain,
% 1.97/2.19 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7186, 183, 7126, 7114, 7130])).
% 1.97/2.19 tff(7188,plain,
% 1.97/2.19 (b(s(s(elem!1)), s(s(s(z))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[454, 7187, 7180])).
% 1.97/2.19 tff(7189,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(7190,plain,
% 1.97/2.19 (((~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(7191,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7190])).
% 1.97/2.19 tff(7192,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.97/2.19 inference(transitivity,[status(thm)],[7191, 7189])).
% 1.97/2.19 tff(7193,plain,
% 1.97/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.97/2.19 inference(quant_inst,[status(thm)],[])).
% 1.97/2.19 tff(7194,plain,
% 1.97/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[7193, 7192])).
% 1.97/2.19 tff(7195,plain,
% 1.97/2.19 (~b(s(s(s(s(z)))), z)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7194, 246, 7139, 7188, 7137, 7179])).
% 1.97/2.19 tff(7196,plain,
% 1.97/2.19 (s(s(s(s(s(s(elem!1)))))) = s(elem!1)),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7030])).
% 1.97/2.19 tff(7197,plain,
% 1.97/2.19 (s(s(s(s(s(s(s(elem!1))))))) = s(s(elem!1))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7196])).
% 1.97/2.19 tff(7198,plain,
% 1.97/2.19 (s(s(elem!1)) = s(s(s(s(s(s(s(elem!1)))))))),
% 1.97/2.19 inference(symmetry,[status(thm)],[7197])).
% 1.97/2.19 tff(7199,plain,
% 1.97/2.19 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z)))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7198])).
% 1.97/2.19 tff(7200,plain,
% 1.97/2.19 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.97/2.19 inference(symmetry,[status(thm)],[7199])).
% 1.97/2.19 tff(7201,assumption,(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(z))))), introduced(assumption)).
% 1.97/2.19 tff(7202,plain,
% 1.97/2.19 (s(s(s(s(z)))) = s(s(s(s(s(s(s(elem!1)))))))),
% 1.97/2.19 inference(symmetry,[status(thm)],[7201])).
% 1.97/2.19 tff(7203,plain,
% 1.97/2.19 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.97/2.19 inference(transitivity,[status(thm)],[7202, 7197])).
% 1.97/2.19 tff(7204,plain,
% 1.97/2.19 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7203])).
% 1.97/2.19 tff(7205,plain,
% 1.97/2.19 (s(s(s(z))) = s(elem!1)),
% 1.97/2.19 inference(transitivity,[status(thm)],[1492, 7204, 92])).
% 1.97/2.19 tff(7206,plain,
% 1.97/2.19 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7205])).
% 1.97/2.19 tff(7207,plain,
% 1.97/2.19 (s(s(z)) = s(s(s(s(s(elem!1)))))),
% 1.97/2.19 inference(transitivity,[status(thm)],[25, 7206, 343, 7157])).
% 1.97/2.19 tff(7208,plain,
% 1.97/2.19 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7207])).
% 1.97/2.19 tff(7209,plain,
% 1.97/2.19 (s(z) = s(s(s(s(elem!1))))),
% 1.97/2.19 inference(transitivity,[status(thm)],[1523, 7208, 325])).
% 1.97/2.19 tff(7210,plain,
% 1.97/2.19 (inj_0(s(z)) = inj_0(s(s(s(s(elem!1)))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7209])).
% 1.97/2.19 tff(7211,plain,
% 1.97/2.19 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(z))),
% 1.97/2.19 inference(symmetry,[status(thm)],[7210])).
% 1.97/2.19 tff(7212,plain,
% 1.97/2.19 (s(s(s(elem!1))) = z),
% 1.97/2.19 inference(transitivity,[status(thm)],[352, 7211, 20])).
% 1.97/2.19 tff(7213,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[355, 7212])).
% 1.97/2.19 tff(7214,plain,((~(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(z)))))) | (~(s(s(s(s(s(elem!1))))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(7215,plain,
% 1.97/2.19 (~(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7214, 7030])).
% 1.97/2.19 tff(7216,plain,
% 1.97/2.19 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z)))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7198])).
% 1.97/2.19 tff(7217,plain,
% 1.97/2.19 ((~r(s(s(elem!1)), s(s(s(s(z)))))) <=> (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z))))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7216])).
% 1.97/2.19 tff(7218,assumption,(r(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.97/2.19 tff(7219,plain,
% 1.97/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(7220,plain,
% 1.97/2.19 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(7221,plain,
% 1.97/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7220])).
% 1.97/2.19 tff(7222,plain,
% 1.97/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.97/2.19 inference(transitivity,[status(thm)],[7221, 7219])).
% 1.97/2.19 tff(7223,plain,
% 1.97/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.97/2.19 inference(quant_inst,[status(thm)],[])).
% 1.97/2.19 tff(7224,plain,
% 1.97/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[7223, 7222])).
% 1.97/2.19 tff(7225,plain,
% 1.97/2.19 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7224, 183, 172, 7218])).
% 1.97/2.19 tff(7226,plain,
% 1.97/2.19 (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z)))))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[7225, 7217])).
% 1.97/2.19 tff(7227,plain,
% 1.97/2.19 (((~![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(z))))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z))))) | r(s(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(s(elem!1))))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z))))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(7228,plain,
% 1.97/2.19 ((~![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(z))))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z))))))),
% 1.97/2.19 inference(quant_inst,[status(thm)],[])).
% 1.97/2.19 tff(7229,plain,
% 1.97/2.19 ((~![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(z))))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z)))))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[7228, 7227])).
% 1.97/2.19 tff(7230,plain,
% 1.97/2.19 ((s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7229, 47])).
% 1.97/2.19 tff(7231,plain,
% 1.97/2.19 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7230, 7226, 7215])).
% 1.97/2.19 tff(7232,plain,
% 1.97/2.19 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[7231, 7200])).
% 1.97/2.19 tff(7233,plain,
% 1.97/2.19 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7157])).
% 1.97/2.19 tff(7234,plain,
% 1.97/2.19 (b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(s(z)))), elem!1)),
% 1.97/2.19 inference(symmetry,[status(thm)],[7233])).
% 1.97/2.19 tff(7235,plain,
% 1.97/2.19 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7157])).
% 1.97/2.19 tff(7236,plain,
% 1.97/2.19 ((~r(s(s(s(s(z)))), elem!1)) <=> (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7235])).
% 1.97/2.19 tff(7237,plain,
% 1.97/2.19 (~r(s(s(s(s(z)))), elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[6142, 183, 2246, 7218])).
% 1.97/2.19 tff(7238,plain,
% 1.97/2.19 (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[7237, 7236])).
% 1.97/2.19 tff(7239,plain,
% 1.97/2.19 (b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[1506, 7238])).
% 1.97/2.19 tff(7240,plain,
% 1.97/2.19 (b(s(s(s(s(z)))), elem!1)),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[7239, 7234])).
% 1.97/2.19 tff(7241,plain,
% 1.97/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(7242,plain,
% 1.97/2.19 (((~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(7243,plain,
% 1.97/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7242])).
% 1.97/2.19 tff(7244,plain,
% 1.97/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.97/2.19 inference(transitivity,[status(thm)],[7243, 7241])).
% 1.97/2.19 tff(7245,plain,
% 1.97/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.97/2.19 inference(quant_inst,[status(thm)],[])).
% 1.97/2.19 tff(7246,plain,
% 1.97/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[7245, 7244])).
% 1.97/2.19 tff(7247,plain,
% 1.97/2.19 (~r(elem!1, s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7246, 183, 2246, 7218])).
% 1.97/2.19 tff(7248,plain,
% 1.97/2.19 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[7247, 7159])).
% 1.97/2.19 tff(7249,plain,
% 1.97/2.19 (b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[1897, 7248])).
% 1.97/2.19 tff(7250,plain,
% 1.97/2.19 (b(elem!1, s(s(s(s(z)))))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[7249, 7156])).
% 1.97/2.19 tff(7251,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(7252,plain,
% 1.97/2.19 (((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(7253,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z))))))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7252])).
% 1.97/2.19 tff(7254,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.97/2.19 inference(transitivity,[status(thm)],[7253, 7251])).
% 1.97/2.19 tff(7255,plain,
% 1.97/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1)))))),
% 1.97/2.19 inference(quant_inst,[status(thm)],[])).
% 1.97/2.19 tff(7256,plain,
% 1.97/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z))))))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[7255, 7254])).
% 1.97/2.19 tff(7257,plain,
% 1.97/2.19 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7256, 246, 947, 7250, 7240])).
% 1.97/2.19 tff(7258,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7257, 7232])).
% 1.97/2.19 tff(7259,plain,((~r(s(s(s(s(z)))), z)) | (~(s(s(s(s(s(elem!1))))) = elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(7260,plain,
% 1.97/2.19 (~r(s(s(s(s(z)))), z)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7259, 7112, 7110, 7101, 1055])).
% 1.97/2.19 tff(7261,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[2424, 47, 2421, 7260, 7195])).
% 1.97/2.19 tff(7262,plain,((s(s(s(s(s(elem!1))))) = s(s(elem!1))) | b(s(s(s(z))), elem!1) | b(s(s(s(s(s(elem!1))))), elem!1) | b(z, elem!1) | b(s(s(elem!1)), z)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(7263,plain,
% 1.97/2.19 (b(s(s(elem!1)), z)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7262, 6938, 55, 1, 6930])).
% 1.97/2.19 tff(7264,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(7265,plain,
% 1.97/2.19 (((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~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(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(7266,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7265])).
% 1.97/2.19 tff(7267,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)))),
% 1.97/2.19 inference(transitivity,[status(thm)],[7266, 7264])).
% 1.97/2.19 tff(7268,plain,
% 1.97/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~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)))))),
% 1.97/2.19 inference(quant_inst,[status(thm)],[])).
% 1.97/2.19 tff(7269,plain,
% 1.97/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[7268, 7267])).
% 1.97/2.19 tff(7270,plain,
% 1.97/2.19 (~b(s(elem!1), s(s(elem!1)))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7269, 246, 6983, 6375, 6373, 7263, 6941])).
% 1.97/2.19 tff(7271,plain,
% 1.97/2.19 (r(s(elem!1), s(s(elem!1)))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[5561, 47, 7270, 6947])).
% 1.97/2.19 tff(7272,plain,
% 1.97/2.19 (~b(s(z), s(s(elem!1)))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[6395, 246, 6929, 6375, 6373])).
% 1.97/2.19 tff(7273,plain,
% 1.97/2.19 (r(s(z), s(s(elem!1)))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[233, 7272])).
% 1.97/2.19 tff(7274,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[5597, 183, 7273, 7271, 6993])).
% 1.97/2.19 tff(7275,plain,(b(s(s(s(z))), elem!1) | b(z, elem!1) | (s(s(s(s(s(elem!1))))) = elem!1) | r(s(s(elem!1)), elem!1) | b(s(s(elem!1)), s(z)) | b(s(s(elem!1)), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(7276,plain,
% 1.97/2.19 (b(s(s(s(z))), elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7275, 5035, 69, 2232, 2124, 55])).
% 1.97/2.19 tff(7277,plain,
% 1.97/2.19 (~(elem!1 = s(z))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[5773, 7276, 2124])).
% 1.97/2.19 tff(7278,plain,
% 1.97/2.19 (~(s(z) = elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[9, 7277])).
% 1.97/2.19 tff(7279,plain,
% 1.97/2.19 (~(elem!1 = s(z))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[5773, 3697, 2124])).
% 1.97/2.19 tff(7280,plain,
% 1.97/2.19 (~(s(z) = elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[9, 7279])).
% 1.97/2.19 tff(7281,plain,
% 1.97/2.19 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[5804, 7280])).
% 1.97/2.19 tff(7282,plain,
% 1.97/2.19 (~(elem!1 = s(s(s(z))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[5785, 3697])).
% 1.97/2.19 tff(7283,plain,
% 1.97/2.19 (~r(z, s(z))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[6384, 217, 267])).
% 1.97/2.19 tff(7284,plain,
% 1.97/2.19 (b(z, s(z))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[169, 7283])).
% 1.97/2.19 tff(7285,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(7286,plain,
% 1.97/2.19 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(7287,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z)))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7286])).
% 1.97/2.19 tff(7288,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))))),
% 1.97/2.19 inference(transitivity,[status(thm)],[7287, 7285])).
% 1.97/2.19 tff(7289,plain,
% 1.97/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))),
% 1.97/2.20 inference(quant_inst,[status(thm)],[])).
% 1.97/2.20 tff(7290,plain,
% 1.97/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z)))),
% 1.97/2.20 inference(modus_ponens,[status(thm)],[7289, 7288])).
% 1.97/2.20 tff(7291,plain,
% 1.97/2.20 (~b(elem!1, z)),
% 1.97/2.20 inference(unit_resolution,[status(thm)],[7290, 246, 5572, 2001, 7284])).
% 1.97/2.20 tff(7292,plain,
% 1.97/2.20 (r(elem!1, z)),
% 1.97/2.20 inference(unit_resolution,[status(thm)],[1143, 7291, 5401])).
% 1.97/2.20 tff(7293,plain,
% 1.97/2.20 (~(elem!1 = s(s(elem!1)))),
% 1.97/2.20 inference(unit_resolution,[status(thm)],[5450, 6634])).
% 1.97/2.20 tff(7294,plain,
% 1.97/2.20 (~b(s(s(s(z))), s(z))),
% 1.97/2.20 inference(unit_resolution,[status(thm)],[6174, 4651, 1056, 236])).
% 1.97/2.20 tff(7295,plain,
% 1.97/2.20 (r(s(s(s(z))), s(z))),
% 1.97/2.20 inference(unit_resolution,[status(thm)],[52, 7294])).
% 1.97/2.20 tff(7296,plain,
% 1.97/2.20 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.97/2.20 inference(unit_resolution,[status(thm)],[4248, 183, 173, 7295])).
% 1.97/2.20 tff(7297,plain,
% 1.97/2.20 (b(s(s(s(z))), s(s(elem!1)))),
% 1.97/2.20 inference(unit_resolution,[status(thm)],[689, 7296, 119])).
% 1.97/2.20 tff(7298,plain,
% 1.97/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))),
% 1.97/2.20 inference(rewrite,[status(thm)],[])).
% 1.97/2.20 tff(7299,plain,
% 1.97/2.20 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))),
% 1.97/2.20 inference(rewrite,[status(thm)],[])).
% 1.97/2.20 tff(7300,plain,
% 1.97/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1))))),
% 1.97/2.20 inference(monotonicity,[status(thm)],[7299])).
% 1.97/2.20 tff(7301,plain,
% 1.97/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))),
% 1.97/2.20 inference(transitivity,[status(thm)],[7300, 7298])).
% 1.97/2.20 tff(7302,plain,
% 1.97/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))),
% 1.97/2.20 inference(quant_inst,[status(thm)],[])).
% 1.97/2.20 tff(7303,plain,
% 1.97/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[7302, 7301])).
% 2.04/2.20 tff(7304,plain,
% 2.04/2.20 (~b(elem!1, s(s(elem!1)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7303, 246, 2362, 2001, 3697, 7297])).
% 2.04/2.20 tff(7305,plain,
% 2.04/2.20 (r(elem!1, s(s(elem!1)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1268, 7304, 1204])).
% 2.04/2.20 tff(7306,plain,
% 2.04/2.20 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4240, 183, 173, 7295])).
% 2.04/2.20 tff(7307,plain,
% 2.04/2.20 (b(s(s(elem!1)), s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[454, 7306, 4234])).
% 2.04/2.20 tff(7308,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(7309,plain,
% 2.04/2.20 (((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z))) <=> ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(7310,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[7309])).
% 2.04/2.20 tff(7311,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.04/2.20 inference(transitivity,[status(thm)],[7310, 7308])).
% 2.04/2.20 tff(7312,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z)))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(7313,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[7312, 7311])).
% 2.04/2.20 tff(7314,plain,
% 2.04/2.20 (~b(s(s(elem!1)), z)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7313, 246, 2001, 236, 3697, 7307, 4651])).
% 2.04/2.20 tff(7315,plain,
% 2.04/2.20 (r(s(s(elem!1)), z)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[523, 7314])).
% 2.04/2.20 tff(7316,plain,
% 2.04/2.20 ($false),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7107, 183, 2246, 7315, 7305])).
% 2.04/2.20 tff(7317,plain,((~b(z, s(s(s(z))))) | (~r(elem!1, z)) | (elem!1 = s(s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.20 tff(7318,plain,
% 2.04/2.20 (~b(z, s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7317, 7292, 7293, 6635, 2001, 3697, 7284, 7281, 2133, 5572])).
% 2.04/2.20 tff(7319,plain,
% 2.04/2.20 (r(z, s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[6165, 7318])).
% 2.04/2.20 tff(7320,plain,
% 2.04/2.20 (~r(elem!1, s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[2254, 7319, 7292])).
% 2.04/2.20 tff(7321,plain,
% 2.04/2.20 (b(elem!1, s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[470, 7320, 7282])).
% 2.04/2.20 tff(7322,plain,
% 2.04/2.20 (~r(s(s(s(z))), s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4259, 7321, 2124, 2232, 2001, 7281])).
% 2.04/2.20 tff(7323,plain,
% 2.04/2.20 (b(s(s(s(z))), s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[52, 7322])).
% 2.04/2.20 tff(7324,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(7325,plain,
% 2.04/2.20 (((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(7326,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[7325])).
% 2.04/2.20 tff(7327,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 2.04/2.20 inference(transitivity,[status(thm)],[7326, 7324])).
% 2.04/2.20 tff(7328,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(7329,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[7328, 7327])).
% 2.04/2.20 tff(7330,plain,
% 2.04/2.20 ($false),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7329, 246, 5572, 2001, 7284, 3697, 7323])).
% 2.04/2.20 tff(7331,plain,((~r(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), elem!1) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.20 tff(7332,plain,
% 2.04/2.20 (~r(s(z), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7331, 6373, 7276, 2124, 2232, 5365])).
% 2.04/2.20 tff(7333,plain,
% 2.04/2.20 (b(s(z), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1034, 7332, 7278])).
% 2.04/2.20 tff(7334,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(7335,plain,
% 2.04/2.20 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(7336,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[7335])).
% 2.04/2.20 tff(7337,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 2.04/2.20 inference(transitivity,[status(thm)],[7336, 7334])).
% 2.04/2.20 tff(7338,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(7339,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[7338, 7337])).
% 2.04/2.20 tff(7340,plain,
% 2.04/2.20 (~b(s(s(s(z))), s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7339, 246, 7333, 6373, 7276])).
% 2.04/2.20 tff(7341,plain,
% 2.04/2.20 (r(s(s(s(z))), s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[52, 7340])).
% 2.04/2.20 tff(7342,plain,
% 2.04/2.20 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[5804, 7278])).
% 2.04/2.20 tff(7343,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(7344,plain,
% 2.04/2.20 (((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(7345,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[7344])).
% 2.04/2.20 tff(7346,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))),
% 2.04/2.20 inference(transitivity,[status(thm)],[7345, 7343])).
% 2.04/2.20 tff(7347,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(7348,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[7347, 7346])).
% 2.04/2.20 tff(7349,plain,
% 2.04/2.20 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7348, 246, 7333, 6375, 6373, 7276])).
% 2.04/2.20 tff(7350,plain,
% 2.04/2.20 (r(s(s(s(z))), s(s(elem!1)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[689, 7349, 7342])).
% 2.04/2.20 tff(7351,plain,
% 2.04/2.20 (~b(s(z), s(s(elem!1)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[6395, 246, 7333, 6375, 6373])).
% 2.04/2.20 tff(7352,plain,
% 2.04/2.20 (r(s(z), s(s(elem!1)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[233, 7351])).
% 2.04/2.20 tff(7353,plain,
% 2.04/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(7354,plain,
% 2.04/2.20 (((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(7355,plain,
% 2.04/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z)))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[7354])).
% 2.04/2.20 tff(7356,plain,
% 2.04/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))))),
% 2.04/2.20 inference(transitivity,[status(thm)],[7355, 7353])).
% 2.04/2.20 tff(7357,plain,
% 2.04/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(7358,plain,
% 2.04/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z)))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[7357, 7356])).
% 2.04/2.20 tff(7359,plain,
% 2.04/2.20 ($false),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7358, 183, 7352, 7350, 7341])).
% 2.04/2.20 tff(7360,plain,(b(s(s(elem!1)), s(elem!1)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), elem!1) | (s(s(s(s(s(elem!1))))) = elem!1) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.20 tff(7361,plain,
% 2.04/2.20 (b(s(s(elem!1)), s(elem!1))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7360, 69, 2232, 2124, 55])).
% 2.04/2.20 tff(7362,plain,
% 2.04/2.20 (b(s(s(elem!1)), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[156, 5447, 2232])).
% 2.04/2.21 tff(7363,plain,
% 2.04/2.21 (r(elem!1, s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[214, 210, 5375])).
% 2.04/2.21 tff(7364,plain,
% 2.04/2.21 (~r(elem!1, s(s(elem!1)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4199, 7363, 173])).
% 2.04/2.21 tff(7365,plain,
% 2.04/2.21 (b(elem!1, s(s(elem!1)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1268, 7364, 1204])).
% 2.04/2.21 tff(7366,plain,
% 2.04/2.21 (~r(z, s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[292, 7363, 5365])).
% 2.04/2.21 tff(7367,plain,
% 2.04/2.21 (b(z, s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[169, 7366])).
% 2.04/2.21 tff(7368,plain,
% 2.04/2.21 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5610, 947, 5365, 2362, 7367, 1])).
% 2.04/2.21 tff(7369,plain,
% 2.04/2.21 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[86, 7368, 69])).
% 2.04/2.21 tff(7370,plain,
% 2.04/2.21 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4983, 7369, 2362, 947])).
% 2.04/2.21 tff(7371,plain,
% 2.04/2.21 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1557, 5624, 7370])).
% 2.04/2.21 tff(7372,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4060, 246, 2362, 947, 363, 1200])).
% 2.04/2.21 tff(7373,plain,((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(7374,plain,
% 2.04/2.21 (~b(s(elem!1), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7373, 947, 2362, 363])).
% 2.04/2.21 tff(7375,plain,
% 2.04/2.21 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5677, 1673, 7374])).
% 2.04/2.21 tff(7376,plain,
% 2.04/2.21 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1702, 7375])).
% 2.04/2.21 tff(7377,plain,
% 2.04/2.21 (r(s(elem!1), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5548, 7376, 1673])).
% 2.04/2.21 tff(7378,plain,
% 2.04/2.21 (~r(z, s(elem!1))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5525, 183, 5365, 7377])).
% 2.04/2.21 tff(7379,plain,
% 2.04/2.21 (b(z, s(elem!1))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[2561, 7378])).
% 2.04/2.21 tff(7380,plain,
% 2.04/2.21 (~r(s(elem!1), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5533, 183, 5365, 7377])).
% 2.04/2.21 tff(7381,plain,
% 2.04/2.21 (b(s(elem!1), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[2581, 7380])).
% 2.04/2.21 tff(7382,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(7383,plain,
% 2.04/2.21 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z))) <=> ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(7384,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[7383])).
% 2.04/2.21 tff(7385,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))),
% 2.04/2.21 inference(transitivity,[status(thm)],[7384, 7382])).
% 2.04/2.21 tff(7386,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z)))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(7387,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[7386, 7385])).
% 2.04/2.21 tff(7388,plain,
% 2.04/2.21 (~b(s(s(elem!1)), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7387, 246, 7367, 363, 7381, 7379])).
% 2.04/2.21 tff(7389,plain,
% 2.04/2.21 (r(s(s(elem!1)), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[523, 7388])).
% 2.04/2.21 tff(7390,plain,
% 2.04/2.21 (~r(s(s(s(s(s(elem!1))))), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5671, 7389, 7371])).
% 2.04/2.21 tff(7391,plain,
% 2.04/2.21 (b(s(s(s(s(s(elem!1))))), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1601, 7390])).
% 2.04/2.21 tff(7392,plain,
% 2.04/2.21 (~r(s(z), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[6720, 7389, 173])).
% 2.04/2.21 tff(7393,plain,
% 2.04/2.21 (b(s(z), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1069, 7392])).
% 2.04/2.21 tff(7394,plain,
% 2.04/2.21 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5578, 246, 7393, 7367, 7391])).
% 2.04/2.21 tff(7395,plain,
% 2.04/2.21 (r(s(s(s(s(s(elem!1))))), s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[6447, 7394])).
% 2.04/2.21 tff(7396,plain,
% 2.04/2.21 (b(s(z), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5732, 7393, 2232, 69, 1, 210, 7367, 7376, 5624, 5700, 5692, 5698])).
% 2.04/2.21 tff(7397,plain,
% 2.04/2.21 (~b(s(z), s(s(elem!1)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5589, 246, 7396, 2362, 947])).
% 2.04/2.21 tff(7398,plain,
% 2.04/2.21 (r(s(z), s(s(elem!1)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[233, 7397])).
% 2.04/2.21 tff(7399,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5754, 183, 7398, 7371, 7395])).
% 2.04/2.21 tff(7400,plain,((~(s(s(s(z))) = elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | r(s(s(elem!1)), elem!1) | (s(s(s(s(s(elem!1))))) = elem!1) | b(s(s(s(z))), elem!1) | b(elem!1, s(z)) | (~r(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(7401,plain,
% 2.04/2.21 (~(s(s(s(z))) = elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7400, 7365, 2362, 2232, 69, 1, 210, 173, 363, 55])).
% 2.04/2.21 tff(7402,plain,
% 2.04/2.21 (r(s(s(s(z))), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[647, 7401, 1])).
% 2.04/2.21 tff(7403,plain,
% 2.04/2.21 (~r(s(s(s(z))), s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[2282, 7402, 2232, 210])).
% 2.04/2.21 tff(7404,plain,
% 2.04/2.21 (~b(s(s(s(z))), s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5444, 7402, 5365, 5701, 5374, 7367, 7363])).
% 2.04/2.21 tff(7405,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[52, 7404, 7403])).
% 2.04/2.21 tff(7406,plain,(b(elem!1, s(z)) | r(s(s(elem!1)), elem!1) | b(s(s(s(z))), elem!1) | (~b(s(s(elem!1)), elem!1)) | (s(s(s(s(s(elem!1))))) = elem!1) | (~r(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | b(z, elem!1) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(7407,plain,
% 2.04/2.21 (b(elem!1, s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7406, 1, 2232, 7362, 69, 2133, 7361, 55, 5451])).
% 2.04/2.21 tff(7408,plain,
% 2.04/2.21 (~(s(s(elem!1)) = s(elem!1))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5640, 5447])).
% 2.04/2.21 tff(7409,plain,
% 2.04/2.21 (~(s(elem!1) = s(s(elem!1)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[6946, 7408])).
% 2.04/2.21 tff(7410,plain,
% 2.04/2.21 (~b(s(z), s(s(elem!1)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[6397, 6376, 2277, 2362, 6385])).
% 2.04/2.21 tff(7411,plain,
% 2.04/2.21 (r(s(z), s(s(elem!1)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[233, 7410])).
% 2.04/2.21 tff(7412,plain,
% 2.04/2.21 (~r(z, s(s(elem!1)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[6407, 7411, 170])).
% 2.04/2.21 tff(7413,plain,
% 2.04/2.21 (b(z, s(s(elem!1)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[264, 7412])).
% 2.04/2.21 tff(7414,plain,
% 2.04/2.21 (r(s(s(s(z))), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[647, 3011, 1])).
% 2.04/2.21 tff(7415,plain,
% 2.04/2.21 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5485, 7414, 267])).
% 2.04/2.21 tff(7416,plain,
% 2.04/2.21 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[86, 7415, 69])).
% 2.04/2.21 tff(7417,plain,
% 2.04/2.21 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[6937, 7416, 173, 2001, 2362, 1044])).
% 2.04/2.21 tff(7418,plain,
% 2.04/2.21 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[3815, 7417])).
% 2.04/2.21 tff(7419,plain,
% 2.04/2.21 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 2.04/2.21 inference(symmetry,[status(thm)],[7418])).
% 2.04/2.21 tff(7420,plain,
% 2.04/2.21 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[7419])).
% 2.04/2.21 tff(7421,plain,
% 2.04/2.21 (b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.04/2.21 inference(symmetry,[status(thm)],[7420])).
% 2.04/2.21 tff(7422,plain,
% 2.04/2.21 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[7419])).
% 2.04/2.21 tff(7423,plain,
% 2.04/2.21 ((~r(s(s(s(s(z)))), s(s(elem!1)))) <=> (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[7422])).
% 2.04/2.21 tff(7424,plain,
% 2.04/2.21 (~r(z, s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[6592, 7414, 267])).
% 2.04/2.21 tff(7425,plain,
% 2.04/2.21 (b(z, s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[6165, 7424])).
% 2.04/2.21 tff(7426,plain,
% 2.04/2.21 (~r(s(s(s(z))), s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[6468, 1100, 119, 267, 171, 173])).
% 2.04/2.21 tff(7427,plain,
% 2.04/2.21 (b(s(s(s(z))), s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[52, 7426])).
% 2.04/2.21 tff(7428,plain,
% 2.04/2.21 ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[6477, 246, 2362, 2001, 6430, 7427])).
% 2.04/2.21 tff(7429,plain,
% 2.04/2.21 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7428, 7425])).
% 2.04/2.21 tff(7430,plain,
% 2.04/2.21 (r(s(s(s(z))), s(s(elem!1)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[689, 7429, 119])).
% 2.04/2.21 tff(7431,plain,
% 2.04/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(7432,plain,
% 2.04/2.21 (((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(7433,plain,
% 2.04/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[7432])).
% 2.04/2.21 tff(7434,plain,
% 2.04/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)))),
% 2.04/2.21 inference(transitivity,[status(thm)],[7433, 7431])).
% 2.04/2.21 tff(7435,plain,
% 2.04/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(7436,plain,
% 2.04/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[7435, 7434])).
% 2.04/2.21 tff(7437,plain,
% 2.04/2.21 (~r(s(z), s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7436, 183, 1113, 7414, 7430])).
% 2.04/2.21 tff(7438,plain,
% 2.04/2.21 (b(s(z), s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1291, 7437])).
% 2.04/2.21 tff(7439,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(7440,plain,
% 2.04/2.21 (((~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(7441,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[7440])).
% 2.04/2.21 tff(7442,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.04/2.21 inference(transitivity,[status(thm)],[7441, 7439])).
% 2.04/2.21 tff(7443,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(7444,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[7443, 7442])).
% 2.04/2.21 tff(7445,plain,
% 2.04/2.21 (~b(s(s(s(s(z)))), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7444, 246, 2401, 2003, 4651, 1833])).
% 2.04/2.21 tff(7446,plain,
% 2.04/2.21 (r(s(s(s(s(z)))), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[6040, 7445])).
% 2.04/2.21 tff(7447,plain,
% 2.04/2.21 (~b(s(s(s(s(z)))), s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[3591, 246, 2401, 2003, 1833])).
% 2.04/2.21 tff(7448,plain,
% 2.04/2.21 (r(s(s(s(s(z)))), s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[6103, 7447])).
% 2.04/2.21 tff(7449,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[2418, 183, 171, 7448, 7446])).
% 2.04/2.21 tff(7450,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(7451,plain,
% 2.04/2.21 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7450, 7438, 171, 7427, 7425])).
% 2.04/2.21 tff(7452,plain,
% 2.04/2.21 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1702, 7451])).
% 2.04/2.21 tff(7453,plain,
% 2.04/2.21 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(elem!1)))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[7418])).
% 2.04/2.21 tff(7454,plain,
% 2.04/2.21 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(elem!1))))))),
% 2.04/2.21 inference(symmetry,[status(thm)],[7453])).
% 2.04/2.21 tff(7455,plain,
% 2.04/2.21 (s(elem!1) = s(s(s(s(elem!1))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[108, 7454, 325])).
% 2.04/2.21 tff(7456,plain,
% 2.04/2.21 (inj_0(s(elem!1)) = inj_0(s(s(s(s(elem!1)))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[7455])).
% 2.04/2.21 tff(7457,plain,
% 2.04/2.21 (elem!1 = s(s(s(elem!1)))),
% 2.04/2.21 inference(transitivity,[status(thm)],[3154, 7456, 351])).
% 2.04/2.21 tff(7458,plain,
% 2.04/2.21 (b(s(z), elem!1) <=> b(s(z), s(s(s(elem!1))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[7457])).
% 2.04/2.21 tff(7459,plain,
% 2.04/2.21 (b(s(z), s(s(s(elem!1))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[1044, 7458])).
% 2.04/2.21 tff(7460,plain,
% 2.04/2.21 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[7457])).
% 2.04/2.21 tff(7461,plain,
% 2.04/2.21 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[2362, 7460])).
% 2.04/2.21 tff(7462,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(7463,plain,
% 2.04/2.21 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(7464,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[7463])).
% 2.04/2.21 tff(7465,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[7464, 7462])).
% 2.04/2.21 tff(7466,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(elem!1)))))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(7467,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[7466, 7465])).
% 2.04/2.21 tff(7468,plain,
% 2.04/2.21 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7467, 246, 6430, 7427, 7425, 7461, 7459])).
% 2.04/2.21 tff(7469,plain,
% 2.04/2.21 (r(s(s(elem!1)), s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[454, 7468, 4234])).
% 2.04/2.21 tff(7470,plain,
% 2.04/2.21 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[6305, 183, 173, 7469, 7452])).
% 2.04/2.21 tff(7471,plain,
% 2.04/2.21 (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[7470, 7423])).
% 2.04/2.21 tff(7472,plain,
% 2.04/2.21 (b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1506, 7471])).
% 2.04/2.21 tff(7473,plain,
% 2.04/2.21 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[7472, 7421])).
% 2.04/2.21 tff(7474,plain,
% 2.04/2.21 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(elem!1))),
% 2.04/2.21 inference(symmetry,[status(thm)],[7456])).
% 2.04/2.21 tff(7475,plain,
% 2.04/2.21 (s(s(s(elem!1))) = elem!1),
% 2.04/2.21 inference(transitivity,[status(thm)],[352, 7474, 343])).
% 2.04/2.21 tff(7476,plain,
% 2.04/2.21 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[7475])).
% 2.04/2.21 tff(7477,plain,
% 2.04/2.21 (r(elem!1, s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 2.04/2.21 inference(symmetry,[status(thm)],[7476])).
% 2.04/2.21 tff(7478,plain,
% 2.04/2.21 (~b(elem!1, s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[2011, 7427, 2001, 1044])).
% 2.04/2.21 tff(7479,plain,
% 2.04/2.21 (~(elem!1 = s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[3013, 3011])).
% 2.04/2.21 tff(7480,plain,
% 2.04/2.21 (r(elem!1, s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[470, 7479, 7478])).
% 2.04/2.21 tff(7481,plain,
% 2.04/2.21 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[7480, 7477])).
% 2.04/2.21 tff(7482,plain,
% 2.04/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(7483,plain,
% 2.04/2.22 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(7484,plain,
% 2.04/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[7483])).
% 2.04/2.22 tff(7485,plain,
% 2.04/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.04/2.22 inference(transitivity,[status(thm)],[7484, 7482])).
% 2.04/2.22 tff(7486,plain,
% 2.04/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(7487,plain,
% 2.04/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[7486, 7485])).
% 2.04/2.22 tff(7488,plain,
% 2.04/2.22 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[7487, 183, 7452, 7481])).
% 2.04/2.22 tff(7489,plain,
% 2.04/2.22 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[6333, 47, 6705, 7488])).
% 2.04/2.22 tff(7490,plain,
% 2.04/2.22 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[7475])).
% 2.04/2.22 tff(7491,plain,
% 2.04/2.22 (b(elem!1, s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.04/2.22 inference(symmetry,[status(thm)],[7490])).
% 2.04/2.22 tff(7492,plain,
% 2.04/2.22 (r(elem!1, s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[7457])).
% 2.04/2.22 tff(7493,plain,
% 2.04/2.22 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.04/2.22 inference(symmetry,[status(thm)],[7492])).
% 2.04/2.22 tff(7494,plain,
% 2.04/2.22 ((~r(s(s(s(elem!1))), s(s(elem!1)))) <=> (~r(elem!1, s(s(elem!1))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[7493])).
% 2.04/2.22 tff(7495,plain,
% 2.04/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(7496,plain,
% 2.04/2.22 (((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(7497,plain,
% 2.04/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[7496])).
% 2.04/2.22 tff(7498,plain,
% 2.04/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.04/2.22 inference(transitivity,[status(thm)],[7497, 7495])).
% 2.04/2.22 tff(7499,plain,
% 2.04/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(7500,plain,
% 2.04/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[7499, 7498])).
% 2.04/2.22 tff(7501,plain,
% 2.04/2.22 ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[7500, 183, 7469])).
% 2.04/2.22 tff(7502,plain,
% 2.04/2.22 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[7501, 7481])).
% 2.04/2.22 tff(7503,plain,
% 2.04/2.22 (~r(elem!1, s(s(elem!1)))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[7502, 7494])).
% 2.04/2.22 tff(7504,plain,
% 2.04/2.22 (b(elem!1, s(s(elem!1)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1268, 7503, 1204])).
% 2.04/2.22 tff(7505,plain,
% 2.04/2.22 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[7504, 7491])).
% 2.04/2.22 tff(7506,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(7507,plain,
% 2.04/2.22 (((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(7508,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[7507])).
% 2.04/2.22 tff(7509,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.04/2.22 inference(transitivity,[status(thm)],[7508, 7506])).
% 2.04/2.22 tff(7510,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(7511,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[7510, 7509])).
% 2.04/2.22 tff(7512,plain,
% 2.04/2.22 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[7511, 246, 1100, 6430, 7505, 7489])).
% 2.04/2.22 tff(7513,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[7512, 7473])).
% 2.04/2.22 tff(7514,plain,((s(s(s(z))) = elem!1) | (~b(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (elem!1 = s(s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (s(s(s(z))) = s(s(elem!1))) | (~b(elem!1, s(z))) | (s(s(s(s(s(elem!1))))) = elem!1) | (~r(z, elem!1)) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(7515,plain,
% 2.04/2.22 (s(s(s(z))) = elem!1),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[7514, 6427, 173, 170, 1204, 2362, 6428, 7411, 5805, 2001, 69, 5365, 1])).
% 2.04/2.22 tff(7516,plain,
% 2.04/2.22 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[5623, 7515])).
% 2.04/2.22 tff(7517,plain,
% 2.04/2.22 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4092, 7516, 173, 170, 7413])).
% 2.04/2.22 tff(7518,plain,
% 2.04/2.22 (b(s(s(s(s(s(elem!1))))), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[6447, 7517])).
% 2.04/2.22 tff(7519,plain,
% 2.04/2.22 (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[3815, 7516])).
% 2.04/2.22 tff(7520,plain,
% 2.04/2.22 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[6937, 7519, 173, 2001, 2362, 6428])).
% 2.04/2.22 tff(7521,plain,
% 2.04/2.22 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[86, 7520, 69])).
% 2.04/2.22 tff(7522,plain,
% 2.04/2.22 (~r(s(s(s(s(s(elem!1))))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[5470, 183, 5365, 7521])).
% 2.04/2.22 tff(7523,plain,
% 2.04/2.22 (b(s(s(s(s(s(elem!1))))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1601, 7522])).
% 2.04/2.22 tff(7524,plain,
% 2.04/2.22 (s(s(s(s(z)))) = s(elem!1)),
% 2.04/2.22 inference(monotonicity,[status(thm)],[7515])).
% 2.04/2.22 tff(7525,plain,
% 2.04/2.22 ((s(s(s(s(z)))) = elem!1) <=> (s(elem!1) = elem!1)),
% 2.04/2.22 inference(monotonicity,[status(thm)],[7524])).
% 2.04/2.22 tff(7526,plain,
% 2.04/2.22 ((s(s(s(s(z)))) = elem!1) <=> (elem!1 = s(elem!1))),
% 2.04/2.22 inference(transitivity,[status(thm)],[7525, 2825])).
% 2.04/2.22 tff(7527,plain,
% 2.04/2.22 ((s(s(s(s(z)))) = elem!1) <=> (s(elem!1) = elem!1)),
% 2.04/2.22 inference(transitivity,[status(thm)],[7526, 3423])).
% 2.04/2.22 tff(7528,plain,
% 2.04/2.22 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(s(elem!1) = elem!1))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[7527])).
% 2.04/2.22 tff(7529,plain,
% 2.04/2.22 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(z)))) = elem!1)),
% 2.04/2.22 inference(monotonicity,[status(thm)],[7515])).
% 2.04/2.22 tff(7530,plain,
% 2.04/2.22 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[7529])).
% 2.04/2.22 tff(7531,plain,
% 2.04/2.22 (~(s(s(s(s(z)))) = elem!1)),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[1697, 7530])).
% 2.04/2.22 tff(7532,plain,
% 2.04/2.22 (~(s(elem!1) = elem!1)),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[7531, 7528])).
% 2.04/2.22 tff(7533,plain,
% 2.04/2.22 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(elem!1) = s(s(s(s(s(elem!1))))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[7524])).
% 2.04/2.22 tff(7534,plain,
% 2.04/2.22 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(elem!1))),
% 2.04/2.22 inference(transitivity,[status(thm)],[7533, 1800])).
% 2.04/2.22 tff(7535,plain,
% 2.04/2.22 ((~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(s(elem!1))))) = s(elem!1)))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[7534])).
% 2.04/2.22 tff(7536,plain,
% 2.04/2.22 (~(s(s(s(s(s(elem!1))))) = s(elem!1))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[1501, 7535])).
% 2.04/2.22 tff(7537,plain,
% 2.04/2.22 (~r(s(elem!1), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[5543, 7536, 5365, 7521])).
% 2.04/2.22 tff(7538,plain,
% 2.04/2.22 (b(s(elem!1), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[5655, 7537, 7532])).
% 2.04/2.22 tff(7539,plain,
% 2.04/2.22 (~r(s(z), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[6981, 7538, 7515, 6963, 6428, 2362, 2001])).
% 2.04/2.22 tff(7540,plain,
% 2.04/2.22 (b(s(z), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1069, 7539])).
% 2.04/2.22 tff(7541,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(7542,plain,
% 2.04/2.22 (((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z)))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(7543,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z)))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[7542])).
% 2.04/2.22 tff(7544,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 2.04/2.22 inference(transitivity,[status(thm)],[7543, 7541])).
% 2.04/2.22 tff(7545,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(7546,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z)))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[7545, 7544])).
% 2.04/2.22 tff(7547,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[7546, 246, 7540, 6428, 2362, 7413, 7523, 7518])).
% 2.04/2.22 tff(7548,plain,(b(z, s(z)) | (~b(s(s(elem!1)), elem!1)) | (s(elem!1) = s(s(elem!1))) | (~b(elem!1, s(z))) | (s(s(s(s(s(elem!1))))) = elem!1) | (~r(s(s(elem!1)), s(z))) | (elem!1 = s(s(elem!1))) | b(s(s(s(z))), elem!1) | (s(z) = elem!1) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(7549,plain,
% 2.04/2.22 (b(z, s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[7548, 7362, 7409, 7407, 69, 2133, 5451, 1, 5374, 55])).
% 2.04/2.22 tff(7550,plain,
% 2.04/2.22 (r(z, s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[6803, 7549, 2124, 2232, 1, 5365, 69, 7407])).
% 2.04/2.22 tff(7551,plain,
% 2.04/2.22 (~r(s(s(s(z))), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[6592, 7550, 5365])).
% 2.04/2.22 tff(7552,plain,
% 2.04/2.22 (s(s(s(z))) = elem!1),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[647, 7551, 1])).
% 2.04/2.22 tff(7553,plain,
% 2.04/2.22 (s(s(s(s(z)))) = s(elem!1)),
% 2.04/2.22 inference(monotonicity,[status(thm)],[7552])).
% 2.04/2.22 tff(7554,plain,
% 2.04/2.22 ((s(s(s(s(z)))) = elem!1) <=> (s(elem!1) = elem!1)),
% 2.04/2.22 inference(monotonicity,[status(thm)],[7553])).
% 2.04/2.22 tff(7555,plain,
% 2.04/2.22 ((s(s(s(s(z)))) = elem!1) <=> (elem!1 = s(elem!1))),
% 2.04/2.22 inference(transitivity,[status(thm)],[7554, 2825])).
% 2.04/2.22 tff(7556,plain,
% 2.04/2.22 ((s(s(s(s(z)))) = elem!1) <=> (s(elem!1) = elem!1)),
% 2.04/2.22 inference(transitivity,[status(thm)],[7555, 3423])).
% 2.04/2.22 tff(7557,plain,
% 2.04/2.22 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(s(elem!1) = elem!1))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[7556])).
% 2.04/2.22 tff(7558,plain,
% 2.04/2.22 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(z)))) = elem!1)),
% 2.04/2.22 inference(monotonicity,[status(thm)],[7552])).
% 2.04/2.22 tff(7559,plain,
% 2.04/2.22 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[7558])).
% 2.04/2.22 tff(7560,plain,
% 2.04/2.22 (~(s(s(s(s(z)))) = elem!1)),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[1697, 7559])).
% 2.04/2.22 tff(7561,plain,
% 2.04/2.22 (~(s(elem!1) = elem!1)),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[7560, 7557])).
% 2.04/2.22 tff(7562,plain,
% 2.04/2.22 (elem!1 = s(s(s(z)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1677, 7552])).
% 2.04/2.22 tff(7563,plain,
% 2.04/2.22 (b(s(s(s(z))), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[6830, 7562, 7407])).
% 2.04/2.22 tff(7564,plain,
% 2.04/2.22 (b(s(z), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[6928, 7563, 1, 5451, 5365, 7362, 2133, 7407, 7549, 69, 2232])).
% 2.04/2.22 tff(7565,plain,
% 2.04/2.22 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[5623, 7552])).
% 2.04/2.22 tff(7566,plain,
% 2.04/2.22 (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[3815, 7565])).
% 2.04/2.22 tff(7567,plain,
% 2.04/2.22 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[6937, 7566, 2133, 7407, 7362, 7564])).
% 2.04/2.22 tff(7568,plain,
% 2.04/2.22 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[86, 7567, 69])).
% 2.04/2.22 tff(7569,plain,
% 2.04/2.22 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(elem!1) = s(s(s(s(s(elem!1))))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[7553])).
% 2.04/2.22 tff(7570,plain,
% 2.04/2.22 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(elem!1))),
% 2.04/2.22 inference(transitivity,[status(thm)],[7569, 1800])).
% 2.04/2.22 tff(7571,plain,
% 2.04/2.22 ((~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(s(elem!1))))) = s(elem!1)))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[7570])).
% 2.04/2.22 tff(7572,plain,
% 2.04/2.22 (~(s(s(s(s(s(elem!1))))) = s(elem!1))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[1501, 7571])).
% 2.04/2.22 tff(7573,plain,
% 2.04/2.22 (~r(s(elem!1), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[5543, 7572, 5365, 7568])).
% 2.04/2.22 tff(7574,plain,
% 2.04/2.22 (b(s(elem!1), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[5655, 7573, 7561])).
% 2.04/2.22 tff(7575,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(7576,plain,
% 2.04/2.22 (((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(7577,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[7576])).
% 2.04/2.22 tff(7578,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 2.04/2.22 inference(transitivity,[status(thm)],[7577, 7575])).
% 2.04/2.22 tff(7579,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(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))))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(7580,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[7579, 7578])).
% 2.04/2.22 tff(7581,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[7580, 246, 7564, 7362, 7407, 7361, 7574])).
% 2.04/2.22 tff(7582,plain,(b(s(s(s(z))), elem!1) | (s(s(s(s(s(elem!1))))) = elem!1) | r(s(s(elem!1)), elem!1) | b(s(s(elem!1)), s(z)) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(7583,plain,
% 2.04/2.22 (b(s(s(s(z))), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[7582, 69, 2232, 2124, 55])).
% 2.04/2.22 tff(7584,plain,
% 2.04/2.22 (~(elem!1 = s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[5773, 7583, 2124])).
% 2.04/2.22 tff(7585,plain,
% 2.04/2.22 (r(elem!1, s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[214, 5376, 7279])).
% 2.04/2.22 tff(7586,plain,
% 2.04/2.22 ((s(s(s(s(s(elem!1))))) = elem!1) <=> (s(elem!1) = elem!1)),
% 2.04/2.22 inference(monotonicity,[status(thm)],[5861])).
% 2.04/2.22 tff(7587,plain,
% 2.04/2.22 ((s(s(s(s(s(elem!1))))) = elem!1) <=> (elem!1 = s(elem!1))),
% 2.04/2.22 inference(transitivity,[status(thm)],[7586, 2825])).
% 2.04/2.22 tff(7588,plain,
% 2.04/2.22 ((s(s(s(s(s(elem!1))))) = elem!1) <=> (s(elem!1) = elem!1)),
% 2.04/2.22 inference(transitivity,[status(thm)],[7587, 3423])).
% 2.04/2.22 tff(7589,plain,
% 2.04/2.22 ((~(s(s(s(s(s(elem!1))))) = elem!1)) <=> (~(s(elem!1) = elem!1))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[7588])).
% 2.04/2.22 tff(7590,plain,
% 2.04/2.22 (~(s(elem!1) = elem!1)),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[69, 7589])).
% 2.04/2.22 tff(7591,plain,
% 2.04/2.22 (elem!1 = s(s(elem!1))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[6867, 2125])).
% 2.04/2.22 tff(7592,plain,
% 2.04/2.22 (~(s(s(s(s(z)))) = elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[2399, 5896, 7591])).
% 2.04/2.22 tff(7593,plain,
% 2.04/2.22 (~(elem!1 = s(s(s(s(z)))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[7592, 5880])).
% 2.04/2.22 tff(7594,plain,
% 2.04/2.22 (~r(s(elem!1), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[6072, 217, 267, 2125, 5847])).
% 2.04/2.22 tff(7595,plain,
% 2.04/2.22 (b(s(elem!1), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[5655, 7594, 5653])).
% 2.04/2.22 tff(7596,plain,
% 2.04/2.22 (~b(z, s(elem!1))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[5957, 2593, 3697, 7592, 267, 2002, 1200, 2125])).
% 2.04/2.22 tff(7597,plain,
% 2.04/2.22 (r(z, s(elem!1))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[2561, 7596])).
% 2.04/2.22 tff(7598,plain,
% 2.04/2.22 ((s(s(s(s(s(elem!1))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 2.04/2.22 inference(transitivity,[status(thm)],[5894, 2182])).
% 2.04/2.22 tff(7599,plain,
% 2.04/2.22 ((~(s(s(s(s(s(elem!1))))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[7598])).
% 2.04/2.22 tff(7600,plain,
% 2.04/2.22 (~(s(s(s(z))) = s(elem!1))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[1622, 7599])).
% 2.04/2.22 tff(7601,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(7602,plain,
% 2.04/2.22 (((~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(7603,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1)))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[7602])).
% 2.04/2.22 tff(7604,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))))),
% 2.04/2.22 inference(transitivity,[status(thm)],[7603, 7601])).
% 2.04/2.22 tff(7605,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(7606,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1)))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[7605, 7604])).
% 2.04/2.22 tff(7607,plain,
% 2.04/2.22 (~b(s(s(s(z))), s(elem!1))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[7606, 246, 2002, 3697, 1200])).
% 2.04/2.22 tff(7608,plain,
% 2.04/2.22 (r(s(s(s(z))), s(elem!1))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[2675, 7607, 7600])).
% 2.04/2.22 tff(7609,plain,
% 2.04/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(7610,plain,
% 2.04/2.23 (((~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(7611,plain,
% 2.04/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1)))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[7610])).
% 2.04/2.23 tff(7612,plain,
% 2.04/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1))))),
% 2.04/2.23 inference(transitivity,[status(thm)],[7611, 7609])).
% 2.04/2.23 tff(7613,plain,
% 2.04/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z)))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(7614,plain,
% 2.04/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))) | (~r(z, s(elem!1)))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[7613, 7612])).
% 2.04/2.23 tff(7615,plain,
% 2.04/2.23 (~r(s(s(s(z))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[7614, 183, 7608, 7597])).
% 2.04/2.23 tff(7616,plain,
% 2.04/2.23 (b(s(s(s(z))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[995, 7615])).
% 2.04/2.23 tff(7617,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(7618,plain,
% 2.04/2.23 (((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(7619,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[7618])).
% 2.04/2.23 tff(7620,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 2.04/2.23 inference(transitivity,[status(thm)],[7619, 7617])).
% 2.04/2.23 tff(7621,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(7622,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[7621, 7620])).
% 2.04/2.23 tff(7623,plain,
% 2.04/2.23 (~b(s(z), s(s(s(z))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[7622, 246, 1056, 236, 7616])).
% 2.04/2.23 tff(7624,plain,
% 2.04/2.23 (r(s(z), s(s(s(z))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1291, 7623])).
% 2.04/2.23 tff(7625,plain,
% 2.04/2.23 (~r(s(z), s(s(s(s(z)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[6088, 183, 7624, 2593])).
% 2.04/2.23 tff(7626,plain,
% 2.04/2.23 ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[6092, 47, 7625])).
% 2.04/2.23 tff(7627,plain,
% 2.04/2.23 (b(s(z), s(s(s(s(z)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[7626, 5790])).
% 2.04/2.23 tff(7628,plain,
% 2.04/2.23 ((s(elem!1) = s(z)) <=> (s(s(s(s(s(elem!1))))) = s(z))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[5874])).
% 2.04/2.23 tff(7629,plain,
% 2.04/2.23 ((s(s(s(s(s(elem!1))))) = s(z)) <=> (s(elem!1) = s(z))),
% 2.04/2.23 inference(symmetry,[status(thm)],[7628])).
% 2.04/2.23 tff(7630,plain,
% 2.04/2.23 ((~(s(s(s(s(s(elem!1))))) = s(z))) <=> (~(s(elem!1) = s(z)))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[7629])).
% 2.04/2.23 tff(7631,plain,
% 2.04/2.23 (~(s(elem!1) = s(z))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[331, 7630])).
% 2.04/2.23 tff(7632,plain,
% 2.04/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(7633,plain,
% 2.04/2.23 (((~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(7634,plain,
% 2.04/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z)))))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[7633])).
% 2.04/2.23 tff(7635,plain,
% 2.04/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))))),
% 2.04/2.23 inference(transitivity,[status(thm)],[7634, 7632])).
% 2.04/2.23 tff(7636,plain,
% 2.04/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(z))))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(7637,plain,
% 2.04/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z)))))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[7636, 7635])).
% 2.04/2.23 tff(7638,plain,
% 2.04/2.23 (~r(s(elem!1), s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[7637, 183, 7624, 5904])).
% 2.04/2.23 tff(7639,plain,
% 2.04/2.23 ((s(elem!1) = s(z)) | b(s(elem!1), s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[2989, 47, 7638])).
% 2.04/2.23 tff(7640,plain,
% 2.04/2.23 (b(s(elem!1), s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[7639, 7631])).
% 2.04/2.23 tff(7641,plain,
% 2.04/2.23 (~r(s(s(s(s(z)))), s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[6098, 7624, 2593])).
% 2.04/2.23 tff(7642,plain,
% 2.04/2.23 (b(s(s(s(s(z)))), s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[6103, 7641])).
% 2.04/2.23 tff(7643,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(7644,plain,
% 2.04/2.23 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(z)))) <=> ((~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(7645,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[7644])).
% 2.04/2.23 tff(7646,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.04/2.23 inference(transitivity,[status(thm)],[7645, 7643])).
% 2.04/2.23 tff(7647,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(7648,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[7647, 7646])).
% 2.04/2.23 tff(7649,plain,
% 2.04/2.23 ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[7648, 246, 1056, 7642])).
% 2.04/2.23 tff(7650,plain,
% 2.04/2.23 (~b(s(elem!1), s(s(s(s(z)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[7649, 7640, 7627])).
% 2.04/2.23 tff(7651,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[7650, 5938])).
% 2.04/2.23 tff(7652,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~(s(s(elem!1)) = elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(7653,plain,
% 2.04/2.23 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[7652, 5572, 2125, 5847, 3697, 267, 2002, 7595])).
% 2.04/2.23 tff(7654,plain,
% 2.04/2.23 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1702, 7653])).
% 2.04/2.23 tff(7655,plain,
% 2.04/2.23 (~b(elem!1, s(s(s(s(z)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5965, 246, 2002, 3697, 7654])).
% 2.04/2.23 tff(7656,plain,
% 2.04/2.23 ((elem!1 = s(s(s(s(z))))) | r(elem!1, s(s(s(s(z)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5969, 47, 7655])).
% 2.04/2.23 tff(7657,plain,
% 2.04/2.23 (r(elem!1, s(s(s(s(z)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[7656, 7593])).
% 2.04/2.23 tff(7658,plain,
% 2.04/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(7659,plain,
% 2.04/2.23 (((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(7660,plain,
% 2.04/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z))))))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[7659])).
% 2.04/2.23 tff(7661,plain,
% 2.04/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.04/2.23 inference(transitivity,[status(thm)],[7660, 7658])).
% 2.04/2.23 tff(7662,plain,
% 2.04/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(7663,plain,
% 2.04/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z))))))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[7662, 7661])).
% 2.04/2.23 tff(7664,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[7663, 183, 474, 6095, 5972])).
% 2.04/2.23 tff(7665,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(7666,plain,
% 2.04/2.23 (~r(s(s(s(s(z)))), s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[7665, 7657, 474])).
% 2.04/2.23 tff(7667,plain,
% 2.04/2.23 (b(s(s(s(s(z)))), s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[6103, 7666])).
% 2.04/2.23 tff(7668,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(7669,plain,
% 2.04/2.23 (((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(7670,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[7669])).
% 2.04/2.23 tff(7671,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.04/2.23 inference(transitivity,[status(thm)],[7670, 7668])).
% 2.04/2.23 tff(7672,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(7673,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[7672, 7671])).
% 2.04/2.23 tff(7674,plain,
% 2.04/2.23 (~b(z, s(s(s(s(z)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[7673, 246, 5572, 5847, 7667])).
% 2.04/2.23 tff(7675,plain,
% 2.04/2.23 ((z = s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[2645, 47, 7674])).
% 2.04/2.23 tff(7676,plain,
% 2.04/2.23 (r(z, s(s(s(s(z)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[7675, 2635])).
% 2.04/2.23 tff(7677,plain,
% 2.04/2.23 (~b(s(s(s(s(z)))), elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[6027, 246, 2002, 3697, 7654])).
% 2.04/2.23 tff(7678,plain,
% 2.04/2.23 (r(s(s(s(s(z)))), elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[2442, 47, 7592, 7677])).
% 2.04/2.23 tff(7679,plain,
% 2.04/2.23 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(7680,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[7679])).
% 2.04/2.23 tff(7681,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.04/2.23 inference(transitivity,[status(thm)],[7680, 3292])).
% 2.04/2.23 tff(7682,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(7683,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[7682, 7681])).
% 2.04/2.24 tff(7684,plain,
% 2.04/2.24 (~b(s(s(s(s(z)))), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[7683, 246, 5572, 5847, 7667])).
% 2.04/2.24 tff(7685,plain,
% 2.04/2.24 (r(s(s(s(s(z)))), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[6040, 7684])).
% 2.04/2.24 tff(7686,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[6044, 183, 267, 7685, 7678, 7676])).
% 2.04/2.24 tff(7687,plain,((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~(s(s(elem!1)) = elem!1)) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(7688,plain,
% 2.04/2.24 (~r(s(z), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[7687, 2002, 474, 267, 3697, 2125, 5653])).
% 2.04/2.24 tff(7689,plain,
% 2.04/2.24 (b(s(z), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1034, 7688, 2277])).
% 2.04/2.24 tff(7690,plain,
% 2.04/2.24 (~b(s(z), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[6080, 246, 7689, 2002, 3697])).
% 2.04/2.24 tff(7691,plain,
% 2.04/2.24 (r(s(z), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1291, 7690])).
% 2.04/2.24 tff(7692,plain,
% 2.04/2.24 (~r(s(z), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[6132, 7689, 5847, 2002, 3697, 5401, 474])).
% 2.04/2.24 tff(7693,plain,
% 2.04/2.24 (b(s(z), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1069, 7692])).
% 2.04/2.24 tff(7694,plain,
% 2.04/2.24 (~b(elem!1, z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1064, 7693, 5847, 7689])).
% 2.04/2.24 tff(7695,plain,
% 2.04/2.24 (r(elem!1, z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1143, 7694, 5401])).
% 2.04/2.24 tff(7696,plain,
% 2.04/2.24 (~r(s(s(s(s(z)))), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[7665, 6009, 474])).
% 2.04/2.24 tff(7697,plain,
% 2.04/2.24 (b(s(s(s(s(z)))), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[6103, 7696])).
% 2.04/2.24 tff(7698,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(7699,plain,
% 2.04/2.24 (((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(7700,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z))))))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[7699])).
% 2.04/2.24 tff(7701,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 2.04/2.24 inference(transitivity,[status(thm)],[7700, 7698])).
% 2.04/2.24 tff(7702,plain,
% 2.04/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(7703,plain,
% 2.04/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z))))))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[7702, 7701])).
% 2.04/2.24 tff(7704,plain,
% 2.04/2.24 ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[7703, 246, 1044, 236, 2002, 1833])).
% 2.04/2.24 tff(7705,plain,
% 2.04/2.24 (~b(z, s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[7704, 7697])).
% 2.04/2.24 tff(7706,plain,
% 2.04/2.24 ((z = s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2645, 47, 7705])).
% 2.04/2.24 tff(7707,plain,
% 2.04/2.24 (r(z, s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[7706, 2635])).
% 2.04/2.24 tff(7708,plain,
% 2.04/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(7709,plain,
% 2.04/2.24 (((~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(7710,plain,
% 2.04/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[7709])).
% 2.04/2.24 tff(7711,plain,
% 2.04/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 2.04/2.24 inference(transitivity,[status(thm)],[7710, 7708])).
% 2.04/2.24 tff(7712,plain,
% 2.04/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, z)))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(7713,plain,
% 2.04/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[7712, 7711])).
% 2.04/2.24 tff(7714,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[7713, 183, 2246, 6009, 7707])).
% 2.04/2.24 tff(7715,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(z))))) | (~r(elem!1, s(z))) | (s(s(s(s(z)))) = elem!1) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(7716,plain,
% 2.04/2.24 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[7715, 7695, 7689, 5847, 2002, 474, 7592, 3697])).
% 2.04/2.24 tff(7717,plain,
% 2.04/2.24 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1702, 7716])).
% 2.04/2.24 tff(7718,plain,
% 2.04/2.24 (~r(s(s(s(s(z)))), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[6098, 7717, 7691])).
% 2.04/2.24 tff(7719,plain,
% 2.04/2.24 (b(s(s(s(s(z)))), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[6103, 7718])).
% 2.04/2.24 tff(7720,plain,
% 2.04/2.24 (~b(s(s(s(s(z)))), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[7683, 246, 7693, 5847, 7719])).
% 2.04/2.24 tff(7721,plain,
% 2.04/2.24 (r(s(s(s(s(z)))), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[6040, 7720])).
% 2.04/2.24 tff(7722,plain,
% 2.04/2.24 (~r(s(s(s(s(z)))), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[6142, 183, 7695, 7721])).
% 2.04/2.24 tff(7723,plain,
% 2.04/2.24 (b(s(s(s(s(z)))), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2442, 47, 7592, 7722])).
% 2.04/2.24 tff(7724,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[6150, 246, 7689, 2002, 3697, 7719, 7723])).
% 2.04/2.24 tff(7725,plain,((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~r(elem!1, s(z))) | (s(z) = elem!1) | (~r(z, elem!1)) | (~(s(s(elem!1)) = elem!1)) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(7726,plain,
% 2.04/2.24 (~b(elem!1, s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[7725, 7585, 3697, 7280, 267, 2125, 7590])).
% 2.04/2.24 tff(7727,plain,
% 2.04/2.24 (r(elem!1, s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[470, 7726, 7282])).
% 2.04/2.24 tff(7728,plain,
% 2.04/2.24 (~b(s(s(s(z))), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[6196, 7727, 3697, 7585, 7280, 267])).
% 2.04/2.24 tff(7729,plain,
% 2.04/2.24 (r(s(s(s(z))), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[52, 7728])).
% 2.04/2.24 tff(7730,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[5796, 183, 7585, 7727, 7729])).
% 2.04/2.24 tff(7731,plain,((~(s(s(elem!1)) = elem!1)) | (~b(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (s(s(s(s(s(elem!1))))) = elem!1) | b(s(s(elem!1)), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(7732,plain,
% 2.04/2.24 (~(s(s(elem!1)) = elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[7731, 7583, 5365, 69, 2124])).
% 2.04/2.24 tff(7733,plain,
% 2.04/2.24 (~(elem!1 = s(s(elem!1)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[5450, 7732])).
% 2.04/2.24 tff(7734,plain,
% 2.04/2.24 (~(s(z) = elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[9, 7584])).
% 2.04/2.24 tff(7735,plain,
% 2.04/2.24 (b(s(s(elem!1)), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[156, 7732, 2232])).
% 2.04/2.24 tff(7736,plain,
% 2.04/2.24 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[5804, 10])).
% 2.04/2.24 tff(7737,plain,
% 2.04/2.24 (~r(s(s(elem!1)), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[6425, 54, 55, 5365, 3, 2362])).
% 2.04/2.24 tff(7738,plain,
% 2.04/2.24 (b(s(s(elem!1)), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[523, 7737])).
% 2.04/2.24 tff(7739,plain,
% 2.04/2.24 (~r(s(s(s(z))), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[6468, 7738, 7736, 5365, 170, 173])).
% 2.04/2.24 tff(7740,plain,
% 2.04/2.24 (b(s(s(s(z))), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[52, 7739])).
% 2.04/2.24 tff(7741,plain,
% 2.04/2.24 (b(elem!1, s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[214, 6376, 3])).
% 2.04/2.24 tff(7742,plain,
% 2.04/2.24 (b(s(z), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1034, 6385, 10])).
% 2.04/2.24 tff(7743,plain,
% 2.04/2.24 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(7744,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[7743])).
% 2.04/2.24 tff(7745,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 2.04/2.24 inference(transitivity,[status(thm)],[7744, 7334])).
% 2.04/2.24 tff(7746,plain,
% 2.04/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(7747,plain,
% 2.04/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[7746, 7745])).
% 2.04/2.24 tff(7748,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[7747, 246, 7742, 7741, 3697, 7740])).
% 2.04/2.24 tff(7749,plain,(b(z, s(z)) | (~b(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(z))) | (elem!1 = s(z)) | b(z, elem!1) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(7750,plain,
% 2.04/2.24 (b(z, s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[7749, 7583, 2133, 7584, 55, 7735])).
% 2.04/2.24 tff(7751,plain,
% 2.04/2.24 (b(elem!1, s(s(elem!1)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1268, 4200, 1204])).
% 2.04/2.24 tff(7752,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(7753,plain,
% 2.04/2.24 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(z)))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(7754,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[7753])).
% 2.04/2.24 tff(7755,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.04/2.24 inference(transitivity,[status(thm)],[7754, 7752])).
% 2.04/2.24 tff(7756,plain,
% 2.04/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(7757,plain,
% 2.04/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[7756, 7755])).
% 2.04/2.24 tff(7758,plain,
% 2.04/2.24 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[7757, 246, 2362, 7751, 3697])).
% 2.04/2.24 tff(7759,plain,
% 2.04/2.24 (r(s(s(elem!1)), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[454, 7758, 5806])).
% 2.04/2.24 tff(7760,plain,
% 2.04/2.24 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[6281, 5805])).
% 2.04/2.24 tff(7761,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4240, 183, 173, 3886, 430])).
% 2.04/2.24 tff(7762,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(7763,plain,
% 2.04/2.24 (~r(s(s(s(z))), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[7762, 7759, 173])).
% 2.04/2.24 tff(7764,plain,
% 2.04/2.24 (b(s(s(s(z))), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[52, 7763])).
% 2.04/2.24 tff(7765,plain,
% 2.04/2.24 (~r(elem!1, s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[6196, 7764, 3697, 474, 2277, 267])).
% 2.04/2.24 tff(7766,plain,
% 2.04/2.24 (b(elem!1, s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[470, 7765, 7282])).
% 2.04/2.24 tff(7767,plain,
% 2.04/2.24 (~b(s(z), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[6206, 7766, 3697, 7764])).
% 2.04/2.24 tff(7768,plain,
% 2.04/2.24 (r(s(z), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1034, 7767, 2277])).
% 2.04/2.24 tff(7769,plain,
% 2.04/2.24 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[5581, 7768, 267, 236])).
% 2.04/2.24 tff(7770,plain,
% 2.04/2.24 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[86, 7769, 69])).
% 2.04/2.24 tff(7771,plain,
% 2.04/2.24 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[6216, 246, 7766, 3697, 7764, 7770])).
% 2.04/2.24 tff(7772,plain,
% 2.04/2.24 (r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1626, 7771])).
% 2.04/2.24 tff(7773,plain,
% 2.04/2.24 (~r(s(z), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[5432, 7768, 267])).
% 2.04/2.24 tff(7774,plain,
% 2.04/2.24 (b(s(z), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1069, 7773])).
% 2.04/2.24 tff(7775,plain,
% 2.04/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(7776,plain,
% 2.04/2.24 (((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(7777,plain,
% 2.04/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[7776])).
% 2.04/2.24 tff(7778,plain,
% 2.04/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.04/2.24 inference(transitivity,[status(thm)],[7777, 7775])).
% 2.04/2.24 tff(7779,plain,
% 2.04/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(7780,plain,
% 2.04/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[7779, 7778])).
% 2.04/2.24 tff(7781,plain,
% 2.04/2.24 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[7780, 183, 173, 7759, 7772])).
% 2.04/2.24 tff(7782,plain,
% 2.04/2.24 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4983, 7770, 2362, 7751])).
% 2.04/2.24 tff(7783,plain,
% 2.04/2.24 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[361, 47, 7782, 7781])).
% 2.04/2.24 tff(7784,plain,
% 2.04/2.24 (~b(s(z), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[6346, 7783, 7764, 7774, 7772, 236, 173, 7766, 474, 7760])).
% 2.04/2.24 tff(7785,plain,
% 2.04/2.24 (r(s(z), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1291, 7784])).
% 2.04/2.24 tff(7786,plain,
% 2.04/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(7787,plain,
% 2.04/2.24 (((~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(7788,plain,
% 2.04/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[7787])).
% 2.04/2.24 tff(7789,plain,
% 2.04/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.04/2.24 inference(transitivity,[status(thm)],[7788, 7786])).
% 2.04/2.24 tff(7790,plain,
% 2.04/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(z))))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(7791,plain,
% 2.04/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[7790, 7789])).
% 2.04/2.24 tff(7792,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[7791, 183, 173, 7785, 7759])).
% 2.04/2.24 tff(7793,plain,((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (s(s(s(s(s(elem!1))))) = elem!1) | (~r(z, elem!1)) | (s(z) = elem!1) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(7794,plain,
% 2.04/2.25 (~r(elem!1, s(z))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[7793, 7750, 2133, 7583, 7735, 69, 5365, 7734, 7733])).
% 2.04/2.25 tff(7795,plain,
% 2.04/2.25 (b(elem!1, s(z))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[214, 7794, 7584])).
% 2.04/2.25 tff(7796,plain,
% 2.04/2.25 (~r(s(z), elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[7331, 7795, 7583, 2124, 2232, 5365])).
% 2.04/2.25 tff(7797,plain,
% 2.04/2.25 (b(s(z), elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[1034, 7796, 7734])).
% 2.04/2.25 tff(7798,plain,
% 2.04/2.25 (~b(s(s(s(z))), s(z))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[7339, 246, 7797, 7795, 7583])).
% 2.04/2.25 tff(7799,plain,
% 2.04/2.25 (r(s(s(s(z))), s(z))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[52, 7798])).
% 2.04/2.25 tff(7800,plain,
% 2.04/2.25 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[5804, 7734])).
% 2.04/2.25 tff(7801,plain,
% 2.04/2.25 (~(s(s(elem!1)) = s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[421, 7800])).
% 2.04/2.25 tff(7802,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(7803,plain,
% 2.04/2.25 (((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(z)))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(7804,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[7803])).
% 2.04/2.25 tff(7805,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.04/2.25 inference(transitivity,[status(thm)],[7804, 7802])).
% 2.04/2.25 tff(7806,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(7807,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[7806, 7805])).
% 2.04/2.25 tff(7808,plain,
% 2.04/2.25 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[7807, 246, 7797, 7735, 7795, 7583])).
% 2.04/2.25 tff(7809,plain,
% 2.04/2.25 (r(s(s(elem!1)), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[454, 7808, 7801])).
% 2.04/2.25 tff(7810,plain,
% 2.04/2.25 ($false),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[7762, 7809, 7799, 2133])).
% 2.04/2.25 tff(7811,plain,((s(s(s(s(s(elem!1))))) = elem!1) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), elem!1) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.25 tff(7812,plain,
% 2.04/2.25 (s(s(s(s(s(elem!1))))) = elem!1),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[7811, 2124, 2232, 55])).
% 2.04/2.25 tff(7813,plain,
% 2.04/2.25 (s(s(s(s(s(s(elem!1)))))) = s(elem!1)),
% 2.04/2.25 inference(monotonicity,[status(thm)],[7812])).
% 2.04/2.25 tff(7814,plain,
% 2.04/2.25 (s(s(s(s(s(s(s(elem!1))))))) = s(s(elem!1))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[7813])).
% 2.04/2.25 tff(7815,plain,
% 2.04/2.25 (s(s(elem!1)) = s(s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.25 inference(symmetry,[status(thm)],[7814])).
% 2.04/2.25 tff(7816,plain,
% 2.04/2.25 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z)))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[7815])).
% 2.04/2.25 tff(7817,plain,
% 2.04/2.25 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.04/2.25 inference(symmetry,[status(thm)],[7816])).
% 2.04/2.25 tff(7818,plain,
% 2.04/2.25 (~(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(z)))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[7214, 7812])).
% 2.04/2.25 tff(7819,plain,
% 2.04/2.25 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z)))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[7815])).
% 2.04/2.25 tff(7820,plain,
% 2.04/2.25 ((~r(s(s(elem!1)), s(s(s(s(z)))))) <=> (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z))))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[7819])).
% 2.04/2.25 tff(7821,plain,
% 2.04/2.25 ((s(s(s(s(s(elem!1))))) = s(z)) <=> (elem!1 = s(z))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[7812])).
% 2.04/2.25 tff(7822,plain,
% 2.04/2.25 ((s(s(s(s(s(elem!1))))) = s(z)) <=> (s(z) = elem!1)),
% 2.04/2.25 inference(transitivity,[status(thm)],[7821, 4])).
% 2.04/2.25 tff(7823,plain,
% 2.04/2.25 ((~(s(s(s(s(s(elem!1))))) = s(z))) <=> (~(s(z) = elem!1))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[7822])).
% 2.04/2.25 tff(7824,plain,
% 2.04/2.25 (~(s(z) = elem!1)),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[331, 7823])).
% 2.04/2.25 tff(7825,plain,
% 2.04/2.25 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[5804, 7824])).
% 2.04/2.25 tff(7826,plain,
% 2.04/2.25 (~(s(s(s(z))) = elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[7041, 7812])).
% 2.04/2.25 tff(7827,plain,
% 2.04/2.25 (r(s(s(s(z))), elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[647, 1, 7826])).
% 2.04/2.25 tff(7828,plain,
% 2.04/2.25 (~r(s(s(s(z))), z)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[5411, 183, 5365, 7827])).
% 2.04/2.25 tff(7829,plain,
% 2.04/2.25 (b(s(s(s(z))), z)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[995, 7828])).
% 2.04/2.25 tff(7830,plain,
% 2.04/2.25 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[5804, 7086])).
% 2.04/2.25 tff(7831,plain,
% 2.04/2.25 (~r(s(s(elem!1)), z)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[6425, 54, 55, 5365, 7084, 2362])).
% 2.04/2.25 tff(7832,plain,
% 2.04/2.25 (b(s(s(elem!1)), z)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[523, 7831])).
% 2.04/2.25 tff(7833,plain,
% 2.04/2.25 (~r(s(s(s(z))), s(z))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[6468, 7832, 7830, 5365, 170, 173])).
% 2.04/2.25 tff(7834,plain,
% 2.04/2.25 (b(s(s(s(z))), s(z))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[52, 7833])).
% 2.04/2.25 tff(7835,plain,
% 2.04/2.25 (~r(z, s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[6592, 634, 5365])).
% 2.04/2.25 tff(7836,plain,
% 2.04/2.25 (b(z, s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[6165, 7835])).
% 2.04/2.25 tff(7837,plain,
% 2.04/2.25 (~r(s(s(s(z))), z)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[5411, 183, 5365, 634])).
% 2.04/2.25 tff(7838,plain,
% 2.04/2.25 (b(s(s(s(z))), z)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[995, 7837])).
% 2.04/2.25 tff(7839,plain,
% 2.04/2.25 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[4659, 7832, 7838, 7836])).
% 2.04/2.25 tff(7840,plain,
% 2.04/2.25 (r(s(s(s(z))), s(s(elem!1)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[689, 7839, 7830])).
% 2.04/2.25 tff(7841,plain,
% 2.04/2.25 (~b(s(z), s(s(elem!1)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[6397, 6385, 7086, 2362, 6376])).
% 2.04/2.25 tff(7842,plain,
% 2.04/2.25 (r(s(z), s(s(elem!1)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[233, 7841])).
% 2.04/2.25 tff(7843,plain,
% 2.04/2.25 (~r(s(z), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[7436, 183, 7842, 634, 7840])).
% 2.04/2.25 tff(7844,plain,
% 2.04/2.25 (b(s(z), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[1291, 7843])).
% 2.04/2.25 tff(7845,plain,
% 2.04/2.25 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[7450, 7844, 7836, 170, 7834])).
% 2.04/2.25 tff(7846,plain,
% 2.04/2.25 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[1702, 7845])).
% 2.04/2.25 tff(7847,plain,
% 2.04/2.25 (~(s(s(elem!1)) = s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[421, 7830])).
% 2.04/2.25 tff(7848,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(7849,plain,
% 2.04/2.25 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z)))))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(7850,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[7849])).
% 2.04/2.25 tff(7851,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.04/2.25 inference(transitivity,[status(thm)],[7850, 7848])).
% 2.04/2.25 tff(7852,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(7853,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[7852, 7851])).
% 2.04/2.25 tff(7854,plain,
% 2.04/2.25 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[7853, 246, 7832, 7834, 7836, 7838])).
% 2.04/2.25 tff(7855,plain,
% 2.04/2.25 (r(s(s(elem!1)), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[454, 7854, 7847])).
% 2.04/2.25 tff(7856,plain,
% 2.04/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(7857,plain,
% 2.04/2.25 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(7858,plain,
% 2.04/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[7857])).
% 2.04/2.25 tff(7859,plain,
% 2.04/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.04/2.25 inference(transitivity,[status(thm)],[7858, 7856])).
% 2.04/2.25 tff(7860,plain,
% 2.04/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(7861,plain,
% 2.04/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[7860, 7859])).
% 2.04/2.25 tff(7862,plain,
% 2.04/2.25 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[7861, 183, 7855, 7846])).
% 2.04/2.25 tff(7863,plain,
% 2.04/2.25 (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z)))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[7862, 7217])).
% 2.04/2.25 tff(7864,plain,
% 2.04/2.25 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z)))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[7230, 7863, 7215])).
% 2.04/2.25 tff(7865,plain,
% 2.04/2.25 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[7864, 7200])).
% 2.04/2.25 tff(7866,plain,
% 2.04/2.25 (b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(s(z)))), elem!1)),
% 2.04/2.25 inference(monotonicity,[status(thm)],[7030])).
% 2.04/2.25 tff(7867,plain,
% 2.04/2.25 (~(s(s(s(z))) = elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[7041, 7030])).
% 2.04/2.25 tff(7868,plain,
% 2.04/2.25 (~(elem!1 = s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[3013, 7867])).
% 2.04/2.25 tff(7869,plain,
% 2.04/2.25 (b(elem!1, s(z))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[214, 6376, 7084])).
% 2.04/2.25 tff(7870,plain,
% 2.04/2.25 (b(s(z), elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[1034, 6385, 7086])).
% 2.04/2.25 tff(7871,plain,
% 2.04/2.25 (~b(elem!1, s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[2011, 7834, 7870, 7869])).
% 2.04/2.25 tff(7872,plain,
% 2.04/2.25 (r(elem!1, s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[470, 7871, 7868])).
% 2.04/2.25 tff(7873,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(7874,plain,
% 2.04/2.25 (((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(7875,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[7874])).
% 2.04/2.25 tff(7876,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.04/2.25 inference(transitivity,[status(thm)],[7875, 7873])).
% 2.04/2.25 tff(7877,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(7878,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[7877, 7876])).
% 2.04/2.25 tff(7879,plain,
% 2.04/2.25 (~b(elem!1, z)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[7878, 246, 2362, 7869, 7832, 7834, 7836])).
% 2.04/2.25 tff(7880,plain,
% 2.04/2.25 (r(elem!1, z)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[1143, 7879, 5701])).
% 2.04/2.25 tff(7881,plain,
% 2.04/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(7882,plain,
% 2.04/2.25 (((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(7883,plain,
% 2.04/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[7882])).
% 2.04/2.25 tff(7884,plain,
% 2.04/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.04/2.25 inference(transitivity,[status(thm)],[7883, 7881])).
% 2.04/2.25 tff(7885,plain,
% 2.04/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(7886,plain,
% 2.04/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[7885, 7884])).
% 2.04/2.25 tff(7887,plain,
% 2.04/2.25 (~r(s(s(s(s(z)))), elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[7886, 183, 7880, 7872, 7846])).
% 2.04/2.25 tff(7888,plain,
% 2.04/2.25 (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[7887, 7236])).
% 2.04/2.25 tff(7889,plain,
% 2.04/2.25 (b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[1506, 7888])).
% 2.04/2.25 tff(7890,plain,
% 2.04/2.25 (b(s(s(s(s(z)))), elem!1)),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[7889, 7866])).
% 2.04/2.25 tff(7891,plain,
% 2.04/2.25 (r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[7030])).
% 2.04/2.25 tff(7892,plain,
% 2.04/2.25 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 2.04/2.25 inference(symmetry,[status(thm)],[7891])).
% 2.04/2.25 tff(7893,plain,
% 2.04/2.25 ((~r(elem!1, s(s(s(s(z)))))) <=> (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[7892])).
% 2.04/2.25 tff(7894,plain,
% 2.04/2.25 (~r(elem!1, s(s(s(s(z)))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[7165, 183, 7872, 7846])).
% 2.04/2.25 tff(7895,plain,
% 2.04/2.25 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[7894, 7893])).
% 2.04/2.25 tff(7896,plain,
% 2.04/2.25 (b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[1897, 7895])).
% 2.04/2.25 tff(7897,plain,
% 2.04/2.25 (b(elem!1, s(s(s(s(z)))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[7896, 7156])).
% 2.04/2.25 tff(7898,plain,
% 2.04/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(7899,plain,
% 2.04/2.25 (((~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(7900,plain,
% 2.04/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[7899])).
% 2.04/2.25 tff(7901,plain,
% 2.04/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 2.04/2.25 inference(transitivity,[status(thm)],[7900, 7898])).
% 2.04/2.25 tff(7902,plain,
% 2.04/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(elem!1)))))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(7903,plain,
% 2.04/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[7902, 7901])).
% 2.04/2.26 tff(7904,plain,
% 2.04/2.26 (~r(elem!1, s(s(elem!1)))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[7903, 183, 7872, 7855])).
% 2.04/2.26 tff(7905,plain,
% 2.04/2.26 (b(elem!1, s(s(elem!1)))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[1268, 7904, 1204])).
% 2.04/2.26 tff(7906,plain,
% 2.04/2.26 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[7256, 246, 7905, 7897, 7890])).
% 2.04/2.26 tff(7907,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[7906, 7865])).
% 2.04/2.26 tff(7908,plain,(b(z, s(z)) | (~(s(s(s(s(s(elem!1))))) = elem!1)) | (elem!1 = s(s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(z))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(7909,plain,
% 2.04/2.26 (b(z, s(z))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[7908, 5451, 7812, 7362, 7827, 2133, 55])).
% 2.04/2.26 tff(7910,plain,
% 2.04/2.26 (~r(z, s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[6592, 634, 267])).
% 2.04/2.26 tff(7911,plain,
% 2.04/2.26 (b(z, s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[6165, 7910])).
% 2.04/2.26 tff(7912,plain,
% 2.04/2.26 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[7762, 430, 2133])).
% 2.04/2.26 tff(7913,plain,
% 2.04/2.26 (b(s(s(elem!1)), s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[454, 7912, 7847])).
% 2.04/2.26 tff(7914,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(7915,plain,
% 2.04/2.26 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z))) <=> ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(7916,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[7915])).
% 2.04/2.26 tff(7917,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[7916, 7914])).
% 2.04/2.26 tff(7918,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z)))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(7919,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[7918, 7917])).
% 2.04/2.26 tff(7920,plain,
% 2.04/2.26 (~b(s(s(elem!1)), z)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[7919, 246, 236, 7913, 7911, 5413])).
% 2.04/2.26 tff(7921,plain,
% 2.04/2.26 (r(s(s(elem!1)), z)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[523, 7920])).
% 2.04/2.26 tff(7922,plain,
% 2.04/2.26 (b(elem!1, s(z))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[2282, 430, 2232, 634])).
% 2.04/2.26 tff(7923,plain,
% 2.04/2.26 (b(s(z), elem!1)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[6629, 236, 267, 2232, 634, 7086])).
% 2.04/2.26 tff(7924,plain,
% 2.04/2.26 (~b(elem!1, z)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[1135, 246, 7923, 7922, 236])).
% 2.04/2.26 tff(7925,plain,
% 2.04/2.26 (r(elem!1, z)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[1143, 7924, 5401])).
% 2.04/2.26 tff(7926,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(7927,plain,
% 2.04/2.26 (((~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(7928,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[7927])).
% 2.04/2.26 tff(7929,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[7928, 7926])).
% 2.04/2.26 tff(7930,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(elem!1)))))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(7931,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[7930, 7929])).
% 2.04/2.26 tff(7932,plain,
% 2.04/2.26 (~b(z, s(s(elem!1)))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[7931, 246, 7913, 7911, 5413])).
% 2.04/2.26 tff(7933,plain,
% 2.04/2.26 (r(z, s(s(elem!1)))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[264, 7932])).
% 2.04/2.26 tff(7934,plain,
% 2.04/2.26 (~r(elem!1, s(s(elem!1)))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[6918, 7933, 267])).
% 2.04/2.26 tff(7935,plain,
% 2.04/2.26 (b(elem!1, s(s(elem!1)))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[1268, 7934, 1204])).
% 2.04/2.26 tff(7936,plain,
% 2.04/2.26 (~r(s(s(s(s(z)))), z)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[7259, 7935, 7030, 7925, 7921])).
% 2.04/2.26 tff(7937,plain,
% 2.04/2.26 (b(s(s(s(s(z)))), z)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[6040, 7936])).
% 2.04/2.26 tff(7938,plain,
% 2.04/2.26 (~b(elem!1, s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[4259, 7922, 2124, 2232, 430, 7830])).
% 2.04/2.26 tff(7939,plain,
% 2.04/2.26 (r(elem!1, s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[470, 7938, 7868])).
% 2.04/2.26 tff(7940,plain,
% 2.04/2.26 (~b(s(z), s(s(elem!1)))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[6397, 3018, 7086, 2362, 2265])).
% 2.04/2.26 tff(7941,plain,
% 2.04/2.26 (r(s(z), s(s(elem!1)))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[233, 7940])).
% 2.04/2.26 tff(7942,plain,
% 2.04/2.26 (b(s(s(s(z))), s(s(elem!1)))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[689, 4249, 7830])).
% 2.04/2.26 tff(7943,plain,
% 2.04/2.26 (~b(s(z), s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[7145, 246, 7923, 2362, 236, 7942, 7911])).
% 2.04/2.26 tff(7944,plain,
% 2.04/2.26 (r(s(z), s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[1291, 7943])).
% 2.04/2.26 tff(7945,plain,
% 2.04/2.26 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[7177, 7944, 7030, 7923, 7922, 7941, 7939])).
% 2.04/2.26 tff(7946,plain,
% 2.04/2.26 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[1702, 7945])).
% 2.04/2.26 tff(7947,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[7194, 246, 7942, 7913, 7911, 7946, 7937])).
% 2.04/2.26 tff(7948,plain,((~r(s(s(s(z))), s(z))) | (~(s(s(s(s(s(elem!1))))) = elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(z))) | (elem!1 = s(s(elem!1))) | (~r(z, elem!1)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), elem!1) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(7949,plain,
% 2.04/2.26 (~r(s(s(s(z))), s(z))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[7948, 7362, 7812, 7909, 5451, 5365, 2124, 2232, 7827])).
% 2.04/2.26 tff(7950,plain,
% 2.04/2.26 (b(s(s(s(z))), s(z))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[52, 7949])).
% 2.04/2.26 tff(7951,plain,
% 2.04/2.26 ((s(s(s(s(s(elem!1))))) = s(z)) <=> (elem!1 = s(z))),
% 2.04/2.26 inference(transitivity,[status(thm)],[7822, 5])).
% 2.04/2.26 tff(7952,plain,
% 2.04/2.26 ((~(s(s(s(s(s(elem!1))))) = s(z))) <=> (~(elem!1 = s(z)))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[7951])).
% 2.04/2.26 tff(7953,plain,
% 2.04/2.26 (~(elem!1 = s(z))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[331, 7952])).
% 2.04/2.26 tff(7954,plain,
% 2.04/2.26 (~r(elem!1, s(z))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[5444, 7950, 5365, 5701, 7824, 7827, 7909])).
% 2.04/2.26 tff(7955,plain,
% 2.04/2.26 (b(elem!1, s(z))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[214, 7954, 7953])).
% 2.04/2.26 tff(7956,plain,
% 2.04/2.26 (b(s(z), elem!1)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[6629, 7909, 5365, 2232, 7827, 7824])).
% 2.04/2.26 tff(7957,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(7958,plain,
% 2.04/2.26 (((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(7959,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[7958])).
% 2.04/2.26 tff(7960,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[7959, 7957])).
% 2.04/2.26 tff(7961,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(7962,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[7961, 7960])).
% 2.04/2.26 tff(7963,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[7962, 246, 7956, 7955, 7909, 7950, 7829])).
% 2.04/2.26 tff(7964,plain,(b(s(s(s(z))), elem!1) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), elem!1) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(7965,plain,
% 2.04/2.26 (b(s(s(s(z))), elem!1)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[7964, 2124, 2232, 55])).
% 2.04/2.26 tff(7966,plain,
% 2.04/2.26 (~b(s(s(elem!1)), elem!1)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[7749, 54, 2133, 7953, 55, 7965])).
% 2.04/2.26 tff(7967,plain,
% 2.04/2.26 (s(s(elem!1)) = elem!1),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[156, 7966, 2232])).
% 2.04/2.26 tff(7968,plain,
% 2.04/2.26 (b(elem!1, s(z))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[214, 6376, 7953])).
% 2.04/2.26 tff(7969,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[2130, 7968, 7967, 2124])).
% 2.04/2.26 tff(7970,plain,(b(z, s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), elem!1) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(7971,plain,
% 2.04/2.26 (b(z, s(z))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[7970, 2124, 2232, 55])).
% 2.04/2.26 tff(7972,plain,
% 2.04/2.26 ((s(s(s(s(z)))) = elem!1) <=> (s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[7157])).
% 2.04/2.26 tff(7973,plain,
% 2.04/2.26 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(z)))) = elem!1)),
% 2.04/2.26 inference(symmetry,[status(thm)],[7972])).
% 2.04/2.26 tff(7974,plain,
% 2.04/2.26 ((~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[7973])).
% 2.04/2.26 tff(7975,plain,
% 2.04/2.26 (~(s(s(s(s(z)))) = elem!1)),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[1501, 7974])).
% 2.04/2.26 tff(7976,plain,
% 2.04/2.26 (r(elem!1, s(z))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[214, 5376, 7084])).
% 2.04/2.26 tff(7977,plain,
% 2.04/2.26 (b(s(s(elem!1)), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[2125])).
% 2.04/2.26 tff(7978,plain,
% 2.04/2.26 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(elem!1))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[5858])).
% 2.04/2.26 tff(7979,plain,
% 2.04/2.26 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 2.04/2.26 inference(symmetry,[status(thm)],[7978])).
% 2.04/2.26 tff(7980,plain,
% 2.04/2.26 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 2.04/2.26 inference(transitivity,[status(thm)],[7030, 5380])).
% 2.04/2.26 tff(7981,plain,
% 2.04/2.26 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(elem!1)))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[7980])).
% 2.04/2.26 tff(7982,plain,
% 2.04/2.26 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(elem!1))))))),
% 2.04/2.26 inference(symmetry,[status(thm)],[7981])).
% 2.04/2.26 tff(7983,plain,
% 2.04/2.26 (s(elem!1) = s(s(s(s(elem!1))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[108, 7982, 325])).
% 2.04/2.26 tff(7984,plain,
% 2.04/2.26 (inj_0(s(elem!1)) = inj_0(s(s(s(s(elem!1)))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[7983])).
% 2.04/2.26 tff(7985,plain,
% 2.04/2.26 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(elem!1))),
% 2.04/2.26 inference(symmetry,[status(thm)],[7984])).
% 2.04/2.26 tff(7986,plain,
% 2.04/2.26 (s(elem!1) = s(s(s(elem!1)))),
% 2.04/2.26 inference(symmetry,[status(thm)],[5858])).
% 2.04/2.26 tff(7987,plain,
% 2.04/2.26 (s(elem!1) = elem!1),
% 2.04/2.26 inference(transitivity,[status(thm)],[7986, 352, 7985, 343])).
% 2.04/2.26 tff(7988,plain,
% 2.04/2.26 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), elem!1)),
% 2.04/2.26 inference(monotonicity,[status(thm)],[7987])).
% 2.04/2.26 tff(7989,plain,
% 2.04/2.26 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(elem!1))),
% 2.04/2.26 inference(symmetry,[status(thm)],[7988])).
% 2.04/2.26 tff(7990,plain,
% 2.04/2.26 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[7989, 7979])).
% 2.04/2.26 tff(7991,plain,
% 2.04/2.26 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[3697, 7990])).
% 2.04/2.26 tff(7992,plain,
% 2.04/2.26 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), elem!1)),
% 2.04/2.26 inference(monotonicity,[status(thm)],[2125])).
% 2.04/2.26 tff(7993,plain,
% 2.04/2.26 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(elem!1)))),
% 2.04/2.26 inference(symmetry,[status(thm)],[7992])).
% 2.04/2.26 tff(7994,plain,
% 2.04/2.26 (b(s(s(s(z))), s(s(elem!1)))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[3697, 7993])).
% 2.04/2.26 tff(7995,plain,
% 2.04/2.26 (b(s(s(s(z))), s(elem!1))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[3697, 7989])).
% 2.04/2.26 tff(7996,plain,
% 2.04/2.26 ((s(elem!1) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[7986])).
% 2.04/2.26 tff(7997,plain,
% 2.04/2.26 ((s(s(s(elem!1))) = s(s(z))) <=> (s(elem!1) = s(s(z)))),
% 2.04/2.26 inference(symmetry,[status(thm)],[7996])).
% 2.04/2.26 tff(7998,plain,
% 2.04/2.26 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(elem!1) = s(s(z))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[7997])).
% 2.04/2.26 tff(7999,plain,
% 2.04/2.26 ((s(s(s(s(s(elem!1))))) = s(s(elem!1))) <=> (elem!1 = s(s(elem!1)))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[7030])).
% 2.04/2.26 tff(8000,plain,
% 2.04/2.26 ((s(s(s(s(s(elem!1))))) = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 2.04/2.26 inference(transitivity,[status(thm)],[7999, 133])).
% 2.04/2.26 tff(8001,plain,
% 2.04/2.26 ((s(s(elem!1)) = elem!1) <=> (s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.04/2.26 inference(symmetry,[status(thm)],[8000])).
% 2.04/2.26 tff(8002,plain,
% 2.04/2.26 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[2125, 8001])).
% 2.04/2.26 tff(8003,plain,
% 2.04/2.26 ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(s(s(elem!1))))))),
% 2.04/2.26 inference(commutativity,[status(thm)],[])).
% 2.04/2.26 tff(8004,plain,
% 2.04/2.26 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[2125, 7157])).
% 2.04/2.26 tff(8005,plain,
% 2.04/2.26 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8004])).
% 2.04/2.26 tff(8006,plain,
% 2.04/2.26 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(s(s(elem!1))))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[8005, 8003])).
% 2.04/2.26 tff(8007,plain,
% 2.04/2.26 ((s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 2.04/2.26 inference(symmetry,[status(thm)],[8006])).
% 2.04/2.26 tff(8008,plain,
% 2.04/2.26 ((s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))) <=> (s(elem!1) = elem!1)),
% 2.04/2.26 inference(monotonicity,[status(thm)],[5858, 7030])).
% 2.04/2.26 tff(8009,plain,
% 2.04/2.26 ((s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))) <=> (elem!1 = s(elem!1))),
% 2.04/2.26 inference(transitivity,[status(thm)],[8008, 2825])).
% 2.04/2.26 tff(8010,plain,
% 2.04/2.26 ((elem!1 = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(s(s(s(elem!1))))))),
% 2.04/2.26 inference(symmetry,[status(thm)],[8009])).
% 2.04/2.26 tff(8011,plain,
% 2.04/2.26 ((elem!1 = s(elem!1)) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[8010, 8007])).
% 2.04/2.26 tff(8012,plain,
% 2.04/2.26 (elem!1 = s(elem!1)),
% 2.04/2.26 inference(transitivity,[status(thm)],[3154, 7984, 351, 5858])).
% 2.04/2.26 tff(8013,plain,
% 2.04/2.26 (s(s(elem!1)) = s(s(s(elem!1)))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[8012, 8011])).
% 2.04/2.26 tff(8014,assumption,(s(s(elem!1)) = s(s(s(elem!1)))), introduced(assumption)).
% 2.04/2.26 tff(8015,assumption,(s(s(s(elem!1))) = s(s(z))), introduced(assumption)).
% 2.04/2.26 tff(8016,plain,
% 2.04/2.26 (s(s(z)) = s(s(s(elem!1)))),
% 2.04/2.26 inference(symmetry,[status(thm)],[8015])).
% 2.04/2.26 tff(8017,plain,
% 2.04/2.26 (inj_0(s(s(z))) = inj_0(s(s(s(elem!1))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8016])).
% 2.04/2.26 tff(8018,plain,
% 2.04/2.26 (s(z) = elem!1),
% 2.04/2.26 inference(transitivity,[status(thm)],[1523, 8017, 103, 8014, 352, 349, 343])).
% 2.04/2.26 tff(8019,plain,
% 2.04/2.26 ((s(s(s(s(s(elem!1))))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[344])).
% 2.04/2.26 tff(8020,plain,
% 2.04/2.26 ((s(s(s(s(s(elem!1))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 2.04/2.26 inference(transitivity,[status(thm)],[8019, 417])).
% 2.04/2.26 tff(8021,plain,
% 2.04/2.26 ((~(s(s(s(s(s(elem!1))))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(elem!1))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8020])).
% 2.04/2.26 tff(8022,plain,
% 2.04/2.26 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[1622, 8021])).
% 2.04/2.26 tff(8023,plain,
% 2.04/2.26 (~(s(z) = elem!1)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[121, 8022])).
% 2.04/2.26 tff(8024,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[8023, 8018])).
% 2.04/2.26 tff(8025,plain,((~(s(s(s(elem!1))) = s(s(z)))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~(s(s(s(s(s(elem!1))))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(8026,plain,
% 2.04/2.26 (~(s(s(s(elem!1))) = s(s(z)))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[8025, 8013, 8002])).
% 2.04/2.26 tff(8027,plain,
% 2.04/2.26 (~(s(elem!1) = s(s(z)))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[8026, 7998])).
% 2.04/2.26 tff(8028,plain,
% 2.04/2.26 (b(s(elem!1), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[7987])).
% 2.04/2.26 tff(8029,plain,
% 2.04/2.26 (b(elem!1, s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 2.04/2.26 inference(symmetry,[status(thm)],[8028])).
% 2.04/2.26 tff(8030,assumption,(b(s(s(s(z))), s(s(s(elem!1))))), introduced(assumption)).
% 2.04/2.26 tff(8031,plain,
% 2.04/2.26 (s(elem!1) = s(s(s(elem!1)))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[2392])).
% 2.04/2.26 tff(8032,plain,
% 2.04/2.26 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8031])).
% 2.04/2.26 tff(8033,plain,
% 2.04/2.26 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8031])).
% 2.04/2.26 tff(8034,plain,
% 2.04/2.26 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.04/2.26 inference(symmetry,[status(thm)],[8033])).
% 2.04/2.26 tff(8035,plain,
% 2.04/2.26 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 2.04/2.26 inference(transitivity,[status(thm)],[7030, 2392])).
% 2.04/2.26 tff(8036,plain,
% 2.04/2.26 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(elem!1)))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8035])).
% 2.04/2.26 tff(8037,plain,
% 2.04/2.26 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(elem!1))))))),
% 2.04/2.26 inference(symmetry,[status(thm)],[8036])).
% 2.04/2.26 tff(8038,plain,
% 2.04/2.26 (s(elem!1) = s(s(elem!1))),
% 2.04/2.26 inference(transitivity,[status(thm)],[108, 8037, 325, 8034])).
% 2.04/2.26 tff(8039,plain,
% 2.04/2.26 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8038])).
% 2.04/2.26 tff(8040,plain,
% 2.04/2.26 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 2.04/2.26 inference(symmetry,[status(thm)],[8039])).
% 2.04/2.26 tff(8041,plain,
% 2.04/2.26 ((~(s(s(s(s(z)))) = s(s(elem!1)))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8040])).
% 2.04/2.26 tff(8042,plain,
% 2.04/2.26 ((s(s(s(s(z)))) = elem!1) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[2392])).
% 2.04/2.26 tff(8043,plain,
% 2.04/2.26 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(s(s(s(s(z)))) = s(s(elem!1))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8042])).
% 2.04/2.26 tff(8044,plain,
% 2.04/2.26 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(z)))) = elem!1)),
% 2.04/2.26 inference(monotonicity,[status(thm)],[7030])).
% 2.04/2.26 tff(8045,plain,
% 2.04/2.26 ((~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8044])).
% 2.04/2.26 tff(8046,plain,
% 2.04/2.26 (~(s(s(s(s(z)))) = elem!1)),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[1501, 8045])).
% 2.04/2.26 tff(8047,plain,
% 2.04/2.26 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[8046, 8043])).
% 2.04/2.26 tff(8048,plain,
% 2.04/2.26 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[8047, 8041])).
% 2.04/2.26 tff(8049,plain,
% 2.04/2.26 (s(s(s(elem!1))) = s(elem!1)),
% 2.04/2.26 inference(symmetry,[status(thm)],[8031])).
% 2.04/2.26 tff(8050,plain,
% 2.04/2.26 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8049])).
% 2.04/2.26 tff(8051,plain,
% 2.04/2.26 ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(z)))), s(elem!1)))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8050])).
% 2.04/2.26 tff(8052,plain,
% 2.04/2.26 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8049])).
% 2.04/2.26 tff(8053,plain,
% 2.04/2.26 (r(s(elem!1), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 2.04/2.26 inference(symmetry,[status(thm)],[8052])).
% 2.04/2.26 tff(8054,plain,
% 2.04/2.26 (r(s(elem!1), s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8038])).
% 2.04/2.26 tff(8055,plain,
% 2.04/2.26 (r(s(s(elem!1)), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 2.04/2.26 inference(symmetry,[status(thm)],[8054])).
% 2.04/2.26 tff(8056,plain,
% 2.04/2.26 (r(s(s(elem!1)), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[6841])).
% 2.04/2.26 tff(8057,plain,
% 2.04/2.26 (r(elem!1, s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 2.04/2.26 inference(symmetry,[status(thm)],[8056])).
% 2.04/2.26 tff(8058,plain,
% 2.04/2.26 (r(elem!1, s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[8057, 8055])).
% 2.04/2.26 tff(8059,plain,
% 2.04/2.26 (r(s(elem!1), s(s(s(z))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[413, 8058])).
% 2.04/2.26 tff(8060,plain,
% 2.04/2.26 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[8059, 8053])).
% 2.04/2.26 tff(8061,plain,
% 2.04/2.26 (s(s(elem!1)) = s(s(s(elem!1)))),
% 2.04/2.26 inference(transitivity,[status(thm)],[8033, 326, 8036, 92, 8031])).
% 2.04/2.26 tff(8062,plain,
% 2.04/2.26 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8061])).
% 2.04/2.26 tff(8063,plain,
% 2.04/2.26 (s(s(s(elem!1))) = s(s(elem!1))),
% 2.04/2.26 inference(transitivity,[status(thm)],[8049, 108, 8037, 325, 8034])).
% 2.04/2.26 tff(8064,plain,
% 2.04/2.26 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(elem!1)), s(z))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8063])).
% 2.04/2.26 tff(8065,plain,
% 2.04/2.26 ((~r(s(s(s(elem!1))), s(z))) <=> (~r(s(s(elem!1)), s(z)))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8064])).
% 2.04/2.26 tff(8066,plain,
% 2.04/2.26 (b(elem!1, s(z)) <=> b(s(s(elem!1)), s(z))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[2392])).
% 2.04/2.26 tff(8067,plain,
% 2.04/2.26 (b(elem!1, s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 2.04/2.26 inference(transitivity,[status(thm)],[8066, 8062])).
% 2.04/2.26 tff(8068,plain,
% 2.04/2.26 (~b(z, s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[6174, 2003, 1056, 236])).
% 2.04/2.26 tff(8069,plain,
% 2.04/2.26 (r(z, s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[2221, 47, 8068, 5476])).
% 2.04/2.26 tff(8070,plain,
% 2.04/2.26 (~r(elem!1, s(z))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[6162, 8069, 267, 413])).
% 2.04/2.26 tff(8071,plain,
% 2.04/2.26 (b(elem!1, s(z))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[214, 8070, 7084])).
% 2.04/2.26 tff(8072,plain,
% 2.04/2.26 (b(s(s(s(elem!1))), s(z))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[8071, 8067])).
% 2.04/2.26 tff(8073,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(8074,plain,
% 2.04/2.26 (((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1)))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(8075,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8074])).
% 2.04/2.26 tff(8076,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[8075, 8073])).
% 2.04/2.27 tff(8077,plain,
% 2.04/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.04/2.27 inference(quant_inst,[status(thm)],[])).
% 2.04/2.27 tff(8078,plain,
% 2.04/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[8077, 8076])).
% 2.04/2.27 tff(8079,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8078, 246, 1056, 236, 2003, 8030, 8072])).
% 2.04/2.27 tff(8080,plain,((~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~(s(s(s(s(s(elem!1))))) = elem!1)) | (~(elem!1 = s(s(elem!1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.27 tff(8081,plain,
% 2.04/2.27 (~b(s(s(s(z))), s(z))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8080, 413, 236, 8030, 7030, 2392, 267, 1056])).
% 2.04/2.27 tff(8082,plain,
% 2.04/2.27 (r(s(s(s(z))), s(z))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[52, 8081])).
% 2.04/2.27 tff(8083,assumption,(r(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 2.04/2.27 tff(8084,plain,
% 2.04/2.27 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[3171, 8053])).
% 2.04/2.27 tff(8085,plain,
% 2.04/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(8086,plain,
% 2.04/2.27 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(8087,plain,
% 2.04/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z)))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[8086])).
% 2.04/2.27 tff(8088,plain,
% 2.04/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[8087, 8085])).
% 2.04/2.27 tff(8089,plain,
% 2.04/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.04/2.27 inference(quant_inst,[status(thm)],[])).
% 2.04/2.27 tff(8090,plain,
% 2.04/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z)))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[8089, 8088])).
% 2.04/2.27 tff(8091,plain,
% 2.04/2.27 ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z)))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8090, 183, 430])).
% 2.04/2.27 tff(8092,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8091, 8084, 8083])).
% 2.04/2.27 tff(8093,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~(elem!1 = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.27 tff(8094,plain,
% 2.04/2.27 (~r(s(s(s(elem!1))), s(z))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8093, 8082, 8059, 2392])).
% 2.04/2.27 tff(8095,plain,
% 2.04/2.27 (~r(s(s(elem!1)), s(z))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[8094, 8065])).
% 2.04/2.27 tff(8096,plain,
% 2.04/2.27 (b(s(s(elem!1)), s(z))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[197, 8095])).
% 2.04/2.27 tff(8097,plain,
% 2.04/2.27 (b(s(s(s(elem!1))), s(z))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[8096, 8062])).
% 2.04/2.27 tff(8098,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(8099,plain,
% 2.04/2.27 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(8100,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[8099])).
% 2.04/2.27 tff(8101,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))),
% 2.04/2.27 inference(transitivity,[status(thm)],[8100, 8098])).
% 2.04/2.27 tff(8102,plain,
% 2.04/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))),
% 2.04/2.27 inference(quant_inst,[status(thm)],[])).
% 2.04/2.27 tff(8103,plain,
% 2.04/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[8102, 8101])).
% 2.04/2.27 tff(8104,plain,
% 2.04/2.27 (~b(s(s(s(elem!1))), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8103, 246, 1056, 236, 8097])).
% 2.04/2.27 tff(8105,plain,
% 2.04/2.27 (r(s(s(s(elem!1))), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[3086, 47, 355, 8104])).
% 2.04/2.27 tff(8106,plain,
% 2.04/2.27 (b(elem!1, z) <=> b(s(s(elem!1)), z)),
% 2.04/2.27 inference(monotonicity,[status(thm)],[2392])).
% 2.04/2.27 tff(8107,plain,
% 2.04/2.27 (b(s(s(elem!1)), z) <=> b(elem!1, z)),
% 2.04/2.27 inference(symmetry,[status(thm)],[8106])).
% 2.04/2.27 tff(8108,plain,
% 2.04/2.27 (b(s(elem!1), z) <=> b(s(s(elem!1)), z)),
% 2.04/2.27 inference(monotonicity,[status(thm)],[8038])).
% 2.04/2.27 tff(8109,plain,
% 2.04/2.27 (b(s(s(s(elem!1))), z) <=> b(s(elem!1), z)),
% 2.04/2.27 inference(monotonicity,[status(thm)],[8049])).
% 2.04/2.27 tff(8110,plain,
% 2.04/2.27 (b(s(s(s(elem!1))), z) <=> b(elem!1, z)),
% 2.04/2.27 inference(transitivity,[status(thm)],[8109, 8108, 8107])).
% 2.04/2.27 tff(8111,plain,
% 2.04/2.27 ((~b(s(s(s(elem!1))), z)) <=> (~b(elem!1, z))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[8110])).
% 2.04/2.27 tff(8112,plain,
% 2.04/2.27 (~b(elem!1, z)),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[8104, 8111])).
% 2.04/2.27 tff(8113,plain,
% 2.04/2.27 (r(elem!1, z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1143, 8112, 1438])).
% 2.04/2.27 tff(8114,plain,
% 2.04/2.27 (~r(z, s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[2254, 8113, 413])).
% 2.04/2.27 tff(8115,plain,
% 2.04/2.27 (b(z, s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[6165, 8114])).
% 2.04/2.27 tff(8116,plain,
% 2.04/2.27 (s(s(s(elem!1))) = s(s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[8049, 108, 8037, 325, 8034, 7198])).
% 2.04/2.27 tff(8117,plain,
% 2.04/2.27 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z)))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[8116])).
% 2.04/2.27 tff(8118,plain,
% 2.04/2.27 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.04/2.27 inference(symmetry,[status(thm)],[8117])).
% 2.04/2.27 tff(8119,plain,
% 2.04/2.27 (s(s(s(s(s(s(s(elem!1))))))) = elem!1),
% 2.04/2.27 inference(transitivity,[status(thm)],[7197, 6841])).
% 2.04/2.27 tff(8120,plain,
% 2.04/2.27 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[8119])).
% 2.04/2.27 tff(8121,plain,
% 2.04/2.27 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z)))))),
% 2.04/2.27 inference(symmetry,[status(thm)],[8120])).
% 2.04/2.27 tff(8122,plain,
% 2.04/2.27 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[8121, 8118])).
% 2.04/2.27 tff(8123,plain,
% 2.04/2.27 ((s(s(elem!1)) = s(elem!1)) <=> (elem!1 = s(elem!1))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[6841])).
% 2.04/2.27 tff(8124,plain,
% 2.04/2.27 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(elem!1))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[8049])).
% 2.04/2.27 tff(8125,plain,
% 2.04/2.27 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (elem!1 = s(elem!1))),
% 2.04/2.27 inference(transitivity,[status(thm)],[8124, 8123])).
% 2.04/2.27 tff(8126,plain,
% 2.04/2.27 (elem!1 = s(elem!1)),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[8061, 8125])).
% 2.04/2.27 tff(8127,plain,
% 2.04/2.27 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[7030, 2392, 7198])).
% 2.04/2.27 tff(8128,plain,
% 2.04/2.27 (r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z)))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[8127])).
% 2.04/2.27 tff(8129,plain,
% 2.04/2.27 (r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 2.04/2.27 inference(symmetry,[status(thm)],[8128])).
% 2.04/2.27 tff(8130,plain,
% 2.04/2.27 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z)))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[8116])).
% 2.04/2.27 tff(8131,plain,
% 2.04/2.27 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[8130, 8129])).
% 2.04/2.27 tff(8132,plain,
% 2.04/2.27 ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) <=> (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[8131])).
% 2.04/2.27 tff(8133,assumption,(b(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 2.04/2.27 tff(8134,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(8135,plain,
% 2.04/2.27 (((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(8136,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[8135])).
% 2.04/2.27 tff(8137,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[8136, 8134])).
% 2.04/2.27 tff(8138,plain,
% 2.04/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.04/2.27 inference(quant_inst,[status(thm)],[])).
% 2.04/2.27 tff(8139,plain,
% 2.04/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[8138, 8137])).
% 2.04/2.27 tff(8140,plain,
% 2.04/2.27 (~b(s(s(s(s(z)))), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8139, 246, 236, 4651, 1833, 8030, 8133])).
% 2.04/2.27 tff(8141,plain,
% 2.04/2.27 (r(s(s(s(s(z)))), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[2424, 47, 2421, 8140])).
% 2.04/2.27 tff(8142,plain,
% 2.04/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(8143,plain,
% 2.04/2.27 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(8144,plain,
% 2.04/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[8143])).
% 2.04/2.27 tff(8145,plain,
% 2.04/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[8144, 8142])).
% 2.04/2.27 tff(8146,plain,
% 2.04/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.04/2.27 inference(quant_inst,[status(thm)],[])).
% 2.04/2.27 tff(8147,plain,
% 2.04/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[8146, 8145])).
% 2.04/2.27 tff(8148,plain,
% 2.04/2.27 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8147, 183, 8141, 4281])).
% 2.04/2.27 tff(8149,plain,
% 2.04/2.27 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[8148, 8132])).
% 2.04/2.27 tff(8150,plain,
% 2.04/2.27 (b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1897, 8149])).
% 2.04/2.27 tff(8151,plain,
% 2.04/2.27 (elem!1 = s(s(s(s(s(elem!1)))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[3189, 5874])).
% 2.04/2.27 tff(8152,plain,
% 2.04/2.27 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[8151])).
% 2.04/2.27 tff(8153,plain,
% 2.04/2.27 (b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.04/2.27 inference(symmetry,[status(thm)],[8152])).
% 2.04/2.27 tff(8154,plain,
% 2.04/2.27 (b(elem!1, s(s(s(s(z)))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[3377, 8153])).
% 2.04/2.27 tff(8155,assumption,(~b(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 2.04/2.27 tff(8156,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8155, 8154])).
% 2.04/2.27 tff(8157,plain,(b(elem!1, s(s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~(elem!1 = s(elem!1))) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.27 tff(8158,plain,
% 2.04/2.27 (b(elem!1, s(s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8157, 8150, 6838, 8126])).
% 2.04/2.27 tff(8159,plain,
% 2.04/2.27 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[8158, 8122])).
% 2.04/2.27 tff(8160,plain,
% 2.04/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(8161,plain,
% 2.04/2.27 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(8162,plain,
% 2.04/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[8161])).
% 2.04/2.27 tff(8163,plain,
% 2.04/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[8162, 8160])).
% 2.04/2.27 tff(8164,plain,
% 2.04/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.04/2.28 inference(quant_inst,[status(thm)],[])).
% 2.04/2.28 tff(8165,plain,
% 2.04/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[8164, 8163])).
% 2.04/2.28 tff(8166,plain,
% 2.04/2.28 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8165, 183, 8141, 4281])).
% 2.04/2.28 tff(8167,plain,
% 2.04/2.28 (~r(s(s(s(s(z)))), s(elem!1))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[8166, 8051])).
% 2.04/2.28 tff(8168,plain,
% 2.04/2.28 (b(s(s(s(s(z)))), s(elem!1))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1728, 8167, 8048])).
% 2.04/2.28 tff(8169,plain,
% 2.04/2.28 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[8168, 8032])).
% 2.04/2.28 tff(8170,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(8171,plain,
% 2.04/2.28 (((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(8172,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[8171])).
% 2.04/2.28 tff(8173,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.04/2.28 inference(transitivity,[status(thm)],[8172, 8170])).
% 2.04/2.28 tff(8174,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.04/2.28 inference(quant_inst,[status(thm)],[])).
% 2.04/2.28 tff(8175,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[8174, 8173])).
% 2.04/2.28 tff(8176,plain,
% 2.04/2.28 ($false),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8175, 246, 1833, 8030, 8169, 8159])).
% 2.04/2.28 tff(8177,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~(elem!1 = s(s(elem!1)))) | (~(s(s(s(s(s(elem!1))))) = elem!1)) | (~r(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.28 tff(8178,plain,
% 2.04/2.28 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8177, 8105, 2392, 7030, 8030, 236, 8115, 8097])).
% 2.04/2.28 tff(8179,plain,
% 2.04/2.28 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1702, 8178])).
% 2.04/2.28 tff(8180,plain,
% 2.04/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(8181,plain,
% 2.04/2.28 (((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(8182,plain,
% 2.04/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[8181])).
% 2.04/2.28 tff(8183,plain,
% 2.04/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.04/2.28 inference(transitivity,[status(thm)],[8182, 8180])).
% 2.04/2.28 tff(8184,plain,
% 2.04/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.04/2.28 inference(quant_inst,[status(thm)],[])).
% 2.04/2.28 tff(8185,plain,
% 2.04/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[8184, 8183])).
% 2.04/2.28 tff(8186,plain,
% 2.04/2.28 ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8185, 183, 8179, 8105])).
% 2.04/2.28 tff(8187,plain,
% 2.04/2.28 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8186, 8060])).
% 2.04/2.28 tff(8188,plain,
% 2.04/2.28 (~r(s(s(s(s(z)))), s(elem!1))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[8187, 8051])).
% 2.04/2.28 tff(8189,plain,
% 2.04/2.28 (b(s(s(s(s(z)))), s(elem!1))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1728, 8188, 8048])).
% 2.04/2.28 tff(8190,plain,
% 2.04/2.28 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[8189, 8032])).
% 2.04/2.28 tff(8191,plain,
% 2.04/2.28 ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) <=> (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z))))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[8130])).
% 2.04/2.28 tff(8192,plain,
% 2.04/2.28 ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[7487, 183, 8179])).
% 2.04/2.28 tff(8193,plain,
% 2.04/2.28 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8192, 8060])).
% 2.04/2.28 tff(8194,plain,
% 2.04/2.28 (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z)))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[8193, 8191])).
% 2.04/2.28 tff(8195,plain,
% 2.04/2.28 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[7230, 8194, 7215])).
% 2.04/2.28 tff(8196,plain,
% 2.04/2.28 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[8195, 8118])).
% 2.04/2.28 tff(8197,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(8198,plain,
% 2.04/2.28 (((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(8199,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[8198])).
% 2.04/2.28 tff(8200,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.04/2.28 inference(transitivity,[status(thm)],[8199, 8197])).
% 2.04/2.28 tff(8201,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.04/2.28 inference(quant_inst,[status(thm)],[])).
% 2.04/2.28 tff(8202,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[8201, 8200])).
% 2.04/2.28 tff(8203,plain,
% 2.04/2.28 ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8202, 246, 8030, 8190])).
% 2.04/2.28 tff(8204,plain,
% 2.04/2.28 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8203, 8196])).
% 2.04/2.28 tff(8205,assumption,(s(s(s(z))) = s(s(s(s(z))))), introduced(assumption)).
% 2.04/2.28 tff(8206,plain,
% 2.04/2.28 (s(s(s(s(z)))) = s(s(s(z)))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[8205, 3024])).
% 2.04/2.28 tff(8207,assumption,(~(s(s(s(s(z)))) = s(s(s(z))))), introduced(assumption)).
% 2.04/2.28 tff(8208,plain,
% 2.04/2.28 ($false),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8207, 8206])).
% 2.04/2.28 tff(8209,plain,((~(s(s(s(z))) = s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.28 tff(8210,plain,
% 2.04/2.28 (~(s(s(s(z))) = s(s(s(s(z)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8209, 1697])).
% 2.04/2.28 tff(8211,plain,
% 2.04/2.28 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(8212,plain,
% 2.04/2.28 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))),
% 2.04/2.28 inference(quant_inst,[status(thm)],[])).
% 2.04/2.28 tff(8213,plain,
% 2.04/2.28 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[8212, 8211])).
% 2.04/2.28 tff(8214,plain,
% 2.04/2.28 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8213, 47, 8210, 8204])).
% 2.04/2.28 tff(8215,assumption,(r(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 2.04/2.28 tff(8216,plain,
% 2.04/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(8217,plain,
% 2.04/2.28 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(8218,plain,
% 2.04/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[8217])).
% 2.04/2.28 tff(8219,plain,
% 2.04/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 2.04/2.28 inference(transitivity,[status(thm)],[8218, 8216])).
% 2.04/2.28 tff(8220,plain,
% 2.04/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.04/2.28 inference(quant_inst,[status(thm)],[])).
% 2.04/2.28 tff(8221,plain,
% 2.04/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[8220, 8219])).
% 2.04/2.28 tff(8222,plain,
% 2.04/2.28 ($false),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8221, 183, 430, 6095, 8215])).
% 2.04/2.28 tff(8223,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.28 tff(8224,plain,
% 2.04/2.28 (~r(s(s(s(s(z)))), s(z))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8223, 8082, 8214])).
% 2.04/2.28 tff(8225,plain,
% 2.04/2.28 (b(s(s(s(s(z)))), s(z))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[6103, 8224])).
% 2.04/2.28 tff(8226,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(8227,plain,
% 2.04/2.28 (((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(8228,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[8227])).
% 2.04/2.28 tff(8229,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.04/2.28 inference(transitivity,[status(thm)],[8228, 8226])).
% 2.04/2.28 tff(8230,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.04/2.28 inference(quant_inst,[status(thm)],[])).
% 2.04/2.28 tff(8231,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[8230, 8229])).
% 2.04/2.28 tff(8232,plain,
% 2.04/2.28 ($false),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8231, 246, 1056, 236, 8097, 8225, 8190])).
% 2.04/2.28 tff(8233,plain,((~r(elem!1, s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~(elem!1 = s(s(elem!1)))) | (~(s(s(s(s(s(elem!1))))) = elem!1)) | (elem!1 = z) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.28 tff(8234,plain,
% 2.04/2.28 (~r(elem!1, s(s(s(z))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8233, 5572, 7591, 236, 8030, 7030, 5401, 267])).
% 2.04/2.28 tff(8235,plain,
% 2.04/2.28 (b(elem!1, s(s(s(z))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[470, 8234, 7868])).
% 2.04/2.28 tff(8236,plain,
% 2.04/2.28 (b(s(elem!1), s(s(s(z))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[8235, 8029])).
% 2.04/2.28 tff(8237,assumption,(b(s(s(s(z))), s(elem!1))), introduced(assumption)).
% 2.04/2.28 tff(8238,plain,
% 2.04/2.28 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[5858])).
% 2.04/2.28 tff(8239,plain,
% 2.04/2.28 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 2.04/2.28 inference(transitivity,[status(thm)],[8238, 2891])).
% 2.04/2.28 tff(8240,plain,
% 2.04/2.28 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[8239])).
% 2.04/2.28 tff(8241,plain,
% 2.04/2.28 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[6281, 7830])).
% 2.04/2.28 tff(8242,plain,
% 2.04/2.28 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[8241, 8240])).
% 2.04/2.28 tff(8243,plain,
% 2.04/2.28 (r(z, s(elem!1)) <=> r(z, elem!1)),
% 2.04/2.28 inference(monotonicity,[status(thm)],[7987])).
% 2.04/2.28 tff(8244,plain,
% 2.04/2.28 (r(z, elem!1) <=> r(z, s(elem!1))),
% 2.04/2.28 inference(symmetry,[status(thm)],[8243])).
% 2.04/2.28 tff(8245,plain,
% 2.04/2.28 (r(z, s(elem!1))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[267, 8244])).
% 2.04/2.28 tff(8246,plain,
% 2.04/2.28 (r(s(z), s(elem!1)) <=> r(s(z), elem!1)),
% 2.04/2.28 inference(monotonicity,[status(thm)],[7987])).
% 2.04/2.28 tff(8247,plain,
% 2.04/2.28 (r(s(z), elem!1) <=> r(s(z), s(elem!1))),
% 2.04/2.28 inference(symmetry,[status(thm)],[8246])).
% 2.04/2.28 tff(8248,plain,
% 2.04/2.28 (r(s(z), s(elem!1))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[217, 8247])).
% 2.04/2.28 tff(8249,plain,
% 2.04/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z)))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(8250,plain,
% 2.04/2.28 (((~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z)))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(8251,plain,
% 2.04/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[8250])).
% 2.04/2.28 tff(8252,plain,
% 2.04/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z)))),
% 2.04/2.28 inference(transitivity,[status(thm)],[8251, 8249])).
% 2.04/2.28 tff(8253,plain,
% 2.04/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z)))),
% 2.04/2.28 inference(quant_inst,[status(thm)],[])).
% 2.04/2.28 tff(8254,plain,
% 2.04/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[8253, 8252])).
% 2.04/2.28 tff(8255,plain,
% 2.04/2.28 (~r(s(s(s(s(z)))), z)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8254, 183, 5973, 5864])).
% 2.04/2.28 tff(8256,plain,
% 2.04/2.28 (b(s(s(s(s(z)))), z)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[6040, 8255])).
% 2.04/2.28 tff(8257,assumption,(r(s(z), s(elem!1))), introduced(assumption)).
% 2.04/2.28 tff(8258,plain,
% 2.04/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(8259,plain,
% 2.04/2.29 (((~r(s(z), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(8260,plain,
% 2.04/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(elem!1)))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8259])).
% 2.04/2.29 tff(8261,plain,
% 2.04/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 2.04/2.29 inference(transitivity,[status(thm)],[8260, 8258])).
% 2.04/2.29 tff(8262,plain,
% 2.04/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(z)))), s(z))))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(8263,plain,
% 2.04/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[8262, 8261])).
% 2.04/2.29 tff(8264,plain,
% 2.04/2.29 (~r(s(s(s(s(z)))), s(z))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8263, 183, 5973, 8257])).
% 2.04/2.29 tff(8265,plain,
% 2.04/2.29 (b(s(s(s(s(z)))), s(z))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[6103, 8264])).
% 2.04/2.29 tff(8266,assumption,(b(s(s(s(s(z)))), z)), introduced(assumption)).
% 2.04/2.29 tff(8267,assumption,(b(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 2.04/2.29 tff(8268,plain,
% 2.04/2.29 ($false),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[3297, 246, 1056, 236, 8267, 8266])).
% 2.04/2.29 tff(8269,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.29 tff(8270,plain,
% 2.04/2.29 ($false),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8269, 8265, 8256, 236, 1056])).
% 2.04/2.29 tff(8271,plain,((~r(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(s(z), s(elem!1))) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.29 tff(8272,plain,
% 2.04/2.29 (~r(s(s(s(s(z)))), s(elem!1))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8271, 5572, 236, 8248, 8245])).
% 2.04/2.29 tff(8273,plain,
% 2.04/2.29 (b(s(s(s(s(z)))), s(elem!1))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1728, 8272, 8242])).
% 2.04/2.29 tff(8274,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(8275,plain,
% 2.04/2.29 (((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(8276,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8275])).
% 2.04/2.29 tff(8277,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 2.04/2.29 inference(transitivity,[status(thm)],[8276, 8274])).
% 2.04/2.29 tff(8278,plain,
% 2.04/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(8279,plain,
% 2.04/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[8278, 8277])).
% 2.04/2.29 tff(8280,plain,
% 2.04/2.29 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8279, 246, 8273, 8237, 8236])).
% 2.04/2.29 tff(8281,plain,
% 2.04/2.29 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8213, 47, 8210, 8280])).
% 2.04/2.29 tff(8282,plain,
% 2.04/2.29 (b(s(elem!1), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[7987])).
% 2.04/2.29 tff(8283,plain,
% 2.04/2.29 (b(elem!1, s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 2.04/2.29 inference(symmetry,[status(thm)],[8282])).
% 2.04/2.29 tff(8284,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(8285,plain,
% 2.04/2.29 (((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(8286,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8285])).
% 2.04/2.29 tff(8287,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 2.04/2.29 inference(transitivity,[status(thm)],[8286, 8284])).
% 2.04/2.29 tff(8288,plain,
% 2.04/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(8289,plain,
% 2.04/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[8288, 8287])).
% 2.04/2.29 tff(8290,plain,
% 2.04/2.29 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8289, 246, 8273, 8237, 8236])).
% 2.04/2.29 tff(8291,plain,
% 2.04/2.29 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1702, 8290])).
% 2.04/2.29 tff(8292,plain,
% 2.04/2.29 (~r(s(s(s(s(z)))), s(z))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[6098, 6096, 2593])).
% 2.04/2.29 tff(8293,plain,
% 2.04/2.29 (b(s(s(s(s(z)))), s(z))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[6103, 8292])).
% 2.04/2.29 tff(8294,plain,
% 2.04/2.29 (~b(s(s(s(s(z)))), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[7683, 246, 1056, 236, 8293])).
% 2.04/2.29 tff(8295,plain,
% 2.04/2.29 (r(s(s(s(s(z)))), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[6040, 8294])).
% 2.04/2.29 tff(8296,plain,
% 2.04/2.29 (~b(z, s(s(s(s(z)))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[7673, 246, 1056, 236, 8293])).
% 2.04/2.29 tff(8297,plain,
% 2.04/2.29 ((z = s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[2645, 47, 8296])).
% 2.04/2.29 tff(8298,plain,
% 2.04/2.29 (r(z, s(s(s(s(z)))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8297, 2635])).
% 2.04/2.29 tff(8299,assumption,(b(s(elem!1), s(s(s(z))))), introduced(assumption)).
% 2.04/2.29 tff(8300,assumption,(~(s(s(s(elem!1))) = s(s(z)))), introduced(assumption)).
% 2.04/2.29 tff(8301,plain,
% 2.04/2.29 (~(s(elem!1) = s(s(z)))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[8300, 7998])).
% 2.04/2.29 tff(8302,plain,
% 2.04/2.29 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(z)))))),
% 2.04/2.29 inference(symmetry,[status(thm)],[2891])).
% 2.04/2.29 tff(8303,plain,
% 2.04/2.29 ((~(s(s(s(s(z)))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8302])).
% 2.04/2.29 tff(8304,plain,
% 2.04/2.29 (~(s(elem!1) = s(s(s(s(z)))))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[6006, 8303])).
% 2.04/2.29 tff(8305,assumption,(r(s(elem!1), z)), introduced(assumption)).
% 2.04/2.29 tff(8306,plain,
% 2.04/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(8307,plain,
% 2.04/2.29 (((~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(z))))))) <=> ((~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(8308,plain,
% 2.04/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8307])).
% 2.04/2.29 tff(8309,plain,
% 2.04/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.04/2.29 inference(transitivity,[status(thm)],[8308, 8306])).
% 2.04/2.29 tff(8310,plain,
% 2.04/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(8311,plain,
% 2.04/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z))))))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[8310, 8309])).
% 2.04/2.29 tff(8312,plain,
% 2.04/2.29 (~r(s(elem!1), s(s(s(s(z)))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8311, 183, 8305, 2593, 7218])).
% 2.04/2.29 tff(8313,plain,
% 2.04/2.29 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(z))))) | b(s(elem!1), s(s(s(s(z))))) | r(s(elem!1), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(z))))) | b(s(elem!1), s(s(s(s(z))))) | r(s(elem!1), s(s(s(s(z))))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(8314,plain,
% 2.04/2.29 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(z))))) | b(s(elem!1), s(s(s(s(z))))) | r(s(elem!1), s(s(s(s(z))))))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(8315,plain,
% 2.04/2.29 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(z))))) | b(s(elem!1), s(s(s(s(z))))) | r(s(elem!1), s(s(s(s(z)))))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[8314, 8313])).
% 2.04/2.29 tff(8316,plain,
% 2.04/2.29 ((s(elem!1) = s(s(s(s(z))))) | b(s(elem!1), s(s(s(s(z)))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8315, 47, 8312])).
% 2.04/2.29 tff(8317,plain,
% 2.04/2.29 (b(s(elem!1), s(s(s(s(z)))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8316, 8304])).
% 2.04/2.29 tff(8318,plain,
% 2.04/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z)))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(8319,plain,
% 2.04/2.29 (((~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), s(elem!1)))) <=> ((~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z)))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(8320,plain,
% 2.04/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8319])).
% 2.04/2.29 tff(8321,plain,
% 2.04/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z)))),
% 2.04/2.29 inference(transitivity,[status(thm)],[8320, 8318])).
% 2.04/2.29 tff(8322,plain,
% 2.04/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(8323,plain,
% 2.04/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), z))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[8322, 8321])).
% 2.04/2.29 tff(8324,plain,
% 2.04/2.29 (~r(s(s(s(s(z)))), s(elem!1))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8323, 183, 8305, 7218])).
% 2.04/2.29 tff(8325,plain,
% 2.04/2.29 (b(s(s(s(s(z)))), s(elem!1))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1728, 8324, 6006])).
% 2.04/2.29 tff(8326,assumption,(r(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 2.04/2.29 tff(8327,plain,
% 2.04/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(8328,plain,
% 2.04/2.29 (((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(8329,plain,
% 2.04/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z))))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8328])).
% 2.04/2.29 tff(8330,plain,
% 2.04/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))))),
% 2.04/2.29 inference(transitivity,[status(thm)],[8329, 8327])).
% 2.04/2.29 tff(8331,plain,
% 2.04/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(8332,plain,
% 2.04/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z))))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[8331, 8330])).
% 2.04/2.29 tff(8333,plain,
% 2.04/2.29 (~r(s(z), s(s(z)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8332, 183, 6096, 8326])).
% 2.04/2.29 tff(8334,assumption,(s(z) = s(s(z))), introduced(assumption)).
% 2.04/2.29 tff(8335,plain,
% 2.04/2.29 (inj_0(s(z)) = inj_0(s(s(z)))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8334])).
% 2.04/2.29 tff(8336,plain,
% 2.04/2.29 (inj_0(s(s(z))) = inj_0(s(z))),
% 2.04/2.29 inference(symmetry,[status(thm)],[8335])).
% 2.04/2.29 tff(8337,plain,
% 2.04/2.29 (s(s(z)) = s(z)),
% 2.04/2.29 inference(symmetry,[status(thm)],[8334])).
% 2.04/2.29 tff(8338,plain,
% 2.04/2.29 (s(s(z)) = z),
% 2.04/2.29 inference(transitivity,[status(thm)],[8337, 1523, 8336, 20])).
% 2.04/2.29 tff(8339,plain,
% 2.04/2.29 ($false),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[35, 8338])).
% 2.04/2.29 tff(8340,plain,(~(s(z) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.29 tff(8341,plain,
% 2.04/2.29 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(8342,plain,
% 2.04/2.29 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(8343,plain,
% 2.04/2.29 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[8342, 8341])).
% 2.04/2.29 tff(8344,plain,
% 2.04/2.29 (b(s(z), s(s(z)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8343, 47, 8340, 8333])).
% 2.04/2.29 tff(8345,assumption,(b(s(elem!1), s(s(s(s(z)))))), introduced(assumption)).
% 2.04/2.29 tff(8346,plain,
% 2.04/2.29 (~r(s(z), s(s(s(s(z)))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[6088, 183, 6096, 2593])).
% 2.04/2.29 tff(8347,plain,
% 2.04/2.29 ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z)))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[6092, 47, 8346])).
% 2.04/2.29 tff(8348,plain,
% 2.04/2.29 (b(s(z), s(s(s(s(z)))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8347, 5790])).
% 2.04/2.29 tff(8349,plain,
% 2.04/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(8350,plain,
% 2.04/2.29 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(8351,plain,
% 2.04/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8350])).
% 2.04/2.29 tff(8352,plain,
% 2.04/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.04/2.29 inference(transitivity,[status(thm)],[8351, 8349])).
% 2.04/2.29 tff(8353,plain,
% 2.04/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(8354,plain,
% 2.04/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[8353, 8352])).
% 2.04/2.29 tff(8355,plain,
% 2.04/2.29 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8354, 183, 2593, 8326])).
% 2.04/2.29 tff(8356,plain,
% 2.04/2.29 (b(s(s(z)), s(s(s(s(z)))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1531, 8355])).
% 2.04/2.29 tff(8357,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(8358,plain,
% 2.14/2.30 (((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(8359,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(z))))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[8358])).
% 2.14/2.30 tff(8360,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 2.14/2.30 inference(transitivity,[status(thm)],[8359, 8357])).
% 2.14/2.30 tff(8361,plain,
% 2.14/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 2.14/2.30 inference(quant_inst,[status(thm)],[])).
% 2.14/2.30 tff(8362,plain,
% 2.14/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(z))))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[8361, 8360])).
% 2.14/2.30 tff(8363,plain,
% 2.14/2.30 ($false),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[8362, 246, 8356, 5914, 8348, 8345, 8344])).
% 2.14/2.30 tff(8364,plain,((~r(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.30 tff(8365,plain,
% 2.14/2.30 (~r(s(s(z)), s(s(s(z))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[8364, 8325, 8317, 2593, 6096])).
% 2.14/2.30 tff(8366,assumption,(~r(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 2.14/2.30 tff(8367,assumption,(s(s(z)) = s(s(s(z)))), introduced(assumption)).
% 2.14/2.30 tff(8368,plain,
% 2.14/2.30 (s(s(s(z))) = s(s(z))),
% 2.14/2.30 inference(symmetry,[status(thm)],[8367])).
% 2.14/2.30 tff(8369,assumption,(s(s(s(z))) = s(s(z))), introduced(assumption)).
% 2.14/2.30 tff(8370,plain,
% 2.14/2.30 (s(s(z)) = s(s(s(z)))),
% 2.14/2.30 inference(symmetry,[status(thm)],[8369])).
% 2.14/2.30 tff(8371,plain,
% 2.14/2.30 (inj_0(s(s(z))) = inj_0(s(s(s(z))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[8370])).
% 2.14/2.30 tff(8372,plain,
% 2.14/2.30 (s(z) = s(s(z))),
% 2.14/2.30 inference(transitivity,[status(thm)],[1523, 8371, 24])).
% 2.14/2.30 tff(8373,plain,
% 2.14/2.30 ($false),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[8340, 8372])).
% 2.14/2.30 tff(8374,plain,(~(s(s(s(z))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.30 tff(8375,plain,
% 2.14/2.30 ($false),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[8374, 8368])).
% 2.14/2.30 tff(8376,plain,(~(s(s(z)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.30 tff(8377,assumption,(~b(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 2.14/2.30 tff(8378,plain,
% 2.14/2.30 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z)))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(8379,plain,
% 2.14/2.30 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z)))))),
% 2.14/2.30 inference(quant_inst,[status(thm)],[])).
% 2.14/2.30 tff(8380,plain,
% 2.14/2.30 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[8379, 8378])).
% 2.14/2.30 tff(8381,plain,
% 2.14/2.30 ($false),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[8380, 47, 8377, 8376, 8366])).
% 2.14/2.30 tff(8382,plain,(r(s(s(z)), s(s(s(z)))) | b(s(s(z)), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.30 tff(8383,plain,
% 2.14/2.30 (b(s(s(z)), s(s(s(z))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[8382, 8365])).
% 2.14/2.30 tff(8384,assumption,(r(z, s(s(s(s(z)))))), introduced(assumption)).
% 2.14/2.30 tff(8385,plain,
% 2.14/2.30 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[8279, 246, 8325, 8237, 8299])).
% 2.14/2.30 tff(8386,plain,
% 2.14/2.30 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[8213, 47, 8210, 8385])).
% 2.14/2.30 tff(8387,plain,
% 2.14/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(z)))))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(8388,plain,
% 2.14/2.30 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(z)))))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(8389,plain,
% 2.14/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(z))))))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[8388])).
% 2.14/2.30 tff(8390,plain,
% 2.14/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(z)))))))),
% 2.14/2.30 inference(transitivity,[status(thm)],[8389, 8387])).
% 2.14/2.30 tff(8391,plain,
% 2.14/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z)))),
% 2.14/2.30 inference(quant_inst,[status(thm)],[])).
% 2.14/2.30 tff(8392,plain,
% 2.14/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(z))))))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[8391, 8390])).
% 2.14/2.30 tff(8393,plain,
% 2.14/2.30 (~r(s(s(s(z))), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[8392, 183, 5864, 8386, 8384])).
% 2.14/2.30 tff(8394,plain,
% 2.14/2.30 (b(s(s(s(z))), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[995, 8393])).
% 2.14/2.30 tff(8395,plain,
% 2.14/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(8396,plain,
% 2.14/2.30 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(8397,plain,
% 2.14/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[8396])).
% 2.14/2.30 tff(8398,plain,
% 2.14/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 2.14/2.30 inference(transitivity,[status(thm)],[8397, 8395])).
% 2.14/2.30 tff(8399,plain,
% 2.14/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))),
% 2.14/2.30 inference(quant_inst,[status(thm)],[])).
% 2.14/2.30 tff(8400,plain,
% 2.14/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[8399, 8398])).
% 2.14/2.30 tff(8401,plain,
% 2.14/2.30 (~r(z, s(s(s(z))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[8400, 183, 8386, 8384])).
% 2.14/2.30 tff(8402,plain,
% 2.14/2.30 (b(z, s(s(s(z))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[6165, 8401])).
% 2.14/2.30 tff(8403,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(z)))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(8404,plain,
% 2.14/2.30 (((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(z))))) <=> ((~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(z)))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(8405,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(z))))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[8404])).
% 2.14/2.30 tff(8406,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(z)))))),
% 2.14/2.30 inference(transitivity,[status(thm)],[8405, 8403])).
% 2.14/2.30 tff(8407,plain,
% 2.14/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(z)))))),
% 2.14/2.30 inference(quant_inst,[status(thm)],[])).
% 2.14/2.30 tff(8408,plain,
% 2.14/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(z))))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[8407, 8406])).
% 2.14/2.30 tff(8409,plain,
% 2.14/2.30 (~b(s(elem!1), s(s(z)))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[8408, 246, 8402, 8394, 8299, 8383])).
% 2.14/2.30 tff(8410,plain,
% 2.14/2.30 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(8411,plain,
% 2.14/2.30 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z))))),
% 2.14/2.30 inference(quant_inst,[status(thm)],[])).
% 2.14/2.30 tff(8412,plain,
% 2.14/2.30 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z)))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[8411, 8410])).
% 2.14/2.30 tff(8413,plain,
% 2.14/2.30 ((s(elem!1) = s(s(z))) | r(s(elem!1), s(s(z)))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[8412, 47, 8409])).
% 2.14/2.30 tff(8414,plain,
% 2.14/2.30 (r(s(elem!1), s(s(z)))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[8413, 8301])).
% 2.14/2.30 tff(8415,plain,
% 2.14/2.30 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 2.14/2.30 inference(commutativity,[status(thm)],[])).
% 2.14/2.30 tff(8416,plain,
% 2.14/2.30 ((s(s(z)) = s(elem!1)) <=> (s(s(z)) = s(s(s(elem!1))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[7986])).
% 2.14/2.30 tff(8417,plain,
% 2.14/2.30 ((s(s(z)) = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(z)))),
% 2.14/2.30 inference(transitivity,[status(thm)],[8416, 8415])).
% 2.14/2.30 tff(8418,plain,
% 2.14/2.30 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(z)) = s(elem!1))),
% 2.14/2.30 inference(symmetry,[status(thm)],[8417])).
% 2.14/2.30 tff(8419,plain,
% 2.14/2.30 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(z)) = s(elem!1)))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[8418])).
% 2.14/2.30 tff(8420,plain,
% 2.14/2.30 (~(s(s(z)) = s(elem!1))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[8300, 8419])).
% 2.14/2.30 tff(8421,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(8422,plain,
% 2.14/2.30 (((~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(8423,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(elem!1)))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[8422])).
% 2.14/2.30 tff(8424,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))))),
% 2.14/2.30 inference(transitivity,[status(thm)],[8423, 8421])).
% 2.14/2.30 tff(8425,plain,
% 2.14/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))))),
% 2.14/2.30 inference(quant_inst,[status(thm)],[])).
% 2.14/2.30 tff(8426,plain,
% 2.14/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(elem!1)))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[8425, 8424])).
% 2.14/2.30 tff(8427,plain,
% 2.14/2.30 (~b(s(s(z)), s(elem!1))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[8426, 246, 8402, 8394, 8299, 8383])).
% 2.14/2.30 tff(8428,plain,
% 2.14/2.30 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1)))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(8429,plain,
% 2.14/2.30 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1)))),
% 2.14/2.30 inference(quant_inst,[status(thm)],[])).
% 2.14/2.30 tff(8430,plain,
% 2.14/2.30 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[8429, 8428])).
% 2.14/2.30 tff(8431,plain,
% 2.14/2.30 ((s(s(z)) = s(elem!1)) | r(s(s(z)), s(elem!1))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[8430, 47, 8427])).
% 2.14/2.30 tff(8432,plain,
% 2.14/2.30 (r(s(s(z)), s(elem!1))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[8431, 8420])).
% 2.14/2.30 tff(8433,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(8434,plain,
% 2.14/2.30 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z))) <=> ((~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(8435,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[8434])).
% 2.14/2.31 tff(8436,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 2.14/2.31 inference(transitivity,[status(thm)],[8435, 8433])).
% 2.14/2.31 tff(8437,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 2.14/2.31 inference(quant_inst,[status(thm)],[])).
% 2.14/2.31 tff(8438,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[8437, 8436])).
% 2.14/2.31 tff(8439,plain,
% 2.14/2.31 (~b(s(s(z)), z)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[8438, 246, 236, 8402, 8394, 8383])).
% 2.14/2.31 tff(8440,plain,
% 2.14/2.31 (r(s(s(z)), z)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[3215, 47, 35, 8439])).
% 2.14/2.31 tff(8441,plain,
% 2.14/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(z)))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(8442,plain,
% 2.14/2.31 (((~r(s(s(z)), z)) | (~r(s(elem!1), z)) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(z))))) <=> ((~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(z)))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(8443,plain,
% 2.14/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(elem!1), z)) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(z))))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[8442])).
% 2.14/2.31 tff(8444,plain,
% 2.14/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(elem!1), z)) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(z)))))),
% 2.14/2.31 inference(transitivity,[status(thm)],[8443, 8441])).
% 2.14/2.31 tff(8445,plain,
% 2.14/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(elem!1), z)) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(z)))))),
% 2.14/2.31 inference(quant_inst,[status(thm)],[])).
% 2.14/2.31 tff(8446,plain,
% 2.14/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(z))))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[8445, 8444])).
% 2.14/2.31 tff(8447,plain,
% 2.14/2.31 ($false),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[8446, 183, 8305, 8440, 8432, 8414])).
% 2.14/2.31 tff(8448,plain,((~r(s(elem!1), z)) | (s(s(s(elem!1))) = s(s(z))) | (~(s(s(elem!1)) = elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.31 tff(8449,plain,
% 2.14/2.31 (~r(s(elem!1), z)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[8448, 6096, 2125, 8299, 236, 2593, 8026, 5864, 8298, 8242, 8237, 8295])).
% 2.14/2.31 tff(8450,plain,
% 2.14/2.31 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 2.14/2.31 inference(symmetry,[status(thm)],[5859])).
% 2.14/2.31 tff(8451,plain,
% 2.14/2.31 (elem!1 = s(s(s(s(elem!1))))),
% 2.14/2.31 inference(transitivity,[status(thm)],[5380, 8450])).
% 2.14/2.31 tff(8452,plain,
% 2.14/2.31 (s(elem!1) = s(s(s(s(s(elem!1)))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[8451])).
% 2.14/2.31 tff(8453,plain,
% 2.14/2.31 (s(elem!1) = elem!1),
% 2.14/2.31 inference(transitivity,[status(thm)],[8452, 7030])).
% 2.14/2.31 tff(8454,plain,
% 2.14/2.31 (r(s(elem!1), z) <=> r(elem!1, z)),
% 2.14/2.31 inference(monotonicity,[status(thm)],[8453])).
% 2.14/2.31 tff(8455,plain,
% 2.14/2.31 (r(elem!1, z) <=> r(s(elem!1), z)),
% 2.14/2.31 inference(symmetry,[status(thm)],[8454])).
% 2.14/2.31 tff(8456,plain,
% 2.14/2.31 (r(s(s(elem!1)), z) <=> r(s(elem!1), z)),
% 2.14/2.31 inference(transitivity,[status(thm)],[7017, 8455])).
% 2.14/2.31 tff(8457,plain,
% 2.14/2.31 (r(s(elem!1), z)),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[172, 8456])).
% 2.14/2.31 tff(8458,plain,
% 2.14/2.31 ($false),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[2575, 8457])).
% 2.14/2.31 tff(8459,plain,((~r(s(s(elem!1)), z)) | r(s(elem!1), z) | (~(s(s(s(s(s(elem!1))))) = elem!1)) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.31 tff(8460,plain,
% 2.14/2.31 (~r(s(s(elem!1)), z)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[8459, 8449, 7030, 2125])).
% 2.14/2.31 tff(8461,plain,
% 2.14/2.31 (b(s(s(elem!1)), z)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[523, 8460])).
% 2.14/2.31 tff(8462,plain,
% 2.14/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(z, s(s(s(s(z)))))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(8463,plain,
% 2.14/2.31 (((~r(s(s(s(s(z)))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(z, s(s(s(s(z)))))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(8464,plain,
% 2.14/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(z, s(s(s(s(z))))))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[8463])).
% 2.14/2.31 tff(8465,plain,
% 2.14/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(z, s(s(s(s(z)))))))),
% 2.14/2.31 inference(transitivity,[status(thm)],[8464, 8462])).
% 2.14/2.31 tff(8466,plain,
% 2.14/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(z, s(s(s(s(z)))))))),
% 2.14/2.31 inference(quant_inst,[status(thm)],[])).
% 2.14/2.31 tff(8467,plain,
% 2.14/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(z, s(s(s(s(z))))))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[8466, 8465])).
% 2.14/2.31 tff(8468,plain,
% 2.14/2.31 ($false),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[8467, 183, 5973, 5864, 8384])).
% 2.14/2.31 tff(8469,plain,((~r(s(s(s(s(z)))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.31 tff(8470,plain,
% 2.14/2.31 (~r(s(s(s(s(z)))), s(elem!1))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[8469, 8298, 5864])).
% 2.14/2.31 tff(8471,plain,
% 2.14/2.31 (b(s(s(s(s(z)))), s(elem!1))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[1728, 8470, 8242])).
% 2.14/2.31 tff(8472,plain,
% 2.14/2.31 (b(s(elem!1), z)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[2581, 8449])).
% 2.14/2.31 tff(8473,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(8474,plain,
% 2.14/2.31 (((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(z, s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(8475,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[8474])).
% 2.14/2.31 tff(8476,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 2.14/2.31 inference(transitivity,[status(thm)],[8475, 8473])).
% 2.14/2.31 tff(8477,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.14/2.31 inference(quant_inst,[status(thm)],[])).
% 2.14/2.31 tff(8478,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[8477, 8476])).
% 2.14/2.31 tff(8479,plain,
% 2.14/2.31 ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[8478, 246, 236, 8472, 8237, 8293])).
% 2.14/2.31 tff(8480,plain,
% 2.14/2.31 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[8479, 8471])).
% 2.14/2.31 tff(8481,plain,
% 2.14/2.31 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[8213, 47, 8210, 8480])).
% 2.14/2.31 tff(8482,plain,
% 2.14/2.31 (~r(z, s(s(s(z))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[8400, 183, 8481, 8298])).
% 2.14/2.31 tff(8483,plain,
% 2.14/2.31 (b(z, s(s(s(z))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[6165, 8482])).
% 2.14/2.31 tff(8484,plain,
% 2.14/2.31 (~r(s(s(s(z))), z)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[8392, 183, 5864, 8481, 8298])).
% 2.14/2.31 tff(8485,plain,
% 2.14/2.31 (b(s(s(s(z))), z)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[995, 8484])).
% 2.14/2.31 tff(8486,plain,
% 2.14/2.31 ($false),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[4659, 8485, 8483, 4327, 8461])).
% 2.14/2.31 tff(8487,plain,((~r(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~(s(s(s(s(s(elem!1))))) = elem!1)) | (~(s(s(elem!1)) = elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.31 tff(8488,plain,
% 2.14/2.31 (~r(s(z), s(s(s(z))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[8487, 8291, 8245, 236, 8237, 7030, 2125, 8236, 4327, 5572])).
% 2.14/2.31 tff(8489,plain,
% 2.14/2.31 (b(s(z), s(s(s(z))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[1291, 8488])).
% 2.14/2.31 tff(8490,plain,
% 2.14/2.31 ($false),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[5730, 183, 430, 2593, 6095])).
% 2.14/2.31 tff(8491,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.31 tff(8492,plain,
% 2.14/2.31 (~r(s(s(s(s(z)))), s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[8491, 2593, 430])).
% 2.14/2.31 tff(8493,plain,
% 2.14/2.31 (b(s(s(s(s(z)))), s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[6103, 8492])).
% 2.14/2.31 tff(8494,plain,
% 2.14/2.31 (~r(s(z), s(s(s(z))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[8487, 2593, 5864, 236, 8237, 7030, 2125, 8299, 4327, 1056])).
% 2.14/2.31 tff(8495,plain,
% 2.14/2.31 (b(s(z), s(s(s(z))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[1291, 8494])).
% 2.14/2.31 tff(8496,plain,
% 2.14/2.31 (~b(z, s(s(s(s(z)))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[7673, 246, 1056, 236, 8493])).
% 2.14/2.31 tff(8497,plain,
% 2.14/2.31 ((z = s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[2645, 47, 8496])).
% 2.14/2.31 tff(8498,plain,
% 2.14/2.31 (r(z, s(s(s(s(z)))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[8497, 2635])).
% 2.14/2.31 tff(8499,plain,
% 2.14/2.31 (~r(s(s(s(s(z)))), s(elem!1))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[8469, 8498, 5864])).
% 2.14/2.31 tff(8500,plain,
% 2.14/2.31 (b(s(s(s(s(z)))), s(elem!1))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[1728, 8499, 8242])).
% 2.14/2.31 tff(8501,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z)))))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(8502,plain,
% 2.14/2.31 (((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z)))))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(8503,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z))))))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[8502])).
% 2.14/2.31 tff(8504,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z)))))))),
% 2.14/2.31 inference(transitivity,[status(thm)],[8503, 8501])).
% 2.14/2.31 tff(8505,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.14/2.31 inference(quant_inst,[status(thm)],[])).
% 2.14/2.31 tff(8506,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z))))))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[8505, 8504])).
% 2.14/2.31 tff(8507,plain,
% 2.14/2.31 (~b(z, s(s(s(s(z)))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[8506, 246, 236, 2401, 5914, 8237, 8267])).
% 2.14/2.31 tff(8508,plain,
% 2.14/2.31 ((z = s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[2645, 47, 8507])).
% 2.14/2.31 tff(8509,plain,
% 2.14/2.31 (r(z, s(s(s(s(z)))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[8508, 2635])).
% 2.14/2.31 tff(8510,plain,
% 2.14/2.31 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[8279, 246, 5914, 8237, 8299])).
% 2.14/2.31 tff(8511,plain,
% 2.14/2.31 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[8213, 47, 8210, 8510])).
% 2.14/2.31 tff(8512,plain,
% 2.14/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(8513,plain,
% 2.14/2.31 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(8514,plain,
% 2.14/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[8513])).
% 2.14/2.31 tff(8515,plain,
% 2.14/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 2.14/2.31 inference(transitivity,[status(thm)],[8514, 8512])).
% 2.14/2.31 tff(8516,plain,
% 2.14/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(8517,plain,
% 2.14/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[8516, 8515])).
% 2.14/2.32 tff(8518,plain,
% 2.14/2.32 ($false),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[8517, 183, 997, 8511, 8509])).
% 2.14/2.32 tff(8519,plain,((~b(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.32 tff(8520,plain,
% 2.14/2.32 (~r(s(s(s(z))), z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[8519, 8500, 8237, 8299, 236, 8495, 8493])).
% 2.14/2.32 tff(8521,plain,
% 2.14/2.32 (b(s(s(s(z))), z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[995, 8520])).
% 2.14/2.32 tff(8522,plain,
% 2.14/2.32 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[8279, 246, 8500, 8237, 8299])).
% 2.14/2.32 tff(8523,plain,
% 2.14/2.32 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[8213, 47, 8210, 8522])).
% 2.14/2.32 tff(8524,plain,
% 2.14/2.32 (~r(z, s(s(s(z))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[8400, 183, 8523, 8498])).
% 2.14/2.32 tff(8525,plain,
% 2.14/2.32 (b(z, s(s(s(z))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[6165, 8524])).
% 2.14/2.32 tff(8526,plain,
% 2.14/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(8527,plain,
% 2.14/2.32 (((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(8528,plain,
% 2.14/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[8527])).
% 2.14/2.32 tff(8529,plain,
% 2.14/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 2.14/2.32 inference(transitivity,[status(thm)],[8528, 8526])).
% 2.14/2.32 tff(8530,plain,
% 2.14/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(8531,plain,
% 2.14/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[8530, 8529])).
% 2.14/2.32 tff(8532,plain,
% 2.14/2.32 ($false),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[8531, 246, 236, 8495, 8525, 8521])).
% 2.14/2.32 tff(8533,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~r(z, s(elem!1))) | (~b(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~(s(s(s(s(s(elem!1))))) = elem!1)) | (~(s(s(elem!1)) = elem!1)) | (~b(s(s(s(z))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.32 tff(8534,plain,
% 2.14/2.32 (~r(s(s(s(z))), s(z))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[8533, 8291, 8237, 8236, 8245, 5572, 236, 7030, 2125, 4327])).
% 2.14/2.32 tff(8535,plain,
% 2.14/2.32 (b(s(s(s(z))), s(z))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[52, 8534])).
% 2.14/2.32 tff(8536,plain,
% 2.14/2.32 (~b(s(s(s(z))), z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2098, 8535, 5572, 236])).
% 2.14/2.32 tff(8537,plain,
% 2.14/2.32 (r(s(s(s(z))), z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[995, 8536])).
% 2.14/2.32 tff(8538,plain,
% 2.14/2.32 (~b(s(s(s(s(z)))), s(z))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[8519, 8537, 8237, 8236, 236, 8273, 8489])).
% 2.14/2.32 tff(8539,plain,
% 2.14/2.32 (r(s(s(s(s(z)))), s(z))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[6103, 8538])).
% 2.14/2.32 tff(8540,plain,
% 2.14/2.32 (~r(elem!1, s(s(s(s(z)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[7665, 8539, 474])).
% 2.14/2.32 tff(8541,plain,
% 2.14/2.32 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[8540, 7893])).
% 2.14/2.32 tff(8542,plain,
% 2.14/2.32 (b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[1897, 8541])).
% 2.14/2.32 tff(8543,plain,
% 2.14/2.32 (b(elem!1, s(s(s(s(z)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[8157, 8542, 2125, 8012])).
% 2.14/2.32 tff(8544,plain,
% 2.14/2.32 (b(s(elem!1), s(s(s(s(z)))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[8543, 8283])).
% 2.14/2.32 tff(8545,plain,
% 2.14/2.32 (~b(z, s(s(s(z))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[6174, 8535, 5572, 236])).
% 2.14/2.32 tff(8546,plain,
% 2.14/2.32 (r(z, s(s(s(z))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[6165, 8545])).
% 2.14/2.32 tff(8547,plain,
% 2.14/2.32 (~r(z, s(s(s(s(z)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2641, 183, 8546, 8291])).
% 2.14/2.32 tff(8548,plain,
% 2.14/2.32 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2645, 47, 8547])).
% 2.14/2.32 tff(8549,plain,
% 2.14/2.32 (b(z, s(s(s(s(z)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[8548, 2635])).
% 2.14/2.32 tff(8550,assumption,(b(z, s(s(s(s(z)))))), introduced(assumption)).
% 2.14/2.32 tff(8551,plain,
% 2.14/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(8552,plain,
% 2.14/2.32 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(8553,plain,
% 2.14/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[8552])).
% 2.14/2.32 tff(8554,plain,
% 2.14/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.14/2.32 inference(transitivity,[status(thm)],[8553, 8551])).
% 2.14/2.32 tff(8555,plain,
% 2.14/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(8556,plain,
% 2.14/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[8555, 8554])).
% 2.14/2.32 tff(8557,plain,
% 2.14/2.32 ($false),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[8556, 183, 997, 1908, 8215, 8326])).
% 2.14/2.32 tff(8558,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.32 tff(8559,plain,
% 2.14/2.32 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[8558, 8326, 8215, 997])).
% 2.14/2.32 tff(8560,plain,
% 2.14/2.32 (b(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[1531, 8559])).
% 2.14/2.32 tff(8561,plain,
% 2.14/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(8562,plain,
% 2.14/2.32 (((~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(8563,plain,
% 2.14/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), z))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[8562])).
% 2.14/2.32 tff(8564,plain,
% 2.14/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 2.14/2.32 inference(transitivity,[status(thm)],[8563, 8561])).
% 2.14/2.32 tff(8565,plain,
% 2.14/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(8566,plain,
% 2.14/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), z))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[8565, 8564])).
% 2.14/2.32 tff(8567,plain,
% 2.14/2.32 (~b(s(s(z)), z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[8566, 246, 8560, 5914, 8550, 8345])).
% 2.14/2.32 tff(8568,plain,
% 2.14/2.32 (r(s(s(z)), z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[3215, 47, 35, 8567])).
% 2.14/2.32 tff(8569,plain,
% 2.14/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(8570,plain,
% 2.14/2.32 (((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(8571,plain,
% 2.14/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[8570])).
% 2.14/2.32 tff(8572,plain,
% 2.14/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 2.14/2.32 inference(transitivity,[status(thm)],[8571, 8569])).
% 2.14/2.32 tff(8573,plain,
% 2.14/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(8574,plain,
% 2.14/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[8573, 8572])).
% 2.14/2.32 tff(8575,plain,
% 2.14/2.32 ($false),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[8574, 183, 997, 8326, 8568])).
% 2.14/2.32 tff(8576,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.32 tff(8577,plain,
% 2.14/2.32 (~r(s(s(z)), s(s(s(z))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[8576, 8537, 8273, 8549, 8544, 8281])).
% 2.14/2.32 tff(8578,plain,
% 2.14/2.32 (b(s(s(z)), s(s(s(z))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[8382, 8577])).
% 2.14/2.32 tff(8579,plain,
% 2.14/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(z)))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(8580,plain,
% 2.14/2.32 (((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(z))))) <=> ((~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(z)))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(8581,plain,
% 2.14/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(z))))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[8580])).
% 2.14/2.32 tff(8582,plain,
% 2.14/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(z)))))),
% 2.14/2.32 inference(transitivity,[status(thm)],[8581, 8579])).
% 2.14/2.32 tff(8583,plain,
% 2.14/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(z)))))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(8584,plain,
% 2.14/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(z))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[8583, 8582])).
% 2.14/2.32 tff(8585,plain,
% 2.14/2.32 (~b(s(elem!1), s(s(z)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[8584, 246, 8489, 8535, 8236, 8578])).
% 2.14/2.32 tff(8586,plain,
% 2.14/2.32 ((s(elem!1) = s(s(z))) | r(s(elem!1), s(s(z)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[8412, 47, 8585])).
% 2.14/2.32 tff(8587,plain,
% 2.14/2.32 (r(s(elem!1), s(s(z)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[8586, 8027])).
% 2.14/2.32 tff(8588,plain,
% 2.14/2.32 ((s(s(z)) = s(z)) <=> (s(z) = s(s(z)))),
% 2.14/2.32 inference(commutativity,[status(thm)],[])).
% 2.14/2.32 tff(8589,plain,
% 2.14/2.32 ((s(z) = s(s(z))) <=> (s(s(z)) = s(z))),
% 2.14/2.32 inference(symmetry,[status(thm)],[8588])).
% 2.14/2.32 tff(8590,plain,
% 2.14/2.32 ((~(s(z) = s(s(z)))) <=> (~(s(s(z)) = s(z)))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[8589])).
% 2.14/2.32 tff(8591,plain,
% 2.14/2.32 (~(s(s(z)) = s(z))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[8340, 8590])).
% 2.14/2.32 tff(8592,plain,
% 2.14/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(8593,plain,
% 2.14/2.32 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(8594,plain,
% 2.14/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z)))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[8593])).
% 2.14/2.32 tff(8595,plain,
% 2.14/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 2.14/2.32 inference(transitivity,[status(thm)],[8594, 8592])).
% 2.14/2.32 tff(8596,plain,
% 2.14/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(8597,plain,
% 2.14/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z)))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[8596, 8595])).
% 2.14/2.32 tff(8598,plain,
% 2.14/2.32 (~b(s(s(z)), s(z))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[8597, 246, 5572, 8489, 8535, 8578])).
% 2.14/2.32 tff(8599,plain,
% 2.14/2.32 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(8600,plain,
% 2.14/2.32 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(8601,plain,
% 2.14/2.32 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[8600, 8599])).
% 2.14/2.32 tff(8602,plain,
% 2.14/2.32 ((s(s(z)) = s(z)) | r(s(s(z)), s(z))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[8601, 47, 8598])).
% 2.14/2.32 tff(8603,plain,
% 2.14/2.32 (r(s(s(z)), s(z))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[8602, 8591])).
% 2.14/2.32 tff(8604,plain,
% 2.14/2.32 (r(s(elem!1), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[7986])).
% 2.14/2.32 tff(8605,plain,
% 2.14/2.32 (r(s(s(s(elem!1))), s(z)) <=> r(s(elem!1), s(z))),
% 2.14/2.32 inference(symmetry,[status(thm)],[8604])).
% 2.14/2.32 tff(8606,plain,
% 2.14/2.32 (s(s(s(elem!1))) = elem!1),
% 2.14/2.32 inference(transitivity,[status(thm)],[352, 7985, 343])).
% 2.14/2.32 tff(8607,plain,
% 2.14/2.32 (r(s(s(s(elem!1))), s(z)) <=> r(elem!1, s(z))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[8606])).
% 2.14/2.32 tff(8608,plain,
% 2.14/2.32 (r(elem!1, s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 2.14/2.32 inference(symmetry,[status(thm)],[8607])).
% 2.14/2.32 tff(8609,plain,
% 2.14/2.32 (r(s(s(s(elem!1))), s(z))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[474, 8608])).
% 2.14/2.32 tff(8610,plain,
% 2.14/2.32 (r(s(elem!1), s(z))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[8609, 8605])).
% 2.14/2.32 tff(8611,plain,
% 2.14/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(z)))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(8612,plain,
% 2.14/2.32 (((~r(s(s(z)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(z))))) <=> ((~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(z)))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(8613,plain,
% 2.14/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(z))))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[8612])).
% 2.14/2.33 tff(8614,plain,
% 2.14/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(z)))))),
% 2.14/2.33 inference(transitivity,[status(thm)],[8613, 8611])).
% 2.14/2.33 tff(8615,plain,
% 2.14/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(z)))))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(8616,plain,
% 2.14/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(z))))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[8615, 8614])).
% 2.14/2.33 tff(8617,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[8616, 183, 8610, 8603, 8587])).
% 2.14/2.33 tff(8618,plain,((~r(s(z), elem!1)) | (~(s(s(elem!1)) = elem!1)) | (~(s(s(s(s(s(elem!1))))) = elem!1)) | (~r(elem!1, s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(8619,plain,
% 2.14/2.33 (~r(s(z), elem!1)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[8618, 2125, 7030, 7976, 7995, 236, 7994, 7991, 267])).
% 2.14/2.33 tff(8620,plain,
% 2.14/2.33 (b(s(z), elem!1)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[1034, 8619, 7086])).
% 2.14/2.33 tff(8621,plain,
% 2.14/2.33 (~r(elem!1, s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[6196, 2003, 3697, 474, 2277, 267])).
% 2.14/2.33 tff(8622,plain,
% 2.14/2.33 (~b(elem!1, s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[6206, 2003, 3697, 1044])).
% 2.14/2.33 tff(8623,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[470, 8622, 8621, 1675])).
% 2.14/2.33 tff(8624,plain,((~b(s(s(s(z))), s(z))) | (elem!1 = s(s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~r(elem!1, s(z))) | (s(z) = elem!1) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(8625,plain,
% 2.14/2.33 (~b(s(s(s(z))), s(z))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[8624, 8620, 3697, 7868, 7976, 7086, 267])).
% 2.14/2.33 tff(8626,plain,
% 2.14/2.33 (r(s(s(s(z))), s(z))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[52, 8625])).
% 2.14/2.33 tff(8627,plain,
% 2.14/2.33 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[7762, 8626, 2133])).
% 2.14/2.33 tff(8628,plain,
% 2.14/2.33 (b(s(s(elem!1)), s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[454, 8627, 7847])).
% 2.14/2.33 tff(8629,plain,
% 2.14/2.33 (b(elem!1, s(s(s(z))))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[8628, 7977])).
% 2.14/2.33 tff(8630,plain,
% 2.14/2.33 (~r(s(z), z)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[6132, 8629, 236, 8620, 3697, 5401, 7976])).
% 2.14/2.33 tff(8631,plain,
% 2.14/2.33 (b(s(z), z)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[1069, 8630])).
% 2.14/2.33 tff(8632,plain,
% 2.14/2.33 (~b(elem!1, z)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[1064, 8631, 236, 8620])).
% 2.14/2.33 tff(8633,plain,
% 2.14/2.33 (r(elem!1, z)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[1143, 8632, 5401])).
% 2.14/2.33 tff(8634,plain,
% 2.14/2.33 (b(s(s(s(s(s(elem!1))))), elem!1) <=> b(elem!1, elem!1)),
% 2.14/2.33 inference(monotonicity,[status(thm)],[7030])).
% 2.14/2.33 tff(8635,plain,
% 2.14/2.33 (b(elem!1, elem!1) <=> b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.14/2.33 inference(symmetry,[status(thm)],[8634])).
% 2.14/2.33 tff(8636,plain,
% 2.14/2.33 ((~b(elem!1, elem!1)) <=> (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[8635])).
% 2.14/2.33 tff(8637,plain,
% 2.14/2.33 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[5691, 8636])).
% 2.14/2.33 tff(8638,plain,
% 2.14/2.33 (b(s(s(s(s(s(elem!1))))), elem!1) <=> b(s(elem!1), s(s(elem!1)))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[5861, 5380])).
% 2.14/2.33 tff(8639,plain,
% 2.14/2.33 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.14/2.33 inference(symmetry,[status(thm)],[8638])).
% 2.14/2.33 tff(8640,assumption,(s(elem!1) = s(s(s(z)))), introduced(assumption)).
% 2.14/2.33 tff(8641,plain,
% 2.14/2.33 (s(s(s(z))) = s(elem!1)),
% 2.14/2.33 inference(symmetry,[status(thm)],[8640])).
% 2.14/2.33 tff(8642,plain,
% 2.14/2.33 (b(s(s(s(z))), elem!1) <=> b(s(elem!1), s(s(elem!1)))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[8641, 5380])).
% 2.14/2.33 tff(8643,plain,
% 2.14/2.33 (b(s(s(s(z))), elem!1) <=> b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.14/2.33 inference(transitivity,[status(thm)],[8642, 8639])).
% 2.14/2.33 tff(8644,plain,
% 2.14/2.33 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[3697, 8643])).
% 2.14/2.33 tff(8645,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[82, 8644])).
% 2.14/2.33 tff(8646,plain,((~(s(elem!1) = s(s(s(z))))) | b(s(s(s(s(s(elem!1))))), elem!1) | (~b(s(s(s(z))), elem!1)) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(8647,plain,
% 2.14/2.33 (~(s(elem!1) = s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[8646, 2125, 8637, 3697])).
% 2.14/2.33 tff(8648,plain,
% 2.14/2.33 (r(s(s(s(elem!1))), s(z))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[7976, 8608])).
% 2.14/2.33 tff(8649,plain,
% 2.14/2.33 (~r(s(elem!1), s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[8093, 8626, 7591, 8648])).
% 2.14/2.33 tff(8650,plain,
% 2.14/2.33 (b(s(elem!1), s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[1754, 8649, 8647])).
% 2.14/2.33 tff(8651,plain,
% 2.14/2.33 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[8533, 8631, 7995, 8626, 8245, 8650, 236, 7030, 2125, 7994])).
% 2.14/2.33 tff(8652,plain,
% 2.14/2.33 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[1702, 8651])).
% 2.14/2.33 tff(8653,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[7715, 8652, 8633, 8620, 236, 8629, 7976, 7975, 3697])).
% 2.14/2.33 tff(8654,plain,((~(s(s(elem!1)) = elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), elem!1)) | (~(s(s(s(s(s(elem!1))))) = elem!1)) | (~r(z, elem!1)) | b(s(s(elem!1)), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(8655,plain,
% 2.14/2.33 (~(s(s(elem!1)) = elem!1)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[8654, 7971, 7965, 7812, 5365, 2124])).
% 2.14/2.33 tff(8656,plain,
% 2.14/2.33 (~(elem!1 = s(s(elem!1)))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[5450, 8655])).
% 2.14/2.33 tff(8657,plain,
% 2.14/2.33 (b(s(s(elem!1)), elem!1)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[156, 8655, 2232])).
% 2.14/2.33 tff(8658,plain,
% 2.14/2.33 (~r(s(z), elem!1)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[7331, 2001, 3697, 2124, 2232, 267])).
% 2.14/2.33 tff(8659,plain,
% 2.14/2.33 (b(s(z), elem!1)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[1034, 8658, 2277])).
% 2.14/2.33 tff(8660,plain,
% 2.14/2.33 (~b(s(s(s(z))), s(z))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[7339, 246, 8659, 2001, 3697])).
% 2.14/2.33 tff(8661,plain,
% 2.14/2.33 (r(s(s(s(z))), s(z))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[52, 8660])).
% 2.14/2.33 tff(8662,plain,
% 2.14/2.33 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[7807, 246, 8659, 2362, 2001, 3697])).
% 2.14/2.33 tff(8663,plain,
% 2.14/2.33 (r(s(s(elem!1)), s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[454, 8662, 5806])).
% 2.14/2.33 tff(8664,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[7762, 8663, 8661, 2133])).
% 2.14/2.33 tff(8665,plain,((~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (s(z) = elem!1) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), elem!1) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(8666,plain,
% 2.14/2.33 (~b(elem!1, s(z))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[8665, 8657, 7965, 7824, 2124, 2232, 5365])).
% 2.14/2.33 tff(8667,plain,
% 2.14/2.33 (r(elem!1, s(z))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[214, 8666, 7953])).
% 2.14/2.33 tff(8668,plain,
% 2.14/2.33 (~r(elem!1, s(s(elem!1)))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[4199, 8667, 2133])).
% 2.14/2.33 tff(8669,plain,
% 2.14/2.33 (b(elem!1, s(s(elem!1)))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[1268, 8668, 8656])).
% 2.14/2.33 tff(8670,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(8671,plain,
% 2.14/2.33 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(8672,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[8671])).
% 2.14/2.33 tff(8673,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))),
% 2.14/2.33 inference(transitivity,[status(thm)],[8672, 8670])).
% 2.14/2.33 tff(8674,plain,
% 2.14/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(8675,plain,
% 2.14/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[8674, 8673])).
% 2.14/2.33 tff(8676,plain,
% 2.14/2.33 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[8675, 246, 8657, 8669, 7965])).
% 2.14/2.33 tff(8677,plain,
% 2.14/2.33 (r(s(s(s(z))), s(s(elem!1)))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[689, 8676, 7825])).
% 2.14/2.33 tff(8678,plain,
% 2.14/2.33 (~(s(s(elem!1)) = s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[421, 7825])).
% 2.14/2.33 tff(8679,plain,
% 2.14/2.33 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[7757, 246, 8657, 8669, 7965])).
% 2.14/2.33 tff(8680,plain,
% 2.14/2.33 (r(s(s(elem!1)), s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[454, 8679, 8678])).
% 2.14/2.33 tff(8681,plain,
% 2.14/2.33 (~r(s(s(s(z))), s(z))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[7762, 8680, 2133])).
% 2.14/2.33 tff(8682,plain,
% 2.14/2.33 (b(s(s(s(z))), s(z))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[52, 8681])).
% 2.14/2.33 tff(8683,plain,
% 2.14/2.33 (~(elem!1 = s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[3013, 7826])).
% 2.14/2.33 tff(8684,plain,
% 2.14/2.33 (~b(s(z), elem!1)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[8624, 8682, 7965, 8683, 8667, 7824, 5365])).
% 2.14/2.33 tff(8685,plain,
% 2.14/2.33 (r(s(z), elem!1)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[1034, 8684, 7824])).
% 2.14/2.33 tff(8686,plain,
% 2.14/2.33 (~r(s(z), z)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[5432, 8685, 5365])).
% 2.14/2.33 tff(8687,plain,
% 2.14/2.33 (b(s(z), z)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[1069, 8686])).
% 2.14/2.33 tff(8688,plain,
% 2.14/2.33 (~b(z, s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[6174, 8687, 8682, 7971])).
% 2.14/2.33 tff(8689,plain,
% 2.14/2.33 (r(z, s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[6165, 8688])).
% 2.14/2.33 tff(8690,plain,
% 2.14/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(8691,plain,
% 2.14/2.33 (((~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), z))) <=> ((~r(s(s(elem!1)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(8692,plain,
% 2.14/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[8691])).
% 2.14/2.33 tff(8693,plain,
% 2.14/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.14/2.33 inference(transitivity,[status(thm)],[8692, 8690])).
% 2.14/2.33 tff(8694,plain,
% 2.14/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), z)))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(8695,plain,
% 2.14/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[8694, 8693])).
% 2.14/2.33 tff(8696,plain,
% 2.14/2.33 (~r(s(s(elem!1)), z)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[8695, 183, 8680, 8689])).
% 2.14/2.33 tff(8697,plain,
% 2.14/2.33 (b(s(s(elem!1)), z)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[523, 8696])).
% 2.14/2.33 tff(8698,plain,
% 2.14/2.33 (~b(s(z), s(s(elem!1)))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[5746, 246, 8687, 8697, 7971])).
% 2.14/2.33 tff(8699,plain,
% 2.14/2.33 (r(s(z), s(s(elem!1)))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[233, 8698])).
% 2.14/2.33 tff(8700,plain,
% 2.14/2.33 (~r(s(z), s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[6486, 183, 8699, 8677])).
% 2.14/2.33 tff(8701,plain,
% 2.14/2.33 (b(s(z), s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[1291, 8700])).
% 2.14/2.33 tff(8702,plain,
% 2.14/2.33 (~r(elem!1, s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[6196, 8682, 7965, 8667, 7824, 5365])).
% 2.14/2.33 tff(8703,plain,
% 2.14/2.33 (b(elem!1, s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[470, 8702, 8683])).
% 2.14/2.33 tff(8704,plain,
% 2.14/2.33 (elem!1 = s(s(s(s(s(elem!1)))))),
% 2.14/2.33 inference(symmetry,[status(thm)],[7812])).
% 2.14/2.33 tff(8705,plain,
% 2.14/2.33 ((s(s(s(s(z)))) = elem!1) <=> (s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[8704])).
% 2.14/2.33 tff(8706,plain,
% 2.14/2.33 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(z)))) = elem!1)),
% 2.14/2.33 inference(symmetry,[status(thm)],[8705])).
% 2.14/2.33 tff(8707,plain,
% 2.14/2.33 ((~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[8706])).
% 2.14/2.33 tff(8708,plain,
% 2.14/2.33 (~(s(s(s(s(z)))) = elem!1)),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[1501, 8707])).
% 2.14/2.33 tff(8709,assumption,(elem!1 = s(s(s(s(z))))), introduced(assumption)).
% 2.14/2.33 tff(8710,plain,
% 2.14/2.33 (s(s(s(s(z)))) = elem!1),
% 2.14/2.33 inference(symmetry,[status(thm)],[8709])).
% 2.14/2.33 tff(8711,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[3074, 8710])).
% 2.14/2.33 tff(8712,plain,((~(elem!1 = s(s(s(s(z)))))) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(8713,plain,
% 2.14/2.33 (~(elem!1 = s(s(s(s(z)))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[8712, 8708])).
% 2.14/2.33 tff(8714,assumption,(~(elem!1 = s(s(s(s(z)))))), introduced(assumption)).
% 2.14/2.33 tff(8715,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(8716,plain,
% 2.14/2.33 (((~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(8717,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[8716])).
% 2.14/2.33 tff(8718,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.14/2.33 inference(transitivity,[status(thm)],[8717, 8715])).
% 2.14/2.33 tff(8719,plain,
% 2.14/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(8720,plain,
% 2.14/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[8719, 8718])).
% 2.14/2.33 tff(8721,plain,
% 2.14/2.33 (~b(s(s(s(s(z)))), s(z))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[8720, 246, 2002, 3697, 2401, 1833])).
% 2.14/2.33 tff(8722,plain,
% 2.14/2.33 (r(s(s(s(s(z)))), s(z))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[6103, 8721])).
% 2.14/2.33 tff(8723,plain,
% 2.14/2.33 (~r(elem!1, s(s(s(s(z)))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[7665, 8722, 474])).
% 2.14/2.33 tff(8724,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[5969, 47, 6007, 8723, 8714])).
% 2.14/2.33 tff(8725,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (elem!1 = s(s(s(s(z))))) | (~r(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(8726,plain,
% 2.14/2.33 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[8725, 8713, 8667, 8703, 7965, 8701])).
% 2.14/2.33 tff(8727,plain,
% 2.14/2.33 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[1702, 8726])).
% 2.14/2.33 tff(8728,plain,
% 2.14/2.33 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[7861, 183, 8680, 8727])).
% 2.14/2.33 tff(8729,plain,
% 2.14/2.33 (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z)))))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[8728, 7820])).
% 2.14/2.33 tff(8730,plain,
% 2.14/2.33 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z)))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[7230, 8729, 7818])).
% 2.14/2.33 tff(8731,plain,
% 2.14/2.33 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[8730, 7817])).
% 2.14/2.33 tff(8732,plain,
% 2.14/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(8733,plain,
% 2.14/2.33 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(8734,plain,
% 2.14/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[8733])).
% 2.14/2.33 tff(8735,plain,
% 2.14/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 2.14/2.33 inference(transitivity,[status(thm)],[8734, 8732])).
% 2.14/2.33 tff(8736,plain,
% 2.14/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(8737,plain,
% 2.14/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[8736, 8735])).
% 2.14/2.33 tff(8738,plain,
% 2.14/2.33 (~r(s(s(s(s(z)))), z)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[8737, 183, 5365, 8689, 8727])).
% 2.14/2.33 tff(8739,plain,
% 2.14/2.33 (b(s(s(s(s(z)))), z)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[6040, 8738])).
% 2.14/2.33 tff(8740,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(8741,plain,
% 2.14/2.33 (((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(8742,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[8741])).
% 2.14/2.34 tff(8743,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 2.14/2.34 inference(transitivity,[status(thm)],[8742, 8740])).
% 2.14/2.34 tff(8744,plain,
% 2.14/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(8745,plain,
% 2.14/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[8744, 8743])).
% 2.14/2.34 tff(8746,plain,
% 2.14/2.34 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[8745, 246, 8687, 8697, 7971, 8739])).
% 2.14/2.34 tff(8747,plain,
% 2.14/2.34 ($false),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[8746, 8731])).
% 2.14/2.34 tff(8748,plain,(b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), elem!1) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.34 tff(8749,plain,
% 2.14/2.34 (b(s(s(elem!1)), s(z))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[8748, 2232, 55])).
% 2.14/2.34 tff(8750,plain,
% 2.14/2.34 (s(z) = elem!1),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[1034, 1445, 6385])).
% 2.14/2.34 tff(8751,plain,
% 2.14/2.34 ((s(s(s(s(s(elem!1))))) = s(z)) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 2.14/2.34 inference(monotonicity,[status(thm)],[8750])).
% 2.14/2.34 tff(8752,plain,
% 2.14/2.34 ((s(s(s(s(s(elem!1))))) = s(z)) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 2.14/2.34 inference(transitivity,[status(thm)],[8751, 124])).
% 2.14/2.34 tff(8753,plain,
% 2.14/2.34 ((~(s(s(s(s(s(elem!1))))) = s(z))) <=> (~(elem!1 = s(s(s(s(s(elem!1)))))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[8752])).
% 2.14/2.34 tff(8754,plain,
% 2.14/2.34 (~(elem!1 = s(s(s(s(s(elem!1))))))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[331, 8753])).
% 2.14/2.34 tff(8755,plain,
% 2.14/2.34 (elem!1 = s(z)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[6422, 1445, 55, 54, 6376])).
% 2.14/2.34 tff(8756,plain,
% 2.14/2.34 (s(s(s(z))) = s(s(elem!1))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[121, 8750])).
% 2.14/2.34 tff(8757,plain,
% 2.14/2.34 (~r(s(z), elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[6384, 171, 267])).
% 2.14/2.34 tff(8758,plain,
% 2.14/2.34 (b(s(z), elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[1034, 5374, 8757])).
% 2.14/2.34 tff(8759,plain,
% 2.14/2.34 (~r(elem!1, s(z))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[292, 171, 267])).
% 2.14/2.34 tff(8760,plain,
% 2.14/2.34 (b(elem!1, s(z))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[214, 5375, 8759])).
% 2.14/2.34 tff(8761,plain,
% 2.14/2.34 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5804, 5374])).
% 2.14/2.34 tff(8762,plain,
% 2.14/2.34 (~(s(s(elem!1)) = s(s(s(z))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[421, 8761])).
% 2.14/2.34 tff(8763,plain,
% 2.14/2.34 (~b(s(s(elem!1)), elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[3799, 8760, 201, 8758])).
% 2.14/2.34 tff(8764,plain,
% 2.14/2.34 (s(s(elem!1)) = elem!1),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[156, 8763, 2232])).
% 2.14/2.34 tff(8765,plain,
% 2.14/2.34 ((s(s(s(z))) = s(s(elem!1))) <=> (s(s(s(z))) = elem!1)),
% 2.14/2.34 inference(monotonicity,[status(thm)],[2125])).
% 2.14/2.34 tff(8766,plain,
% 2.14/2.34 ((s(s(s(z))) = s(s(elem!1))) <=> (elem!1 = s(s(s(z))))),
% 2.14/2.34 inference(transitivity,[status(thm)],[8765, 73])).
% 2.14/2.34 tff(8767,plain,
% 2.14/2.34 ((elem!1 = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 2.14/2.34 inference(symmetry,[status(thm)],[8766])).
% 2.14/2.34 tff(8768,plain,
% 2.14/2.34 ((elem!1 = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 2.14/2.34 inference(transitivity,[status(thm)],[8767, 3393])).
% 2.14/2.34 tff(8769,plain,
% 2.14/2.34 (s(s(elem!1)) = s(s(s(z)))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[2292, 8768])).
% 2.14/2.34 tff(8770,assumption,(~(s(s(elem!1)) = s(s(s(z))))), introduced(assumption)).
% 2.14/2.34 tff(8771,plain,
% 2.14/2.34 ($false),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[8770, 8769])).
% 2.14/2.34 tff(8772,plain,((~(elem!1 = s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z)))) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.34 tff(8773,plain,
% 2.14/2.34 (~(elem!1 = s(s(s(z))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[8772, 8764, 8762])).
% 2.14/2.34 tff(8774,plain,
% 2.14/2.34 (s(s(s(elem!1))) = s(elem!1)),
% 2.14/2.34 inference(monotonicity,[status(thm)],[8764])).
% 2.14/2.34 tff(8775,plain,
% 2.14/2.34 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[8774])).
% 2.14/2.34 tff(8776,plain,
% 2.14/2.34 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 2.14/2.34 inference(transitivity,[status(thm)],[8775, 2891])).
% 2.14/2.34 tff(8777,plain,
% 2.14/2.34 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[8776])).
% 2.14/2.34 tff(8778,plain,
% 2.14/2.34 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[6281, 8761])).
% 2.14/2.34 tff(8779,plain,
% 2.14/2.34 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[8778, 8777])).
% 2.14/2.34 tff(8780,plain,
% 2.14/2.34 (~(s(s(s(z))) = elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5385, 8764])).
% 2.14/2.34 tff(8781,plain,
% 2.14/2.34 (r(s(s(s(z))), elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[647, 8780, 1])).
% 2.14/2.34 tff(8782,plain,
% 2.14/2.34 (r(s(s(s(s(s(elem!1))))), elem!1) <=> r(s(elem!1), elem!1)),
% 2.14/2.34 inference(monotonicity,[status(thm)],[5861])).
% 2.14/2.34 tff(8783,plain,
% 2.14/2.34 ((~r(s(s(s(s(s(elem!1))))), elem!1)) <=> (~r(s(elem!1), elem!1))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[8782])).
% 2.14/2.34 tff(8784,plain,
% 2.14/2.34 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5485, 634, 267])).
% 2.14/2.34 tff(8785,plain,
% 2.14/2.34 (~r(s(elem!1), elem!1)),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[8784, 8783])).
% 2.14/2.34 tff(8786,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(8787,plain,
% 2.14/2.34 (((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(8788,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z))))))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[8787])).
% 2.14/2.34 tff(8789,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 2.14/2.34 inference(transitivity,[status(thm)],[8788, 8786])).
% 2.14/2.34 tff(8790,plain,
% 2.14/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(8791,plain,
% 2.14/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z))))))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[8790, 8789])).
% 2.14/2.34 tff(8792,plain,
% 2.14/2.34 (~b(z, s(s(s(s(z)))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[8791, 246, 4651, 2090, 1833])).
% 2.14/2.34 tff(8793,plain,
% 2.14/2.34 ((z = s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[2645, 47, 8792])).
% 2.14/2.34 tff(8794,plain,
% 2.14/2.34 (r(z, s(s(s(s(z)))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[8793, 2635])).
% 2.14/2.34 tff(8795,plain,
% 2.14/2.34 (~b(s(z), s(s(s(z))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[7450, 1833, 4651, 171, 2003])).
% 2.14/2.34 tff(8796,plain,
% 2.14/2.34 (r(s(z), s(s(s(z))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[1291, 8795])).
% 2.14/2.34 tff(8797,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(8798,plain,
% 2.14/2.34 (((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1)))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(8799,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1)))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[8798])).
% 2.14/2.34 tff(8800,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))))),
% 2.14/2.34 inference(transitivity,[status(thm)],[8799, 8797])).
% 2.14/2.34 tff(8801,plain,
% 2.14/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(8802,plain,
% 2.14/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1)))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[8801, 8800])).
% 2.14/2.34 tff(8803,plain,
% 2.14/2.34 (~b(s(z), s(elem!1))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[8802, 246, 1044, 2001, 1200])).
% 2.14/2.34 tff(8804,plain,
% 2.14/2.34 ((s(z) = s(elem!1)) | r(s(z), s(elem!1))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[2973, 47, 8803])).
% 2.14/2.34 tff(8805,plain,
% 2.14/2.34 (r(s(z), s(elem!1))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[8804, 6053])).
% 2.14/2.34 tff(8806,plain,
% 2.14/2.34 ((s(elem!1) = s(z)) | r(s(elem!1), s(z))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[2989, 47, 6959])).
% 2.14/2.34 tff(8807,plain,
% 2.14/2.34 (r(s(elem!1), s(z))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[8806, 7631])).
% 2.14/2.34 tff(8808,plain,
% 2.14/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(elem!1))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(8809,plain,
% 2.14/2.34 (((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(elem!1))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(8810,plain,
% 2.14/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(elem!1)))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[8809])).
% 2.14/2.34 tff(8811,plain,
% 2.14/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(elem!1))))),
% 2.14/2.34 inference(transitivity,[status(thm)],[8810, 8808])).
% 2.14/2.34 tff(8812,plain,
% 2.14/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(elem!1))))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(8813,plain,
% 2.14/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(elem!1)))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[8812, 8811])).
% 2.14/2.34 tff(8814,plain,
% 2.14/2.34 (~r(z, s(elem!1))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[8813, 183, 171, 8807])).
% 2.14/2.34 tff(8815,plain,
% 2.14/2.34 (b(z, s(elem!1))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[2561, 8814])).
% 2.14/2.34 tff(8816,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(z))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(8817,plain,
% 2.14/2.34 (((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(elem!1)))) <=> ((~b(s(z), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(z))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(8818,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(z)))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[8817])).
% 2.14/2.34 tff(8819,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(z))))),
% 2.14/2.34 inference(transitivity,[status(thm)],[8818, 8816])).
% 2.14/2.34 tff(8820,plain,
% 2.14/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(elem!1))))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(8821,plain,
% 2.14/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(z)))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[8820, 8819])).
% 2.14/2.34 tff(8822,plain,
% 2.14/2.34 ((~b(s(elem!1), s(s(s(z))))) | (~b(z, s(elem!1)))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[8821, 246, 1044, 2003, 4651, 1200])).
% 2.14/2.34 tff(8823,plain,
% 2.14/2.34 (~b(s(elem!1), s(s(s(z))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[8822, 8815])).
% 2.14/2.34 tff(8824,plain,
% 2.14/2.34 (r(s(elem!1), s(s(s(z))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[1754, 8823, 5896])).
% 2.14/2.34 tff(8825,plain,
% 2.14/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(8826,plain,
% 2.14/2.34 (((~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(elem!1)))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(8827,plain,
% 2.14/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(z)))))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[8826])).
% 2.14/2.34 tff(8828,plain,
% 2.14/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))))),
% 2.14/2.34 inference(transitivity,[status(thm)],[8827, 8825])).
% 2.14/2.34 tff(8829,plain,
% 2.14/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(elem!1))))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(8830,plain,
% 2.14/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(z)))))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[8829, 8828])).
% 2.14/2.34 tff(8831,plain,
% 2.14/2.34 ($false),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[8830, 183, 6096, 8824, 8805])).
% 2.14/2.34 tff(8832,plain,((~b(s(elem!1), elem!1)) | (~r(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~r(z, s(z))) | (~(s(s(elem!1)) = elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.34 tff(8833,plain,
% 2.14/2.34 (~b(s(elem!1), elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[8832, 8796, 1044, 2003, 4651, 171, 2125, 2001])).
% 2.14/2.34 tff(8834,plain,
% 2.14/2.34 (s(elem!1) = elem!1),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5655, 8833, 4448])).
% 2.14/2.34 tff(8835,plain,
% 2.14/2.34 (elem!1 = s(elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[3953, 8834])).
% 2.14/2.34 tff(8836,plain,
% 2.14/2.34 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(elem!1))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[8835])).
% 2.14/2.34 tff(8837,plain,
% 2.14/2.34 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), elem!1)),
% 2.14/2.34 inference(symmetry,[status(thm)],[8836])).
% 2.14/2.34 tff(8838,plain,
% 2.14/2.34 (s(elem!1) = elem!1),
% 2.14/2.34 inference(symmetry,[status(thm)],[8835])).
% 2.14/2.34 tff(8839,plain,
% 2.14/2.34 (r(z, s(elem!1)) <=> r(z, elem!1)),
% 2.14/2.34 inference(monotonicity,[status(thm)],[8838])).
% 2.14/2.34 tff(8840,plain,
% 2.14/2.34 (r(z, elem!1) <=> r(z, s(elem!1))),
% 2.14/2.34 inference(symmetry,[status(thm)],[8839])).
% 2.14/2.34 tff(8841,plain,
% 2.14/2.34 (r(z, s(elem!1))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[267, 8840])).
% 2.14/2.34 tff(8842,plain,
% 2.14/2.34 (~r(s(s(s(s(z)))), s(elem!1))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[8469, 8841, 8794])).
% 2.14/2.34 tff(8843,plain,
% 2.14/2.34 (b(s(s(s(s(z)))), s(elem!1))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[1728, 8842, 6006])).
% 2.14/2.34 tff(8844,plain,
% 2.14/2.34 (b(s(s(s(s(z)))), elem!1)),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[8843, 8837])).
% 2.14/2.34 tff(8845,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(8846,plain,
% 2.14/2.34 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(8847,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[8846])).
% 2.14/2.34 tff(8848,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.14/2.34 inference(transitivity,[status(thm)],[8847, 8845])).
% 2.14/2.35 tff(8849,plain,
% 2.14/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(8850,plain,
% 2.14/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[8849, 8848])).
% 2.14/2.35 tff(8851,plain,
% 2.14/2.35 (~b(s(s(s(s(z)))), s(z))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[8850, 246, 1044, 2001, 8844])).
% 2.14/2.35 tff(8852,plain,
% 2.14/2.35 (r(s(s(s(s(z)))), s(z))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[6103, 8851])).
% 2.14/2.35 tff(8853,plain,
% 2.14/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(8854,plain,
% 2.14/2.35 (((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(8855,plain,
% 2.14/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[8854])).
% 2.14/2.35 tff(8856,plain,
% 2.14/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 2.14/2.35 inference(transitivity,[status(thm)],[8855, 8853])).
% 2.14/2.35 tff(8857,plain,
% 2.14/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(8858,plain,
% 2.14/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[8857, 8856])).
% 2.14/2.35 tff(8859,plain,
% 2.14/2.35 ($false),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[8858, 183, 171, 8852, 8794])).
% 2.14/2.35 tff(8860,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (s(s(s(s(z)))) = s(elem!1)) | (~r(z, elem!1)) | r(s(elem!1), elem!1) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~(s(s(elem!1)) = elem!1)) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.35 tff(8861,plain,
% 2.14/2.35 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[8860, 2003, 1044, 2001, 6006, 267, 8785, 171, 7911, 2125, 5413])).
% 2.14/2.35 tff(8862,plain,
% 2.14/2.35 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[1702, 8861])).
% 2.14/2.35 tff(8863,plain,
% 2.14/2.35 (~b(elem!1, s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2011, 2003, 2001, 1044])).
% 2.14/2.35 tff(8864,plain,
% 2.14/2.35 (r(elem!1, s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[470, 8863, 1675])).
% 2.14/2.35 tff(8865,plain,
% 2.14/2.35 (~r(s(s(s(s(z)))), elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2618, 183, 8864, 8862])).
% 2.14/2.35 tff(8866,plain,
% 2.14/2.35 (b(s(s(s(s(z)))), elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2442, 47, 7592, 8865])).
% 2.14/2.35 tff(8867,plain,
% 2.14/2.35 (~(elem!1 = s(s(s(s(z)))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[8712, 7592])).
% 2.14/2.35 tff(8868,plain,
% 2.14/2.35 (~r(elem!1, s(s(s(s(z)))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[7165, 183, 8864, 8862])).
% 2.14/2.35 tff(8869,plain,
% 2.14/2.35 (b(elem!1, s(s(s(s(z)))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5969, 47, 8868, 8867])).
% 2.14/2.35 tff(8870,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(8871,plain,
% 2.14/2.35 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(8872,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z))))))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[8871])).
% 2.14/2.35 tff(8873,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.14/2.35 inference(transitivity,[status(thm)],[8872, 8870])).
% 2.14/2.35 tff(8874,plain,
% 2.14/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(8875,plain,
% 2.14/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z))))))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[8874, 8873])).
% 2.14/2.35 tff(8876,plain,
% 2.14/2.35 (~b(s(s(s(s(z)))), s(z))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[8875, 246, 1044, 8869, 8866])).
% 2.14/2.35 tff(8877,plain,
% 2.14/2.35 (r(s(s(s(s(z)))), s(z))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[6103, 8876])).
% 2.14/2.35 tff(8878,plain,
% 2.14/2.35 (~r(s(s(s(s(z)))), z)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[6502, 183, 267, 171, 8877])).
% 2.14/2.35 tff(8879,plain,
% 2.14/2.35 (b(s(s(s(s(z)))), z)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[6040, 8878])).
% 2.14/2.35 tff(8880,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(8881,plain,
% 2.14/2.35 (((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(8882,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[8881])).
% 2.14/2.35 tff(8883,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 2.14/2.35 inference(transitivity,[status(thm)],[8882, 8880])).
% 2.14/2.35 tff(8884,plain,
% 2.14/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(8885,plain,
% 2.14/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[8884, 8883])).
% 2.14/2.35 tff(8886,plain,
% 2.14/2.35 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[8885, 246, 7911, 5413, 8879])).
% 2.14/2.35 tff(8887,plain,
% 2.14/2.35 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[8213, 47, 8210, 8886])).
% 2.14/2.35 tff(8888,plain,
% 2.14/2.35 ((elem!1 = s(elem!1)) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 2.14/2.35 inference(symmetry,[status(thm)],[7587])).
% 2.14/2.35 tff(8889,plain,
% 2.14/2.35 ((elem!1 = s(elem!1)) <=> (s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.14/2.35 inference(transitivity,[status(thm)],[8888, 7004])).
% 2.14/2.35 tff(8890,plain,
% 2.14/2.35 (r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 2.14/2.35 inference(symmetry,[status(thm)],[5927])).
% 2.14/2.35 tff(8891,plain,
% 2.14/2.35 (b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[5861])).
% 2.14/2.35 tff(8892,plain,
% 2.14/2.35 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 2.14/2.35 inference(symmetry,[status(thm)],[8891])).
% 2.14/2.35 tff(8893,plain,
% 2.14/2.35 ((~b(s(elem!1), s(s(s(s(z)))))) <=> (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[8892])).
% 2.14/2.35 tff(8894,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(8895,plain,
% 2.14/2.35 (((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(z))))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(8896,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[8895])).
% 2.14/2.35 tff(8897,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.14/2.35 inference(transitivity,[status(thm)],[8896, 8894])).
% 2.14/2.35 tff(8898,plain,
% 2.14/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(8899,plain,
% 2.14/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z))))))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[8898, 8897])).
% 2.14/2.35 tff(8900,plain,
% 2.14/2.35 (~b(s(elem!1), s(s(s(s(z)))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[8899, 246, 1044, 2001, 1200, 5913])).
% 2.14/2.35 tff(8901,plain,
% 2.14/2.35 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[8900, 8893])).
% 2.14/2.35 tff(8902,plain,
% 2.14/2.35 (r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[1897, 8901])).
% 2.14/2.35 tff(8903,plain,
% 2.14/2.35 (r(s(elem!1), s(s(s(s(z)))))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[8902, 8890])).
% 2.14/2.35 tff(8904,plain,
% 2.14/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(8905,plain,
% 2.14/2.35 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z)))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(8906,plain,
% 2.14/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[8905])).
% 2.14/2.35 tff(8907,plain,
% 2.14/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.14/2.35 inference(transitivity,[status(thm)],[8906, 8904])).
% 2.14/2.35 tff(8908,plain,
% 2.14/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(8909,plain,
% 2.14/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[8908, 8907])).
% 2.14/2.35 tff(8910,plain,
% 2.14/2.35 (~r(s(elem!1), s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[8909, 183, 634, 8215, 8903])).
% 2.14/2.35 tff(8911,plain,
% 2.14/2.35 (b(s(elem!1), s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[1754, 8910, 5896])).
% 2.14/2.35 tff(8912,plain,
% 2.14/2.35 (~b(z, s(elem!1))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[8822, 8911])).
% 2.14/2.35 tff(8913,plain,
% 2.14/2.35 (r(z, s(elem!1))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2561, 8912])).
% 2.14/2.35 tff(8914,plain,
% 2.14/2.35 ($false),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[8813, 183, 171, 8913, 8807])).
% 2.14/2.35 tff(8915,plain,((~b(s(elem!1), elem!1)) | (~r(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~(s(s(elem!1)) = elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.35 tff(8916,plain,
% 2.14/2.35 (~b(s(elem!1), elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[8915, 2003, 1044, 171, 7911, 634, 8887, 2125, 2001, 8866])).
% 2.14/2.35 tff(8917,plain,
% 2.14/2.35 (s(elem!1) = elem!1),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5655, 8916, 8785])).
% 2.14/2.35 tff(8918,plain,
% 2.14/2.35 (elem!1 = s(elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[3953, 8917])).
% 2.14/2.35 tff(8919,plain,
% 2.14/2.35 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[8918, 8889])).
% 2.14/2.35 tff(8920,plain,
% 2.14/2.35 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (elem!1 = s(elem!1))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[2125, 5858])).
% 2.14/2.35 tff(8921,plain,
% 2.14/2.35 ((elem!1 = s(elem!1)) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 2.14/2.35 inference(symmetry,[status(thm)],[8920])).
% 2.14/2.35 tff(8922,plain,
% 2.14/2.35 (s(s(elem!1)) = s(s(s(elem!1)))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[8918, 8921])).
% 2.14/2.35 tff(8923,plain,
% 2.14/2.35 (~(s(s(s(elem!1))) = s(s(z)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[8025, 8922, 8919])).
% 2.14/2.35 tff(8924,plain,
% 2.14/2.35 (r(s(s(s(elem!1))), z) <=> r(s(elem!1), z)),
% 2.14/2.35 inference(monotonicity,[status(thm)],[5858])).
% 2.14/2.35 tff(8925,plain,
% 2.14/2.35 (r(s(elem!1), z) <=> r(s(s(s(elem!1))), z)),
% 2.14/2.35 inference(symmetry,[status(thm)],[8924])).
% 2.14/2.35 tff(8926,plain,
% 2.14/2.35 (elem!1 = s(elem!1)),
% 2.14/2.35 inference(symmetry,[status(thm)],[8917])).
% 2.14/2.35 tff(8927,plain,
% 2.14/2.35 (r(elem!1, z) <=> r(s(elem!1), z)),
% 2.14/2.35 inference(monotonicity,[status(thm)],[8926])).
% 2.14/2.35 tff(8928,plain,
% 2.14/2.35 (r(elem!1, z) <=> r(s(s(s(elem!1))), z)),
% 2.14/2.35 inference(transitivity,[status(thm)],[8927, 8925])).
% 2.14/2.35 tff(8929,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(8930,plain,
% 2.14/2.36 (((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(8931,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[8930])).
% 2.14/2.36 tff(8932,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 2.14/2.36 inference(transitivity,[status(thm)],[8931, 8929])).
% 2.14/2.36 tff(8933,plain,
% 2.14/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(8934,plain,
% 2.14/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[8933, 8932])).
% 2.14/2.36 tff(8935,plain,
% 2.14/2.36 (~b(elem!1, z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[8934, 246, 2001, 2003, 7911, 8879, 8866])).
% 2.14/2.36 tff(8936,plain,
% 2.14/2.36 (r(elem!1, z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[1143, 8935, 5401])).
% 2.14/2.36 tff(8937,plain,
% 2.14/2.36 (r(s(s(s(elem!1))), z)),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[8936, 8928])).
% 2.14/2.36 tff(8938,plain,
% 2.14/2.36 (~r(z, s(s(s(s(z)))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[8858, 183, 171, 8877])).
% 2.14/2.36 tff(8939,plain,
% 2.14/2.36 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z)))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[2645, 47, 8938])).
% 2.14/2.36 tff(8940,plain,
% 2.14/2.36 (b(z, s(s(s(s(z)))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[8939, 2635])).
% 2.14/2.36 tff(8941,plain,
% 2.14/2.36 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5858])).
% 2.14/2.36 tff(8942,plain,
% 2.14/2.36 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.14/2.36 inference(symmetry,[status(thm)],[8941])).
% 2.14/2.36 tff(8943,plain,
% 2.14/2.36 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(elem!1))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[8926])).
% 2.14/2.36 tff(8944,plain,
% 2.14/2.36 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.14/2.36 inference(transitivity,[status(thm)],[8943, 8942])).
% 2.14/2.36 tff(8945,plain,
% 2.14/2.36 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[8866, 8944])).
% 2.14/2.36 tff(8946,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(8947,plain,
% 2.14/2.36 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(8948,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[8947])).
% 2.14/2.36 tff(8949,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 2.14/2.36 inference(transitivity,[status(thm)],[8948, 8946])).
% 2.14/2.36 tff(8950,plain,
% 2.14/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(8951,plain,
% 2.14/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[8950, 8949])).
% 2.14/2.36 tff(8952,plain,
% 2.14/2.36 (~b(s(s(z)), z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[8951, 246, 4651, 3457, 8550, 8266])).
% 2.14/2.36 tff(8953,plain,
% 2.14/2.36 (r(s(s(z)), z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[3215, 47, 35, 8952])).
% 2.14/2.36 tff(8954,plain,
% 2.14/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(8955,plain,
% 2.14/2.36 (((~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(8956,plain,
% 2.14/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[8955])).
% 2.14/2.36 tff(8957,plain,
% 2.14/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.14/2.36 inference(transitivity,[status(thm)],[8956, 8954])).
% 2.14/2.36 tff(8958,plain,
% 2.14/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(8959,plain,
% 2.14/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z))))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[8958, 8957])).
% 2.14/2.36 tff(8960,plain,
% 2.14/2.36 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[8959, 183, 4281, 8953])).
% 2.14/2.36 tff(8961,plain,
% 2.14/2.36 (s(s(s(elem!1))) = elem!1),
% 2.14/2.36 inference(transitivity,[status(thm)],[352, 349, 343])).
% 2.14/2.36 tff(8962,plain,
% 2.14/2.36 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[8961])).
% 2.14/2.36 tff(8963,plain,
% 2.14/2.36 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.14/2.36 inference(symmetry,[status(thm)],[8962])).
% 2.14/2.36 tff(8964,assumption,(b(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 2.14/2.36 tff(8965,plain,
% 2.14/2.36 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[8964, 8963])).
% 2.14/2.36 tff(8966,assumption,(b(s(s(s(s(z)))), s(s(s(elem!1))))), introduced(assumption)).
% 2.14/2.36 tff(8967,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(8968,plain,
% 2.14/2.36 (((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(8969,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[8968])).
% 2.14/2.36 tff(8970,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.14/2.36 inference(transitivity,[status(thm)],[8969, 8967])).
% 2.14/2.36 tff(8971,plain,
% 2.14/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(8972,plain,
% 2.14/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[8971, 8970])).
% 2.14/2.36 tff(8973,plain,
% 2.14/2.36 ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[8972, 246, 3457, 8966])).
% 2.14/2.36 tff(8974,plain,
% 2.14/2.36 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[8973, 8965])).
% 2.14/2.36 tff(8975,plain,
% 2.14/2.36 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z))) | r(s(s(s(elem!1))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z))) | r(s(s(s(elem!1))), s(s(z))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(8976,plain,
% 2.14/2.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z))) | r(s(s(s(elem!1))), s(s(z))))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(8977,plain,
% 2.14/2.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z))) | r(s(s(s(elem!1))), s(s(z)))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[8976, 8975])).
% 2.14/2.36 tff(8978,plain,
% 2.14/2.36 ($false),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[8977, 47, 8300, 8974, 8960])).
% 2.14/2.36 tff(8979,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (s(s(s(elem!1))) = s(s(z))) | (~r(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))) | (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.36 tff(8980,plain,
% 2.14/2.36 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[8979, 8945, 7911, 8940, 8869, 8919, 8937, 8879, 8923])).
% 2.14/2.36 tff(8981,plain,
% 2.14/2.36 (r(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[1531, 8980])).
% 2.14/2.36 tff(8982,plain,
% 2.14/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(8983,plain,
% 2.14/2.36 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(8984,plain,
% 2.14/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[8983])).
% 2.14/2.36 tff(8985,plain,
% 2.14/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.14/2.36 inference(transitivity,[status(thm)],[8984, 8982])).
% 2.14/2.36 tff(8986,plain,
% 2.14/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(8987,plain,
% 2.14/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[8986, 8985])).
% 2.14/2.36 tff(8988,plain,
% 2.14/2.36 (~r(s(s(s(z))), s(s(z)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[8987, 183, 8981, 8887])).
% 2.14/2.36 tff(8989,plain,
% 2.14/2.36 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(8990,plain,
% 2.14/2.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z))))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(8991,plain,
% 2.14/2.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[8990, 8989])).
% 2.14/2.36 tff(8992,plain,
% 2.14/2.36 (b(s(s(s(z))), s(s(z)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[8991, 47, 8374, 8988])).
% 2.14/2.36 tff(8993,plain,
% 2.14/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(8994,plain,
% 2.14/2.36 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(8995,plain,
% 2.14/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[8994])).
% 2.14/2.36 tff(8996,plain,
% 2.14/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.14/2.36 inference(transitivity,[status(thm)],[8995, 8993])).
% 2.14/2.36 tff(8997,plain,
% 2.14/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(8998,plain,
% 2.14/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[8997, 8996])).
% 2.14/2.37 tff(8999,plain,
% 2.14/2.37 (~r(s(s(z)), s(s(s(z))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[8998, 183, 634, 8981, 8887])).
% 2.14/2.37 tff(9000,plain,
% 2.14/2.37 (b(s(s(z)), s(s(s(z))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[8382, 8999])).
% 2.14/2.37 tff(9001,plain,
% 2.14/2.37 (~r(s(z), s(s(s(z))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[6098, 8877, 8862])).
% 2.14/2.37 tff(9002,plain,
% 2.14/2.37 (b(s(z), s(s(s(z))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[1291, 9001])).
% 2.14/2.37 tff(9003,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(9004,plain,
% 2.14/2.37 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(9005,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z))))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[9004])).
% 2.14/2.37 tff(9006,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))))),
% 2.14/2.37 inference(transitivity,[status(thm)],[9005, 9003])).
% 2.14/2.37 tff(9007,plain,
% 2.14/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(9008,plain,
% 2.14/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z))))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[9007, 9006])).
% 2.14/2.37 tff(9009,plain,
% 2.14/2.37 (~b(s(z), s(s(z)))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9008, 246, 9002, 9000, 8992])).
% 2.14/2.37 tff(9010,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(9011,plain,
% 2.14/2.37 (((~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(9012,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[9011])).
% 2.14/2.37 tff(9013,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.14/2.37 inference(transitivity,[status(thm)],[9012, 9010])).
% 2.14/2.37 tff(9014,plain,
% 2.14/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(9015,plain,
% 2.14/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[9014, 9013])).
% 2.14/2.37 tff(9016,plain,
% 2.14/2.37 (~b(s(z), z)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9015, 246, 9002, 2003, 7911])).
% 2.14/2.37 tff(9017,plain,
% 2.14/2.37 (r(s(z), z)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[1069, 9016])).
% 2.14/2.37 tff(9018,assumption,(~b(s(z), s(s(z)))), introduced(assumption)).
% 2.14/2.37 tff(9019,plain,
% 2.14/2.37 (r(s(z), s(s(z)))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[8343, 47, 8340, 9018])).
% 2.14/2.37 tff(9020,assumption,(r(s(s(z)), z)), introduced(assumption)).
% 2.14/2.37 tff(9021,plain,
% 2.14/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(9022,plain,
% 2.14/2.37 (((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(9023,plain,
% 2.14/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[9022])).
% 2.14/2.37 tff(9024,plain,
% 2.14/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 2.14/2.37 inference(transitivity,[status(thm)],[9023, 9021])).
% 2.14/2.37 tff(9025,plain,
% 2.14/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(9026,plain,
% 2.14/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[9025, 9024])).
% 2.14/2.37 tff(9027,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9026, 183, 1114, 9020, 9019])).
% 2.14/2.37 tff(9028,plain,((~r(s(s(z)), z)) | (~r(s(z), z)) | b(s(z), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(9029,plain,
% 2.14/2.37 (~r(s(s(z)), z)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9028, 9017, 9009])).
% 2.14/2.37 tff(9030,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(9031,plain,
% 2.14/2.37 (((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(9032,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[9031])).
% 2.14/2.37 tff(9033,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.14/2.37 inference(transitivity,[status(thm)],[9032, 9030])).
% 2.14/2.37 tff(9034,plain,
% 2.14/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(9035,plain,
% 2.14/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[9034, 9033])).
% 2.14/2.37 tff(9036,plain,
% 2.14/2.37 (~b(s(s(z)), z)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9035, 246, 7911, 9000, 8992])).
% 2.14/2.37 tff(9037,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[3215, 47, 35, 9036, 9029])).
% 2.14/2.37 tff(9038,plain,((~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~(s(s(elem!1)) = elem!1)) | (~b(s(z), elem!1)) | (~r(z, s(z))) | (~b(elem!1, s(z))) | (~r(z, elem!1)) | (s(s(s(s(z)))) = s(elem!1)) | (elem!1 = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(9039,plain,
% 2.14/2.37 (~b(s(s(s(z))), s(z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9038, 8781, 8764, 8758, 171, 8760, 267, 8779, 8773])).
% 2.14/2.37 tff(9040,plain,
% 2.14/2.37 (r(s(s(s(z))), s(z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[52, 9039])).
% 2.14/2.37 tff(9041,plain,
% 2.14/2.37 (elem!1 = s(s(elem!1))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[6867, 8764])).
% 2.14/2.37 tff(9042,plain,
% 2.14/2.37 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[8774])).
% 2.14/2.37 tff(9043,plain,
% 2.14/2.37 (s(s(s(s(elem!1)))) = elem!1),
% 2.14/2.37 inference(transitivity,[status(thm)],[9042, 8764])).
% 2.14/2.37 tff(9044,plain,
% 2.14/2.37 (s(s(s(s(s(elem!1))))) = s(elem!1)),
% 2.14/2.37 inference(monotonicity,[status(thm)],[9043])).
% 2.14/2.37 tff(9045,plain,
% 2.14/2.37 ((s(s(s(s(s(elem!1))))) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[9044])).
% 2.14/2.37 tff(9046,plain,
% 2.14/2.37 ((~(s(s(s(s(s(elem!1))))) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[9045])).
% 2.14/2.37 tff(9047,plain,
% 2.14/2.37 (~(s(elem!1) = s(s(s(z))))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[1622, 9046])).
% 2.14/2.37 tff(9048,plain,
% 2.14/2.37 (~(s(s(s(s(z)))) = elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[2399, 9047, 9041])).
% 2.14/2.37 tff(9049,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[8850, 246, 1044, 2001, 8267, 5913])).
% 2.14/2.37 tff(9050,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(9051,plain,
% 2.14/2.37 (~b(s(s(s(s(z)))), elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9050, 8493, 2001, 1044])).
% 2.14/2.37 tff(9052,plain,
% 2.14/2.37 (r(s(s(s(s(z)))), elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[2442, 47, 3074, 9051])).
% 2.14/2.37 tff(9053,plain,
% 2.14/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(9054,plain,
% 2.14/2.37 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(9055,plain,
% 2.14/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[9054])).
% 2.14/2.37 tff(9056,plain,
% 2.14/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.14/2.37 inference(transitivity,[status(thm)],[9055, 9053])).
% 2.14/2.37 tff(9057,plain,
% 2.14/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(9058,plain,
% 2.14/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[9057, 9056])).
% 2.14/2.37 tff(9059,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9058, 183, 634, 2593, 9052])).
% 2.14/2.37 tff(9060,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (s(s(s(s(z)))) = elem!1) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(9061,plain,
% 2.14/2.37 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9060, 8781, 9048, 8760, 8758, 9040])).
% 2.14/2.37 tff(9062,plain,
% 2.14/2.37 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[1702, 9061])).
% 2.14/2.37 tff(9063,plain,
% 2.14/2.37 (~r(s(s(s(z))), z)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[5411, 183, 267, 8781])).
% 2.14/2.37 tff(9064,plain,
% 2.14/2.37 (b(s(s(s(z))), z)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[995, 9063])).
% 2.14/2.37 tff(9065,plain,
% 2.14/2.37 (~r(z, s(s(s(z))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[6592, 8781, 267])).
% 2.14/2.37 tff(9066,plain,
% 2.14/2.37 (b(z, s(s(s(z))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[6165, 9065])).
% 2.14/2.37 tff(9067,plain,
% 2.14/2.37 (~b(z, s(s(s(s(z)))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[8791, 246, 9066, 9064, 9062])).
% 2.14/2.37 tff(9068,plain,
% 2.14/2.37 ((z = s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[2645, 47, 9067])).
% 2.14/2.37 tff(9069,plain,
% 2.14/2.37 (r(z, s(s(s(s(z)))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9068, 2635])).
% 2.14/2.37 tff(9070,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[8858, 183, 171, 6095, 8384])).
% 2.14/2.37 tff(9071,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(9072,plain,
% 2.14/2.37 (~r(s(s(s(s(z)))), s(z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9071, 9069, 171])).
% 2.14/2.37 tff(9073,plain,
% 2.14/2.37 (b(s(s(s(s(z)))), s(z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[6103, 9072])).
% 2.14/2.37 tff(9074,plain,
% 2.14/2.37 (~b(s(s(s(s(z)))), elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9050, 9073, 8760, 8758])).
% 2.14/2.37 tff(9075,plain,
% 2.14/2.37 (r(s(s(s(s(z)))), elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[2442, 47, 9048, 9074])).
% 2.14/2.37 tff(9076,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[5955, 183, 267, 9069, 9075])).
% 2.14/2.37 tff(9077,plain,(b(s(s(s(z))), elem!1) | (~r(z, elem!1)) | (~r(z, s(z))) | r(s(s(elem!1)), elem!1) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(9078,plain,
% 2.14/2.37 (b(s(s(s(z))), elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9077, 170, 5365, 2232, 8749])).
% 2.14/2.37 tff(9079,plain,
% 2.14/2.37 (b(s(s(elem!1)), elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[207, 8755, 8749])).
% 2.14/2.37 tff(9080,plain,
% 2.14/2.37 (r(z, s(s(s(z)))) <=> r(z, s(s(elem!1)))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[2266])).
% 2.14/2.37 tff(9081,plain,
% 2.14/2.37 (r(z, s(s(elem!1))) <=> r(z, s(s(s(z))))),
% 2.14/2.37 inference(symmetry,[status(thm)],[9080])).
% 2.14/2.37 tff(9082,plain,
% 2.14/2.37 ((~r(z, s(s(elem!1)))) <=> (~r(z, s(s(s(z)))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[9081])).
% 2.14/2.37 tff(9083,plain,
% 2.14/2.37 ((s(s(s(s(s(elem!1))))) = s(s(s(z)))) <=> (s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[2266])).
% 2.14/2.37 tff(9084,plain,
% 2.14/2.37 ((s(s(s(s(s(elem!1))))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 2.14/2.37 inference(transitivity,[status(thm)],[9083, 1535])).
% 2.14/2.37 tff(9085,plain,
% 2.14/2.37 ((~(s(s(s(s(s(elem!1))))) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(s(s(elem!1)))))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[9084])).
% 2.14/2.37 tff(9086,plain,
% 2.14/2.37 (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[1622, 9085])).
% 2.14/2.37 tff(9087,plain,
% 2.14/2.37 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[2266])).
% 2.14/2.37 tff(9088,plain,
% 2.14/2.37 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[6])).
% 2.14/2.37 tff(9089,plain,
% 2.14/2.37 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 2.14/2.37 inference(transitivity,[status(thm)],[9088, 9087])).
% 2.14/2.37 tff(9090,plain,
% 2.14/2.37 (~r(s(z), s(s(s(z))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[6607, 429, 171])).
% 2.14/2.37 tff(9091,plain,
% 2.14/2.37 (b(s(z), s(s(s(z))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[1291, 9090])).
% 2.14/2.37 tff(9092,plain,
% 2.14/2.37 (b(elem!1, s(s(elem!1)))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[9091, 9089])).
% 2.14/2.37 tff(9093,plain,
% 2.14/2.37 ((s(s(s(s(s(elem!1))))) = s(z)) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 2.14/2.37 inference(monotonicity,[status(thm)],[6])).
% 2.14/2.37 tff(9094,plain,
% 2.14/2.37 ((~(s(s(s(s(s(elem!1))))) = s(z))) <=> (~(s(s(s(s(s(elem!1))))) = elem!1))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[9093])).
% 2.14/2.37 tff(9095,plain,
% 2.14/2.37 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[331, 9094])).
% 2.14/2.37 tff(9096,plain,
% 2.14/2.37 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[2266])).
% 2.14/2.37 tff(9097,plain,
% 2.14/2.37 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.14/2.37 inference(symmetry,[status(thm)],[9096])).
% 2.14/2.37 tff(9098,plain,
% 2.14/2.37 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(s(z)))) = elem!1)),
% 2.14/2.37 inference(monotonicity,[status(thm)],[9097])).
% 2.14/2.37 tff(9099,plain,
% 2.14/2.37 ((s(s(s(s(z)))) = elem!1) <=> (s(s(s(elem!1))) = elem!1)),
% 2.14/2.37 inference(symmetry,[status(thm)],[9098])).
% 2.14/2.37 tff(9100,plain,
% 2.14/2.37 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[9099])).
% 2.14/2.37 tff(9101,plain,
% 2.14/2.37 ((s(s(s(s(z)))) = s(z)) <=> (s(s(s(s(z)))) = elem!1)),
% 2.14/2.37 inference(monotonicity,[status(thm)],[6])).
% 2.14/2.37 tff(9102,plain,
% 2.14/2.37 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[9101])).
% 2.14/2.37 tff(9103,plain,
% 2.14/2.37 (~(s(s(s(s(z)))) = elem!1)),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[1713, 9102])).
% 2.14/2.37 tff(9104,plain,
% 2.14/2.37 (~(s(s(s(elem!1))) = elem!1)),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[9103, 9100])).
% 2.14/2.37 tff(9105,plain,
% 2.14/2.37 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[9096])).
% 2.14/2.37 tff(9106,plain,
% 2.14/2.37 ((s(s(z)) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[117])).
% 2.14/2.37 tff(9107,plain,
% 2.14/2.37 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 2.14/2.37 inference(transitivity,[status(thm)],[9106, 2891])).
% 2.14/2.37 tff(9108,plain,
% 2.14/2.37 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[9107])).
% 2.14/2.37 tff(9109,plain,
% 2.14/2.37 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[1526, 9108])).
% 2.14/2.37 tff(9110,plain,
% 2.14/2.37 (b(elem!1, s(s(s(z))))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[2401, 9088])).
% 2.14/2.37 tff(9111,plain,
% 2.14/2.37 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 2.14/2.37 inference(monotonicity,[status(thm)],[9096])).
% 2.14/2.37 tff(9112,plain,
% 2.14/2.37 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 2.14/2.37 inference(symmetry,[status(thm)],[9111])).
% 2.14/2.37 tff(9113,plain,
% 2.14/2.37 (b(s(s(s(s(z)))), elem!1)),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[961, 9112])).
% 2.14/2.37 tff(9114,plain,
% 2.14/2.37 ((s(z) = s(s(z))) <=> (elem!1 = s(elem!1))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[6, 117])).
% 2.14/2.37 tff(9115,plain,
% 2.14/2.37 ((s(z) = s(s(z))) <=> (s(elem!1) = elem!1)),
% 2.14/2.37 inference(transitivity,[status(thm)],[9114, 3423])).
% 2.14/2.37 tff(9116,plain,
% 2.14/2.37 ((~(s(z) = s(s(z)))) <=> (~(s(elem!1) = elem!1))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[9115])).
% 2.14/2.37 tff(9117,plain,
% 2.14/2.37 (~(s(elem!1) = elem!1)),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[8340, 9116])).
% 2.14/2.37 tff(9118,plain,
% 2.14/2.37 (s(s(elem!1)) = s(s(s(z)))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[2266, 3393])).
% 2.14/2.37 tff(9119,plain,
% 2.14/2.37 (~(s(s(s(s(s(elem!1))))) = s(elem!1))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[3239, 9118])).
% 2.14/2.37 tff(9120,plain,
% 2.14/2.37 ((s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 2.14/2.37 inference(symmetry,[status(thm)],[8003])).
% 2.14/2.37 tff(9121,plain,
% 2.14/2.37 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(elem!1))) = s(s(s(s(s(elem!1))))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[9096])).
% 2.14/2.37 tff(9122,plain,
% 2.14/2.37 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 2.14/2.37 inference(transitivity,[status(thm)],[9121, 9120])).
% 2.14/2.37 tff(9123,plain,
% 2.14/2.37 ((~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[9122])).
% 2.14/2.37 tff(9124,plain,
% 2.14/2.37 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[1501, 9123])).
% 2.14/2.37 tff(9125,plain,
% 2.14/2.37 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[9097])).
% 2.14/2.37 tff(9126,plain,
% 2.14/2.37 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 2.14/2.37 inference(transitivity,[status(thm)],[9125, 1825])).
% 2.14/2.37 tff(9127,plain,
% 2.14/2.37 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 2.14/2.38 inference(symmetry,[status(thm)],[9126])).
% 2.14/2.38 tff(9128,plain,
% 2.14/2.38 ((~(s(s(s(s(z)))) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[9127])).
% 2.14/2.38 tff(9129,plain,
% 2.14/2.38 (s(s(elem!1)) = s(s(s(z)))),
% 2.14/2.38 inference(symmetry,[status(thm)],[2266])).
% 2.14/2.38 tff(9130,plain,
% 2.14/2.38 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[9129])).
% 2.14/2.38 tff(9131,plain,
% 2.14/2.38 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 2.14/2.38 inference(symmetry,[status(thm)],[9130])).
% 2.14/2.38 tff(9132,plain,
% 2.14/2.38 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(s(z)))) = s(s(elem!1))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[9131])).
% 2.14/2.38 tff(9133,plain,
% 2.14/2.38 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[1697, 9132])).
% 2.14/2.38 tff(9134,plain,
% 2.14/2.38 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[9133, 9128])).
% 2.14/2.38 tff(9135,plain,
% 2.14/2.38 (b(elem!1, s(s(elem!1)))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[2401, 9089])).
% 2.14/2.38 tff(9136,plain,
% 2.14/2.38 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[4903, 714, 2362, 961, 947])).
% 2.14/2.38 tff(9137,plain,
% 2.14/2.38 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[4794, 246, 2362, 947, 961])).
% 2.14/2.38 tff(9138,plain,
% 2.14/2.38 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[4890, 714, 2362, 947])).
% 2.14/2.38 tff(9139,plain,
% 2.14/2.38 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[4488, 9138, 9137, 4476, 4452])).
% 2.14/2.38 tff(9140,plain,
% 2.14/2.38 ($false),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[3693, 9139, 9136, 775])).
% 2.14/2.38 tff(9141,plain,((~b(s(s(s(s(s(elem!1))))), elem!1)) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.38 tff(9142,plain,
% 2.14/2.38 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[9141, 9135, 9086, 9134, 2362, 961, 9124])).
% 2.14/2.38 tff(9143,plain,
% 2.14/2.38 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[86, 9142, 9095])).
% 2.14/2.38 tff(9144,plain,
% 2.14/2.38 (~r(s(elem!1), elem!1)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[5543, 9143, 267, 9119])).
% 2.14/2.38 tff(9145,plain,
% 2.14/2.38 (b(s(elem!1), elem!1)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[5655, 9144, 9117])).
% 2.14/2.38 tff(9146,plain,
% 2.14/2.38 (~b(s(s(s(s(z)))), s(elem!1))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[5922, 9145, 3697, 9113, 9110])).
% 2.14/2.38 tff(9147,plain,
% 2.14/2.38 (r(s(s(s(s(z)))), s(elem!1))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[1728, 9146, 9109])).
% 2.14/2.38 tff(9148,plain,
% 2.14/2.38 (r(s(s(s(elem!1))), s(elem!1))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[9147, 9105])).
% 2.14/2.38 tff(9149,plain,
% 2.14/2.38 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[4794, 246, 2362, 9135, 961])).
% 2.14/2.38 tff(9150,plain,
% 2.14/2.38 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[4455, 9149, 9134])).
% 2.14/2.38 tff(9151,plain,
% 2.14/2.38 ((s(s(s(z))) = s(s(z))) <=> (s(s(elem!1)) = s(elem!1))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[2266, 117])).
% 2.14/2.38 tff(9152,plain,
% 2.14/2.38 ((~(s(s(s(z))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[9151])).
% 2.14/2.38 tff(9153,plain,
% 2.14/2.38 (~(s(s(elem!1)) = s(elem!1))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[8374, 9152])).
% 2.14/2.38 tff(9154,plain,
% 2.14/2.38 (~b(s(s(elem!1)), s(elem!1))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[7373, 9145, 2362, 9135])).
% 2.14/2.38 tff(9155,plain,
% 2.14/2.38 (r(s(s(elem!1)), s(elem!1))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[5644, 9154, 9153])).
% 2.14/2.38 tff(9156,plain,
% 2.14/2.38 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[3841, 9155, 9150])).
% 2.14/2.38 tff(9157,plain,
% 2.14/2.38 ($false),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[9156, 9148])).
% 2.14/2.38 tff(9158,plain,((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.38 tff(9159,plain,
% 2.14/2.38 (~b(s(s(s(elem!1))), elem!1)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[9158, 9091, 2362, 267, 3697, 6])).
% 2.14/2.38 tff(9160,plain,
% 2.14/2.38 ((s(s(s(elem!1))) = elem!1) | r(s(s(s(elem!1))), elem!1)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[3356, 47, 9159])).
% 2.14/2.38 tff(9161,plain,
% 2.14/2.38 (r(s(s(s(elem!1))), elem!1)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[9160, 9104])).
% 2.14/2.38 tff(9162,plain,
% 2.14/2.38 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[9096, 2266])).
% 2.14/2.38 tff(9163,plain,
% 2.14/2.38 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[9096, 2266])).
% 2.14/2.38 tff(9164,plain,
% 2.14/2.38 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.38 inference(symmetry,[status(thm)],[9163])).
% 2.14/2.38 tff(9165,plain,
% 2.14/2.38 ((~b(s(s(s(elem!1))), s(s(elem!1)))) <=> (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[9164])).
% 2.14/2.38 tff(9166,plain,
% 2.14/2.38 ((s(s(s(elem!1))) = elem!1) | r(s(s(s(elem!1))), elem!1)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[3356, 47, 3699])).
% 2.14/2.38 tff(9167,plain,
% 2.14/2.38 (r(s(s(s(elem!1))), elem!1)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[9166, 9104])).
% 2.14/2.38 tff(9168,plain,
% 2.14/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(9169,plain,
% 2.14/2.38 (((~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), 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))))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(9170,plain,
% 2.14/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1)))))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[9169])).
% 2.14/2.38 tff(9171,plain,
% 2.14/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))))),
% 2.14/2.38 inference(transitivity,[status(thm)],[9170, 9168])).
% 2.14/2.38 tff(9172,plain,
% 2.14/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))))),
% 2.14/2.38 inference(quant_inst,[status(thm)],[])).
% 2.14/2.38 tff(9173,plain,
% 2.14/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1)))))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[9172, 9171])).
% 2.14/2.38 tff(9174,plain,
% 2.14/2.38 (~r(z, s(s(s(elem!1))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[9173, 183, 267, 9167])).
% 2.14/2.38 tff(9175,plain,
% 2.14/2.38 (((~![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)))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(9176,plain,
% 2.14/2.38 ((~![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)))))),
% 2.14/2.38 inference(quant_inst,[status(thm)],[])).
% 2.14/2.38 tff(9177,plain,
% 2.14/2.38 ((~![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))))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[9176, 9175])).
% 2.14/2.38 tff(9178,plain,
% 2.14/2.38 ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[9177, 47, 9174])).
% 2.14/2.38 tff(9179,plain,
% 2.14/2.38 (b(z, s(s(s(elem!1))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[9178, 5369])).
% 2.14/2.38 tff(9180,plain,
% 2.14/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(9181,plain,
% 2.14/2.38 (((~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z))) <=> ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(9182,plain,
% 2.14/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[9181])).
% 2.14/2.38 tff(9183,plain,
% 2.14/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 2.14/2.38 inference(transitivity,[status(thm)],[9182, 9180])).
% 2.14/2.38 tff(9184,plain,
% 2.14/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 2.14/2.38 inference(quant_inst,[status(thm)],[])).
% 2.14/2.38 tff(9185,plain,
% 2.14/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[9184, 9183])).
% 2.14/2.38 tff(9186,plain,
% 2.14/2.38 (~r(s(s(s(elem!1))), z)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[9185, 183, 267, 9167])).
% 2.14/2.38 tff(9187,plain,
% 2.14/2.38 (b(s(s(s(elem!1))), z)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[3086, 47, 355, 9186])).
% 2.14/2.38 tff(9188,plain,
% 2.14/2.38 ((~(s(s(s(s(s(elem!1))))) = s(s(s(z))))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(elem!1))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[9083])).
% 2.14/2.38 tff(9189,plain,
% 2.14/2.38 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[1622, 9188])).
% 2.14/2.38 tff(9190,assumption,(elem!1 = s(s(s(elem!1)))), introduced(assumption)).
% 2.14/2.38 tff(9191,plain,
% 2.14/2.38 (s(s(s(elem!1))) = elem!1),
% 2.14/2.38 inference(symmetry,[status(thm)],[9190])).
% 2.14/2.38 tff(9192,plain,
% 2.14/2.38 (s(s(s(s(z)))) = elem!1),
% 2.14/2.38 inference(transitivity,[status(thm)],[3068, 9191])).
% 2.14/2.38 tff(9193,plain,
% 2.14/2.38 ($false),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[3074, 9192])).
% 2.14/2.38 tff(9194,plain,((~(elem!1 = s(s(s(elem!1))))) | (s(s(s(s(z)))) = elem!1) | (~(s(s(s(z))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.38 tff(9195,plain,
% 2.14/2.38 (~(elem!1 = s(s(s(elem!1))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[9194, 9103, 2266])).
% 2.14/2.38 tff(9196,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(9197,plain,
% 2.14/2.38 (((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(9198,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[9197])).
% 2.14/2.38 tff(9199,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.14/2.38 inference(transitivity,[status(thm)],[9198, 9196])).
% 2.14/2.38 tff(9200,plain,
% 2.14/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.14/2.38 inference(quant_inst,[status(thm)],[])).
% 2.14/2.38 tff(9201,plain,
% 2.14/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[9200, 9199])).
% 2.14/2.38 tff(9202,plain,
% 2.14/2.38 (~b(elem!1, s(s(s(elem!1))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[9201, 246, 2362, 947, 1659])).
% 2.14/2.38 tff(9203,plain,
% 2.14/2.38 (r(elem!1, s(s(s(elem!1))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[3104, 47, 9202, 9195])).
% 2.14/2.38 tff(9204,assumption,(b(z, s(s(s(elem!1))))), introduced(assumption)).
% 2.14/2.38 tff(9205,assumption,(b(s(s(s(elem!1))), z)), introduced(assumption)).
% 2.14/2.38 tff(9206,plain,
% 2.14/2.38 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[4270, 333, 3427])).
% 2.14/2.38 tff(9207,plain,
% 2.14/2.38 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[3693, 9206, 775])).
% 2.14/2.38 tff(9208,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(9209,plain,
% 2.14/2.38 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~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(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(9210,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~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(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[9209])).
% 2.14/2.38 tff(9211,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~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(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 2.14/2.38 inference(transitivity,[status(thm)],[9210, 9208])).
% 2.14/2.38 tff(9212,plain,
% 2.14/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~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(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.14/2.38 inference(quant_inst,[status(thm)],[])).
% 2.14/2.38 tff(9213,plain,
% 2.14/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[9212, 9211])).
% 2.14/2.38 tff(9214,plain,
% 2.14/2.38 ($false),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[9213, 246, 5472, 9207, 1659, 9205, 9204])).
% 2.14/2.38 tff(9215,plain,((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~r(z, elem!1)) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.38 tff(9216,plain,
% 2.14/2.38 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[9215, 1659, 9187, 9179, 267, 9124, 9203])).
% 2.14/2.38 tff(9217,plain,
% 2.14/2.38 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[86, 9216, 9095])).
% 2.14/2.38 tff(9218,plain,
% 2.14/2.38 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[4983, 9217, 2362, 947])).
% 2.14/2.38 tff(9219,plain,
% 2.14/2.38 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[1557, 9218, 9189])).
% 2.14/2.38 tff(9220,plain,
% 2.14/2.38 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[117, 9096])).
% 2.14/2.38 tff(9221,assumption,(b(s(s(s(s(s(elem!1))))), z)), introduced(assumption)).
% 2.14/2.38 tff(9222,plain,
% 2.14/2.38 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[9213, 246, 9221, 1659, 9205, 9204])).
% 2.14/2.38 tff(9223,plain,
% 2.14/2.38 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[3693, 9222, 9124])).
% 2.14/2.38 tff(9224,plain,
% 2.14/2.38 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[4488, 9223, 9138, 9086, 9134])).
% 2.14/2.38 tff(9225,plain,
% 2.14/2.38 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[4983, 714, 2362, 947])).
% 2.14/2.38 tff(9226,plain,
% 2.14/2.38 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[1557, 9225, 9189])).
% 2.14/2.38 tff(9227,plain,
% 2.14/2.38 ((~(s(z) = s(s(z)))) <=> (~(elem!1 = s(elem!1)))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[9114])).
% 2.14/2.38 tff(9228,plain,
% 2.14/2.38 (~(elem!1 = s(elem!1))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[8340, 9227])).
% 2.14/2.38 tff(9229,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(9230,plain,
% 2.14/2.38 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(9231,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(z, s(s(s(elem!1)))))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[9230])).
% 2.14/2.38 tff(9232,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 2.14/2.38 inference(transitivity,[status(thm)],[9231, 9229])).
% 2.14/2.38 tff(9233,plain,
% 2.14/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.14/2.38 inference(quant_inst,[status(thm)],[])).
% 2.14/2.38 tff(9234,plain,
% 2.14/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(z, s(s(s(elem!1)))))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[9233, 9232])).
% 2.14/2.38 tff(9235,plain,
% 2.14/2.38 ($false),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[9234, 246, 1051, 947, 714, 9221, 1659, 9204])).
% 2.14/2.39 tff(9236,plain,((~b(s(s(s(s(s(elem!1))))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.39 tff(9237,plain,
% 2.14/2.39 (~b(elem!1, z)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[9236, 9221, 947, 714, 1659, 9204])).
% 2.14/2.39 tff(9238,plain,
% 2.14/2.39 (r(elem!1, z)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[1143, 9237, 1438])).
% 2.14/2.39 tff(9239,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(9240,plain,
% 2.14/2.39 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), 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(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(9241,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1)))))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[9240])).
% 2.14/2.39 tff(9242,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))))),
% 2.14/2.39 inference(transitivity,[status(thm)],[9241, 9239])).
% 2.14/2.39 tff(9243,plain,
% 2.14/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))))),
% 2.14/2.39 inference(quant_inst,[status(thm)],[])).
% 2.14/2.39 tff(9244,plain,
% 2.14/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1)))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[9243, 9242])).
% 2.14/2.39 tff(9245,plain,
% 2.14/2.39 (~b(z, s(elem!1))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[9244, 246, 2751, 1657, 1659, 9204])).
% 2.14/2.39 tff(9246,plain,
% 2.14/2.39 (r(z, s(elem!1))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[2561, 9245])).
% 2.14/2.39 tff(9247,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(9248,plain,
% 2.14/2.39 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(9249,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1)))))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[9248])).
% 2.14/2.39 tff(9250,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 2.14/2.39 inference(transitivity,[status(thm)],[9249, 9247])).
% 2.14/2.39 tff(9251,plain,
% 2.14/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.14/2.39 inference(quant_inst,[status(thm)],[])).
% 2.14/2.39 tff(9252,plain,
% 2.14/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[9251, 9250])).
% 2.14/2.39 tff(9253,plain,
% 2.14/2.39 (~b(s(s(elem!1)), s(elem!1))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[9252, 246, 2751, 1657, 1659])).
% 2.14/2.39 tff(9254,plain,
% 2.14/2.39 (r(s(s(elem!1)), s(elem!1))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[5644, 9253, 5642])).
% 2.14/2.39 tff(9255,plain,
% 2.14/2.39 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[1959, 9254, 959])).
% 2.14/2.39 tff(9256,plain,
% 2.14/2.39 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[1795, 9255, 3410])).
% 2.14/2.39 tff(9257,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(9258,plain,
% 2.14/2.39 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(9259,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[9258])).
% 2.14/2.39 tff(9260,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.14/2.39 inference(transitivity,[status(thm)],[9259, 9257])).
% 2.14/2.39 tff(9261,plain,
% 2.14/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.14/2.39 inference(quant_inst,[status(thm)],[])).
% 2.14/2.39 tff(9262,plain,
% 2.14/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[9261, 9260])).
% 2.14/2.39 tff(9263,plain,
% 2.14/2.39 ($false),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[9262, 246, 947, 2751, 714, 2866, 1574, 1659])).
% 2.14/2.39 tff(9264,plain,((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.39 tff(9265,plain,
% 2.14/2.39 (~b(elem!1, s(elem!1))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[9264, 9256, 714, 947, 2751, 1659])).
% 2.14/2.39 tff(9266,plain,
% 2.14/2.39 (r(elem!1, s(elem!1))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[2864, 9265, 3425])).
% 2.14/2.39 tff(9267,plain,
% 2.14/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(9268,plain,
% 2.14/2.39 (((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(9269,plain,
% 2.14/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1)))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[9268])).
% 2.14/2.39 tff(9270,plain,
% 2.14/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))))),
% 2.14/2.39 inference(transitivity,[status(thm)],[9269, 9267])).
% 2.14/2.39 tff(9271,plain,
% 2.14/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(elem!1, z)))),
% 2.14/2.39 inference(quant_inst,[status(thm)],[])).
% 2.14/2.39 tff(9272,plain,
% 2.14/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1)))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[9271, 9270])).
% 2.14/2.39 tff(9273,plain,
% 2.14/2.39 ($false),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[9272, 183, 2246, 9266, 9246])).
% 2.14/2.39 tff(9274,plain,((~b(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, z)) | (elem!1 = s(elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(s(s(elem!1))))) = s(elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (s(s(elem!1)) = s(elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.39 tff(9275,plain,
% 2.14/2.39 (~b(s(elem!1), s(s(s(elem!1))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[9274, 9238, 9228, 714, 947, 1659, 9119, 9226, 9153, 9224, 9204])).
% 2.14/2.39 tff(9276,plain,
% 2.14/2.39 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[3461, 9275, 202])).
% 2.14/2.39 tff(9277,plain,
% 2.14/2.39 (r(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[1531, 9276])).
% 2.14/2.39 tff(9278,plain,
% 2.14/2.39 (r(s(elem!1), s(s(s(elem!1))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[9277, 9220])).
% 2.14/2.39 tff(9279,plain,
% 2.14/2.39 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[3381, 9222, 2266])).
% 2.14/2.39 tff(9280,plain,
% 2.14/2.39 (r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[1897, 9279])).
% 2.14/2.39 tff(9281,plain,
% 2.14/2.39 (~r(s(s(s(s(s(elem!1))))), s(s(z)))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[1916, 9277, 9280])).
% 2.14/2.39 tff(9282,plain,
% 2.14/2.39 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[3257, 9281, 9118])).
% 2.14/2.39 tff(9283,plain,
% 2.14/2.39 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[1795, 9282, 9119])).
% 2.14/2.39 tff(9284,plain,
% 2.14/2.39 (~b(s(elem!1), elem!1)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[5208, 9283, 947, 714, 2362])).
% 2.14/2.39 tff(9285,plain,
% 2.14/2.39 (r(s(elem!1), elem!1)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[5655, 9284, 9117])).
% 2.14/2.39 tff(9286,plain,
% 2.14/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(9287,plain,
% 2.14/2.39 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(9288,plain,
% 2.14/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1)))))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[9287])).
% 2.14/2.39 tff(9289,plain,
% 2.14/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 2.14/2.39 inference(transitivity,[status(thm)],[9288, 9286])).
% 2.14/2.39 tff(9290,plain,
% 2.14/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)))),
% 2.14/2.39 inference(quant_inst,[status(thm)],[])).
% 2.14/2.39 tff(9291,plain,
% 2.14/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[9290, 9289])).
% 2.14/2.39 tff(9292,plain,
% 2.14/2.39 ($false),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[9291, 183, 2246, 367, 1348, 3427])).
% 2.14/2.39 tff(9293,plain,((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.39 tff(9294,plain,
% 2.14/2.39 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[9293, 9285, 9238, 9203])).
% 2.14/2.39 tff(9295,plain,
% 2.14/2.39 ($false),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[9294, 9278])).
% 2.14/2.39 tff(9296,plain,((~b(s(s(s(s(s(elem!1))))), z)) | (~(s(z) = elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~(elem!1 = s(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)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.39 tff(9297,plain,
% 2.14/2.39 (~b(s(s(s(s(s(elem!1))))), z)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[9296, 9217, 947, 6, 2362, 202, 1659, 9179, 9187, 5401])).
% 2.14/2.39 tff(9298,plain,
% 2.14/2.39 (r(s(s(s(s(s(elem!1))))), z)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[1601, 9297])).
% 2.14/2.39 tff(9299,plain,
% 2.14/2.39 (~r(s(s(elem!1)), z)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[5671, 9298, 9219])).
% 2.14/2.39 tff(9300,plain,
% 2.14/2.39 (b(s(s(elem!1)), z)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[523, 9299])).
% 2.14/2.39 tff(9301,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(9302,plain,
% 2.14/2.39 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(9303,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[9302])).
% 2.14/2.39 tff(9304,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 2.14/2.39 inference(transitivity,[status(thm)],[9303, 9301])).
% 2.14/2.39 tff(9305,plain,
% 2.14/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.14/2.39 inference(quant_inst,[status(thm)],[])).
% 2.14/2.39 tff(9306,plain,
% 2.14/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[9305, 9304])).
% 2.14/2.39 tff(9307,plain,
% 2.14/2.39 ($false),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[9306, 246, 9300, 1659, 9187, 9179])).
% 2.14/2.39 tff(9308,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~(s(z) = elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~(elem!1 = s(z))) | (~r(z, elem!1)) | b(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.39 tff(9309,plain,
% 2.14/2.39 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[9308, 9092, 6, 2362, 202, 267, 9159])).
% 2.14/2.39 tff(9310,plain,
% 2.14/2.39 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[9309, 9165])).
% 2.14/2.39 tff(9311,plain,
% 2.14/2.39 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[1702, 9310])).
% 2.14/2.39 tff(9312,plain,
% 2.14/2.39 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[9311, 9162])).
% 2.14/2.39 tff(9313,plain,
% 2.14/2.39 (~r(z, s(s(s(elem!1))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[9173, 183, 267, 4357])).
% 2.14/2.39 tff(9314,plain,
% 2.14/2.39 ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[9177, 47, 9313])).
% 2.14/2.39 tff(9315,plain,
% 2.14/2.39 (b(z, s(s(s(elem!1))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[9314, 5369])).
% 2.14/2.39 tff(9316,plain,
% 2.14/2.39 (~r(s(s(s(elem!1))), z)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[9185, 183, 267, 4357])).
% 2.14/2.39 tff(9317,plain,
% 2.14/2.39 (b(s(s(s(elem!1))), z)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[3086, 47, 355, 9316])).
% 2.14/2.39 tff(9318,plain,
% 2.14/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(9319,plain,
% 2.14/2.39 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.14/2.40 inference(rewrite,[status(thm)],[])).
% 2.14/2.40 tff(9320,plain,
% 2.14/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1))))),
% 2.14/2.40 inference(monotonicity,[status(thm)],[9319])).
% 2.14/2.40 tff(9321,plain,
% 2.14/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.14/2.40 inference(transitivity,[status(thm)],[9320, 9318])).
% 2.14/2.40 tff(9322,plain,
% 2.14/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.14/2.40 inference(quant_inst,[status(thm)],[])).
% 2.14/2.40 tff(9323,plain,
% 2.14/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 2.14/2.40 inference(modus_ponens,[status(thm)],[9322, 9321])).
% 2.14/2.40 tff(9324,plain,
% 2.14/2.40 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.14/2.40 inference(unit_resolution,[status(thm)],[9323, 183, 333, 3076, 4357])).
% 2.14/2.40 tff(9325,plain,
% 2.14/2.40 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.14/2.40 inference(unit_resolution,[status(thm)],[3693, 9324, 775])).
% 2.14/2.40 tff(9326,plain,
% 2.14/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 2.14/2.40 inference(rewrite,[status(thm)],[])).
% 2.14/2.40 tff(9327,plain,
% 2.14/2.40 (((~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(elem!1))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 2.14/2.40 inference(rewrite,[status(thm)],[])).
% 2.14/2.40 tff(9328,plain,
% 2.14/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[9327])).
% 2.24/2.40 tff(9329,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 2.24/2.40 inference(transitivity,[status(thm)],[9328, 9326])).
% 2.24/2.40 tff(9330,plain,
% 2.24/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.24/2.40 inference(quant_inst,[status(thm)],[])).
% 2.24/2.40 tff(9331,plain,
% 2.24/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[9330, 9329])).
% 2.24/2.40 tff(9332,plain,
% 2.24/2.40 ($false),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[9331, 246, 5472, 9325, 9317, 9315])).
% 2.24/2.40 tff(9333,plain,((~r(s(s(s(s(s(elem!1))))), elem!1)) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.40 tff(9334,plain,
% 2.24/2.40 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[9333, 9312, 9124, 9161, 267])).
% 2.24/2.40 tff(9335,plain,
% 2.24/2.40 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[86, 9334, 9095])).
% 2.24/2.40 tff(9336,plain,
% 2.24/2.40 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[4890, 9335, 2362, 9092])).
% 2.24/2.40 tff(9337,plain,
% 2.24/2.40 (r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[1547, 47, 9336, 9086])).
% 2.24/2.40 tff(9338,plain,
% 2.24/2.40 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[4983, 9335, 2362, 9092])).
% 2.24/2.40 tff(9339,plain,
% 2.24/2.40 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[1557, 9338, 9189])).
% 2.24/2.40 tff(9340,plain,
% 2.24/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(9341,plain,
% 2.24/2.40 (((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(9342,plain,
% 2.24/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[9341])).
% 2.24/2.40 tff(9343,plain,
% 2.24/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 2.24/2.40 inference(transitivity,[status(thm)],[9342, 9340])).
% 2.24/2.40 tff(9344,plain,
% 2.24/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 2.24/2.40 inference(quant_inst,[status(thm)],[])).
% 2.24/2.40 tff(9345,plain,
% 2.24/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[9344, 9343])).
% 2.24/2.40 tff(9346,plain,
% 2.24/2.40 (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[9345, 183, 9312, 9339])).
% 2.24/2.40 tff(9347,plain,
% 2.24/2.40 ((~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[9121])).
% 2.24/2.40 tff(9348,plain,
% 2.24/2.40 (~(s(s(s(elem!1))) = s(s(s(s(s(elem!1))))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[1501, 9347])).
% 2.24/2.40 tff(9349,plain,
% 2.24/2.40 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[913, 47, 9348, 9346])).
% 2.24/2.40 tff(9350,plain,
% 2.24/2.40 (~r(z, s(s(s(elem!1))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[9173, 183, 267, 9161])).
% 2.24/2.40 tff(9351,plain,
% 2.24/2.40 ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[9177, 47, 9350])).
% 2.24/2.40 tff(9352,plain,
% 2.24/2.40 (b(z, s(s(s(elem!1))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[9351, 5369])).
% 2.24/2.40 tff(9353,plain,
% 2.24/2.40 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[5176, 9339, 9312])).
% 2.24/2.40 tff(9354,plain,
% 2.24/2.40 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[3693, 9353, 9124])).
% 2.24/2.40 tff(9355,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(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(elem!1))))) | (~b(z, s(s(s(elem!1))))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(9356,plain,
% 2.24/2.40 (((~b(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(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(elem!1)))))))) <=> ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(9357,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1)))))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[9356])).
% 2.24/2.40 tff(9358,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))),
% 2.24/2.40 inference(transitivity,[status(thm)],[9357, 9355])).
% 2.24/2.40 tff(9359,plain,
% 2.24/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 2.24/2.40 inference(quant_inst,[status(thm)],[])).
% 2.24/2.40 tff(9360,plain,
% 2.24/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1)))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[9359, 9358])).
% 2.24/2.40 tff(9361,plain,
% 2.24/2.40 (~b(z, s(s(s(s(s(elem!1))))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[9360, 246, 9354, 9352, 9349])).
% 2.24/2.40 tff(9362,plain,
% 2.24/2.40 (r(z, s(s(s(s(s(elem!1))))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[2487, 47, 5706, 9361])).
% 2.24/2.40 tff(9363,plain,
% 2.24/2.40 (~r(z, s(s(elem!1)))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[3314, 9362, 9337])).
% 2.24/2.40 tff(9364,plain,
% 2.24/2.40 (~r(z, s(s(s(z))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[9363, 9082])).
% 2.24/2.40 tff(9365,plain,
% 2.24/2.40 ($false),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[429, 9364])).
% 2.24/2.40 tff(9366,plain,((~r(z, s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~(s(z) = elem!1)) | (~(elem!1 = s(z))) | (~b(s(s(s(z))), elem!1)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.40 tff(9367,plain,
% 2.24/2.40 (~r(z, s(s(s(z))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[9366, 9079, 5365, 8750, 8755, 9078, 170])).
% 2.24/2.40 tff(9368,plain,
% 2.24/2.40 (b(z, s(s(s(z))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[6165, 9367])).
% 2.24/2.40 tff(9369,plain,
% 2.24/2.40 (b(z, s(s(s(z)))) <=> b(z, s(s(elem!1)))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[97])).
% 2.24/2.40 tff(9370,plain,
% 2.24/2.40 (b(z, s(s(elem!1))) <=> b(z, s(s(s(z))))),
% 2.24/2.40 inference(symmetry,[status(thm)],[9369])).
% 2.24/2.40 tff(9371,plain,
% 2.24/2.40 ((~b(z, s(s(elem!1)))) <=> (~b(z, s(s(s(z)))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[9370])).
% 2.24/2.40 tff(9372,plain,
% 2.24/2.40 (~b(z, s(s(s(z))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[259, 9371])).
% 2.24/2.40 tff(9373,plain,
% 2.24/2.40 ($false),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[4651, 9372])).
% 2.24/2.40 tff(9374,plain,(b(z, s(s(elem!1))) | (~b(z, s(s(s(z))))) | (~(s(s(s(z))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.40 tff(9375,plain,
% 2.24/2.40 (b(z, s(s(elem!1)))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[9374, 9368, 8756])).
% 2.24/2.40 tff(9376,plain,
% 2.24/2.40 (r(s(z), z) <=> r(elem!1, z)),
% 2.24/2.40 inference(monotonicity,[status(thm)],[6])).
% 2.24/2.40 tff(9377,plain,
% 2.24/2.40 (r(elem!1, z) <=> r(s(z), z)),
% 2.24/2.40 inference(symmetry,[status(thm)],[9376])).
% 2.24/2.40 tff(9378,plain,
% 2.24/2.40 (~r(s(s(elem!1)), z)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[5671, 959, 5669])).
% 2.24/2.40 tff(9379,plain,
% 2.24/2.40 (b(s(s(elem!1)), z)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[523, 9378])).
% 2.24/2.40 tff(9380,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(9381,plain,
% 2.24/2.40 (((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(9382,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1))))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[9381])).
% 2.24/2.40 tff(9383,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))))),
% 2.24/2.40 inference(transitivity,[status(thm)],[9382, 9380])).
% 2.24/2.40 tff(9384,plain,
% 2.24/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 2.24/2.40 inference(quant_inst,[status(thm)],[])).
% 2.24/2.40 tff(9385,plain,
% 2.24/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[9384, 9383])).
% 2.24/2.40 tff(9386,plain,
% 2.24/2.40 ($false),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[9385, 246, 1051, 2362, 1100, 1099])).
% 2.24/2.40 tff(9387,plain,((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.40 tff(9388,plain,
% 2.24/2.40 (~b(elem!1, z)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[9387, 9379, 2362, 1099])).
% 2.24/2.40 tff(9389,plain,
% 2.24/2.40 (r(elem!1, z)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[1143, 9388, 5401])).
% 2.24/2.40 tff(9390,plain,
% 2.24/2.40 (r(s(z), z)),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[9389, 9377])).
% 2.24/2.40 tff(9391,plain,
% 2.24/2.40 ($false),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[5470, 183, 267, 333, 5669])).
% 2.24/2.40 tff(9392,plain,((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.40 tff(9393,plain,
% 2.24/2.40 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[9392, 5669, 267])).
% 2.24/2.40 tff(9394,plain,
% 2.24/2.40 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[86, 9393, 9095])).
% 2.24/2.40 tff(9395,plain,
% 2.24/2.40 ((s(s(s(s(s(elem!1))))) = s(z)) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 2.24/2.40 inference(transitivity,[status(thm)],[9093, 124])).
% 2.24/2.40 tff(9396,plain,
% 2.24/2.40 ((~(s(s(s(s(s(elem!1))))) = s(z))) <=> (~(elem!1 = s(s(s(s(s(elem!1)))))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[9395])).
% 2.24/2.40 tff(9397,plain,
% 2.24/2.40 (~(elem!1 = s(s(s(s(s(elem!1))))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[331, 9396])).
% 2.24/2.40 tff(9398,plain,
% 2.24/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(elem!1, s(s(s(s(s(elem!1))))))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(9399,plain,
% 2.24/2.40 (((~r(s(s(s(s(s(elem!1))))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(elem!1, s(s(s(s(s(elem!1)))))))) <=> ((~r(elem!1, z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(elem!1, s(s(s(s(s(elem!1))))))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(9400,plain,
% 2.24/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(elem!1, s(s(s(s(s(elem!1)))))))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[9399])).
% 2.24/2.40 tff(9401,plain,
% 2.24/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(elem!1, s(s(s(s(s(elem!1))))))))),
% 2.24/2.40 inference(transitivity,[status(thm)],[9400, 9398])).
% 2.24/2.40 tff(9402,plain,
% 2.24/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(elem!1, s(s(s(s(s(elem!1))))))))),
% 2.24/2.40 inference(quant_inst,[status(thm)],[])).
% 2.24/2.40 tff(9403,plain,
% 2.24/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(elem!1, s(s(s(s(s(elem!1)))))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[9402, 9401])).
% 2.24/2.40 tff(9404,plain,
% 2.24/2.40 (~r(elem!1, s(s(s(s(s(elem!1))))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[9403, 183, 9389, 5669])).
% 2.24/2.40 tff(9405,plain,
% 2.24/2.40 (b(elem!1, s(s(s(s(s(elem!1))))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[5125, 9404, 9397])).
% 2.24/2.40 tff(9406,plain,
% 2.24/2.40 (~b(s(s(s(elem!1))), elem!1)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[4864, 9405, 2362, 9086, 9134, 9394, 9124])).
% 2.24/2.40 tff(9407,plain,
% 2.24/2.40 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(z)))), elem!1)),
% 2.24/2.40 inference(monotonicity,[status(thm)],[6])).
% 2.24/2.40 tff(9408,plain,
% 2.24/2.40 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 2.24/2.40 inference(symmetry,[status(thm)],[9407])).
% 2.24/2.40 tff(9409,plain,
% 2.24/2.40 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 2.24/2.40 inference(transitivity,[status(thm)],[9112, 9408])).
% 2.24/2.40 tff(9410,plain,
% 2.24/2.40 ((~b(s(s(s(elem!1))), elem!1)) <=> (~b(s(s(s(s(z)))), s(z)))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[9409])).
% 2.24/2.40 tff(9411,plain,
% 2.24/2.40 (~b(s(s(s(s(z)))), s(z))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[3699, 9410])).
% 2.24/2.40 tff(9412,plain,
% 2.24/2.40 ($false),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[8267, 9411])).
% 2.24/2.40 tff(9413,plain,(b(s(s(s(elem!1))), elem!1) | (~b(s(s(s(s(z)))), s(z))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.40 tff(9414,plain,
% 2.24/2.40 (~b(s(s(s(s(z)))), s(z))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[9413, 9406, 6])).
% 2.24/2.40 tff(9415,plain,
% 2.24/2.40 (r(s(s(s(s(z)))), s(z))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[6103, 9414])).
% 2.24/2.40 tff(9416,plain,
% 2.24/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(9417,plain,
% 2.24/2.40 (((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(9418,plain,
% 2.24/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[9417])).
% 2.24/2.41 tff(9419,plain,
% 2.24/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 2.24/2.41 inference(transitivity,[status(thm)],[9418, 9416])).
% 2.24/2.41 tff(9420,plain,
% 2.24/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 2.24/2.41 inference(quant_inst,[status(thm)],[])).
% 2.24/2.41 tff(9421,plain,
% 2.24/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[9420, 9419])).
% 2.24/2.41 tff(9422,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[9421, 183, 1114, 6095, 7218])).
% 2.24/2.41 tff(9423,plain,((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(9424,plain,
% 2.24/2.41 (~r(s(s(s(s(z)))), z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[9423, 9415, 9390])).
% 2.24/2.41 tff(9425,plain,
% 2.24/2.41 (b(s(s(s(s(z)))), z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[6040, 9424])).
% 2.24/2.41 tff(9426,plain,
% 2.24/2.41 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(z)))), z)),
% 2.24/2.41 inference(monotonicity,[status(thm)],[3069])).
% 2.24/2.41 tff(9427,plain,
% 2.24/2.41 ((~b(s(s(s(elem!1))), z)) <=> (~b(s(s(s(s(z)))), z))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[9426])).
% 2.24/2.41 tff(9428,assumption,(~b(s(s(s(elem!1))), z)), introduced(assumption)).
% 2.24/2.41 tff(9429,plain,
% 2.24/2.41 (~b(s(s(s(s(z)))), z)),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[9428, 9427])).
% 2.24/2.41 tff(9430,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[8266, 9429])).
% 2.24/2.41 tff(9431,plain,(b(s(s(s(elem!1))), z) | (~b(s(s(s(s(z)))), z)) | (~(s(s(s(z))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(9432,plain,
% 2.24/2.41 (b(s(s(s(elem!1))), z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[9431, 9425, 2266])).
% 2.24/2.41 tff(9433,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(9434,plain,
% 2.24/2.41 (((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(9435,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[9434])).
% 2.24/2.41 tff(9436,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))),
% 2.24/2.41 inference(transitivity,[status(thm)],[9435, 9433])).
% 2.24/2.41 tff(9437,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))),
% 2.24/2.41 inference(quant_inst,[status(thm)],[])).
% 2.24/2.41 tff(9438,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[9437, 9436])).
% 2.24/2.41 tff(9439,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[9438, 246, 1100, 1099, 1659, 9205])).
% 2.24/2.41 tff(9440,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(9441,plain,
% 2.24/2.41 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[9440, 9379, 1099, 9432])).
% 2.24/2.41 tff(9442,plain,
% 2.24/2.41 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[3068, 97])).
% 2.24/2.41 tff(9443,plain,
% 2.24/2.41 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[1833, 9442])).
% 2.24/2.41 tff(9444,assumption,(~b(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 2.24/2.41 tff(9445,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[9444, 9443])).
% 2.24/2.41 tff(9446,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | b(s(s(s(elem!1))), s(s(elem!1))) | (~(s(s(s(z))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(9447,plain,
% 2.24/2.41 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[9446, 9441, 2266])).
% 2.24/2.41 tff(9448,plain,
% 2.24/2.41 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[1702, 9447])).
% 2.24/2.41 tff(9449,plain,
% 2.24/2.41 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[9448, 9162])).
% 2.24/2.41 tff(9450,plain,
% 2.24/2.41 (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[9345, 183, 9449, 959])).
% 2.24/2.41 tff(9451,plain,
% 2.24/2.41 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[913, 47, 9348, 9450])).
% 2.24/2.41 tff(9452,plain,
% 2.24/2.41 (~r(s(z), s(s(s(z))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[6098, 9448, 9415])).
% 2.24/2.41 tff(9453,plain,
% 2.24/2.41 (b(s(z), s(s(s(z))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[1291, 9452])).
% 2.24/2.41 tff(9454,plain,
% 2.24/2.41 (b(elem!1, s(s(elem!1)))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[9453, 9089])).
% 2.24/2.41 tff(9455,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(9456,plain,
% 2.24/2.41 (((~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(9457,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), z))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[9456])).
% 2.24/2.41 tff(9458,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 2.24/2.41 inference(transitivity,[status(thm)],[9457, 9455])).
% 2.24/2.41 tff(9459,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), z)))),
% 2.24/2.41 inference(quant_inst,[status(thm)],[])).
% 2.24/2.41 tff(9460,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), z))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[9459, 9458])).
% 2.24/2.41 tff(9461,plain,
% 2.24/2.41 (~b(z, s(s(s(s(s(elem!1))))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[9460, 246, 9454, 1099, 9394, 9432, 9451])).
% 2.24/2.41 tff(9462,plain,
% 2.24/2.41 (r(z, s(s(s(s(s(elem!1))))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[2487, 47, 5706, 9461])).
% 2.24/2.41 tff(9463,assumption,(s(s(s(elem!1))) = elem!1), introduced(assumption)).
% 2.24/2.41 tff(9464,plain,
% 2.24/2.41 (s(s(s(s(z)))) = elem!1),
% 2.24/2.41 inference(transitivity,[status(thm)],[3068, 9463])).
% 2.24/2.41 tff(9465,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[3074, 9464])).
% 2.24/2.41 tff(9466,plain,((~(s(s(s(elem!1))) = elem!1)) | (s(s(s(s(z)))) = elem!1) | (~(s(s(s(z))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(9467,plain,
% 2.24/2.41 (~(s(s(s(elem!1))) = elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[9466, 9103, 2266])).
% 2.24/2.41 tff(9468,plain,
% 2.24/2.41 (r(s(s(s(elem!1))), elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[3356, 47, 9406, 9467])).
% 2.24/2.41 tff(9469,plain,
% 2.24/2.41 (~r(z, s(s(s(elem!1))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[9173, 183, 267, 9468])).
% 2.24/2.41 tff(9470,plain,
% 2.24/2.41 ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[9177, 47, 9469])).
% 2.24/2.41 tff(9471,plain,
% 2.24/2.41 (b(z, s(s(s(elem!1))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[9470, 5369])).
% 2.24/2.41 tff(9472,plain,
% 2.24/2.41 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[5174, 183, 9449, 959])).
% 2.24/2.41 tff(9473,plain,
% 2.24/2.41 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[3693, 9472, 9124])).
% 2.24/2.41 tff(9474,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(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(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(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(elem!1, s(s(s(s(s(elem!1))))))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(9475,plain,
% 2.24/2.41 (((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), 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(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(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(9476,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(elem!1)))))))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[9475])).
% 2.24/2.41 tff(9477,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 2.24/2.41 inference(transitivity,[status(thm)],[9476, 9474])).
% 2.24/2.41 tff(9478,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(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(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))))))),
% 2.24/2.41 inference(quant_inst,[status(thm)],[])).
% 2.24/2.41 tff(9479,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(elem!1)))))))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[9478, 9477])).
% 2.24/2.41 tff(9480,plain,
% 2.24/2.41 (~b(elem!1, s(s(s(elem!1))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[9479, 246, 9473, 9405, 9451])).
% 2.24/2.41 tff(9481,assumption,(~(elem!1 = s(s(s(elem!1))))), introduced(assumption)).
% 2.24/2.41 tff(9482,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[3104, 47, 4112, 4412, 9481])).
% 2.24/2.41 tff(9483,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,[]))).
% 2.24/2.41 tff(9484,plain,
% 2.24/2.41 (r(elem!1, s(s(s(elem!1))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[9483, 9480, 9195])).
% 2.24/2.41 tff(9485,plain,
% 2.24/2.41 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[5208, 1200, 714, 947, 2362])).
% 2.24/2.41 tff(9486,plain,
% 2.24/2.41 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[1795, 9485, 3410])).
% 2.24/2.41 tff(9487,plain,
% 2.24/2.41 (~b(s(s(elem!1)), s(elem!1))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[7373, 1200, 2362, 947])).
% 2.24/2.41 tff(9488,plain,
% 2.24/2.41 (r(s(s(elem!1)), s(elem!1))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[5644, 9487, 5642])).
% 2.24/2.41 tff(9489,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[1959, 9488, 9486, 959])).
% 2.24/2.41 tff(9490,plain,((~b(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (s(s(elem!1)) = s(elem!1)) | (s(s(s(s(s(elem!1))))) = s(elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(9491,plain,
% 2.24/2.41 (~b(s(elem!1), elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[9490, 959, 9153, 9119, 2362, 9454, 9394])).
% 2.24/2.41 tff(9492,plain,
% 2.24/2.41 (r(s(elem!1), elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[5655, 9491, 9117])).
% 2.24/2.41 tff(9493,plain,
% 2.24/2.41 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[9293, 9492, 9389, 9484])).
% 2.24/2.41 tff(9494,plain,
% 2.24/2.41 (r(s(elem!1), s(s(s(elem!1))))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[1908, 9220])).
% 2.24/2.41 tff(9495,assumption,(~r(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 2.24/2.41 tff(9496,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[9495, 9494])).
% 2.24/2.41 tff(9497,plain,((~r(s(s(z)), s(s(s(s(z)))))) | r(s(elem!1), s(s(s(elem!1)))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(9498,plain,
% 2.24/2.41 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[9497, 9493, 6])).
% 2.24/2.41 tff(9499,plain,
% 2.24/2.41 (b(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[1531, 9498])).
% 2.24/2.41 tff(9500,plain,
% 2.24/2.41 (b(s(elem!1), s(s(s(elem!1))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[3461, 9499, 202])).
% 2.24/2.41 tff(9501,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, 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(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, 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(z, s(s(s(elem!1))))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(9502,plain,
% 2.24/2.41 (((~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(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(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(z, s(s(s(elem!1))))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(9503,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(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(z, s(s(s(elem!1)))))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[9502])).
% 2.24/2.41 tff(9504,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(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(z, s(s(s(elem!1))))))),
% 2.24/2.41 inference(transitivity,[status(thm)],[9503, 9501])).
% 2.24/2.41 tff(9505,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(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))))),
% 2.24/2.41 inference(quant_inst,[status(thm)],[])).
% 2.24/2.41 tff(9506,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, 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(z, s(s(s(elem!1)))))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[9505, 9504])).
% 2.24/2.41 tff(9507,plain,
% 2.24/2.41 (~b(z, s(elem!1))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[9506, 246, 9500, 9473, 9471, 9451])).
% 2.24/2.41 tff(9508,plain,
% 2.24/2.41 (r(z, s(elem!1))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[2561, 9507])).
% 2.24/2.41 tff(9509,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(9510,plain,
% 2.24/2.41 (((~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(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))) <=> ((~b(s(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(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(9511,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[9510])).
% 2.24/2.41 tff(9512,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.24/2.42 inference(transitivity,[status(thm)],[9511, 9509])).
% 2.24/2.42 tff(9513,plain,
% 2.24/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.24/2.42 inference(quant_inst,[status(thm)],[])).
% 2.24/2.42 tff(9514,plain,
% 2.24/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), 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(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[9513, 9512])).
% 2.24/2.42 tff(9515,plain,
% 2.24/2.42 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[9514, 246, 9500, 9473, 9451])).
% 2.24/2.42 tff(9516,plain,
% 2.24/2.42 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[1795, 9515, 9119])).
% 2.24/2.42 tff(9517,plain,
% 2.24/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(z, s(elem!1))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(9518,plain,
% 2.24/2.42 (((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(z, s(s(s(s(s(elem!1)))))))) <=> ((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(z, s(elem!1))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(9519,plain,
% 2.24/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(z, s(elem!1)))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[9518])).
% 2.24/2.42 tff(9520,plain,
% 2.24/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(z, s(elem!1))))),
% 2.24/2.42 inference(transitivity,[status(thm)],[9519, 9517])).
% 2.24/2.42 tff(9521,plain,
% 2.24/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(z, s(s(s(s(s(elem!1))))))))),
% 2.24/2.42 inference(quant_inst,[status(thm)],[])).
% 2.24/2.42 tff(9522,plain,
% 2.24/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(z, s(elem!1)))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[9521, 9520])).
% 2.24/2.42 tff(9523,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[9522, 183, 9516, 9508, 9462])).
% 2.24/2.42 tff(9524,plain,((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~(elem!1 = s(z))) | (~(s(z) = elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(9525,plain,
% 2.24/2.42 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[9524, 5669, 6, 2362, 267, 1099, 202])).
% 2.24/2.42 tff(9526,plain,
% 2.24/2.42 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[1557, 9525, 9189])).
% 2.24/2.42 tff(9527,plain,
% 2.24/2.42 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[6])).
% 2.24/2.42 tff(9528,plain,
% 2.24/2.42 (r(elem!1, s(s(s(z)))) <=> r(s(z), s(s(s(z))))),
% 2.24/2.42 inference(symmetry,[status(thm)],[9527])).
% 2.24/2.42 tff(9529,plain,
% 2.24/2.42 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[2266])).
% 2.24/2.42 tff(9530,plain,
% 2.24/2.42 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(z))))),
% 2.24/2.42 inference(symmetry,[status(thm)],[9529])).
% 2.24/2.42 tff(9531,plain,
% 2.24/2.42 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(s(z))))),
% 2.24/2.42 inference(transitivity,[status(thm)],[9530, 9528])).
% 2.24/2.42 tff(9532,plain,
% 2.24/2.42 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 2.24/2.42 inference(monotonicity,[status(thm)],[6])).
% 2.24/2.42 tff(9533,plain,
% 2.24/2.42 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(s(elem!1)))),
% 2.24/2.42 inference(transitivity,[status(thm)],[9532, 134])).
% 2.24/2.42 tff(9534,plain,
% 2.24/2.42 ((~(s(s(elem!1)) = s(z))) <=> (~(elem!1 = s(s(elem!1))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[9533])).
% 2.24/2.42 tff(9535,plain,
% 2.24/2.42 (~(elem!1 = s(s(elem!1)))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[113, 9534])).
% 2.24/2.42 tff(9536,plain,
% 2.24/2.42 (r(elem!1, s(s(elem!1)))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[1268, 4984, 9535])).
% 2.24/2.42 tff(9537,plain,
% 2.24/2.42 (r(s(z), s(s(s(z))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[9536, 9531])).
% 2.24/2.42 tff(9538,plain,
% 2.24/2.42 (~r(s(s(s(s(z)))), s(z))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6098, 2593, 9537])).
% 2.24/2.42 tff(9539,plain,
% 2.24/2.42 (b(s(s(s(s(z)))), s(z))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6103, 9538])).
% 2.24/2.42 tff(9540,plain,
% 2.24/2.42 (b(s(s(s(elem!1))), elem!1)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[9413, 9539, 6])).
% 2.24/2.42 tff(9541,plain,
% 2.24/2.42 (~b(elem!1, s(s(s(elem!1))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[4537, 9540, 2362, 714, 946])).
% 2.24/2.42 tff(9542,plain,
% 2.24/2.42 (r(elem!1, s(s(s(elem!1))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[9483, 9541, 9195])).
% 2.24/2.42 tff(9543,plain,
% 2.24/2.42 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[2593, 9162])).
% 2.24/2.42 tff(9544,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[3100, 183, 9536, 9543, 9542])).
% 2.24/2.42 tff(9545,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(9546,plain,
% 2.24/2.42 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[9545, 9394, 2362, 9526, 6])).
% 2.24/2.42 tff(9547,plain,
% 2.24/2.42 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[1702, 9546])).
% 2.24/2.42 tff(9548,plain,
% 2.24/2.42 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[9446, 9547, 2266])).
% 2.24/2.42 tff(9549,plain,
% 2.24/2.42 (b(s(z), z) <=> b(elem!1, z)),
% 2.24/2.42 inference(monotonicity,[status(thm)],[6])).
% 2.24/2.42 tff(9550,plain,
% 2.24/2.42 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[9545, 714, 2362, 946, 6])).
% 2.24/2.42 tff(9551,plain,
% 2.24/2.42 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[1702, 9550])).
% 2.24/2.42 tff(9552,plain,
% 2.24/2.42 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[9446, 9551, 2266])).
% 2.24/2.42 tff(9553,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), z)))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(9554,plain,
% 2.24/2.42 (((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), z)))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(9555,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), z))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[9554])).
% 2.24/2.42 tff(9556,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), z)))),
% 2.24/2.42 inference(transitivity,[status(thm)],[9555, 9553])).
% 2.24/2.42 tff(9557,plain,
% 2.24/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))),
% 2.24/2.42 inference(quant_inst,[status(thm)],[])).
% 2.24/2.42 tff(9558,plain,
% 2.24/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), z))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[9557, 9556])).
% 2.24/2.42 tff(9559,plain,
% 2.24/2.42 (~b(s(s(s(elem!1))), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[9558, 246, 1099, 946, 4520, 9552])).
% 2.24/2.42 tff(9560,plain,
% 2.24/2.42 (~b(s(s(s(s(z)))), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[9431, 9559, 2266])).
% 2.24/2.42 tff(9561,plain,
% 2.24/2.42 (r(s(s(s(s(z)))), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6040, 9560])).
% 2.24/2.42 tff(9562,plain,
% 2.24/2.42 (~r(s(z), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[9423, 9561, 6095])).
% 2.24/2.42 tff(9563,plain,
% 2.24/2.42 (b(s(z), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[1069, 9562])).
% 2.24/2.42 tff(9564,plain,
% 2.24/2.42 (b(elem!1, z)),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[9563, 9549])).
% 2.24/2.42 tff(9565,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(9566,plain,
% 2.24/2.42 (((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(9567,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[9566])).
% 2.24/2.42 tff(9568,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.24/2.42 inference(transitivity,[status(thm)],[9567, 9565])).
% 2.24/2.42 tff(9569,plain,
% 2.24/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 2.24/2.42 inference(quant_inst,[status(thm)],[])).
% 2.24/2.42 tff(9570,plain,
% 2.24/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[9569, 9568])).
% 2.24/2.42 tff(9571,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[9570, 246, 9564, 2362, 1099, 714, 946, 4520])).
% 2.24/2.42 tff(9572,plain,((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~(s(z) = elem!1)) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(9573,plain,
% 2.24/2.42 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[9572, 6095, 1099, 714, 946, 6, 2362])).
% 2.24/2.42 tff(9574,plain,
% 2.24/2.42 (r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[1547, 47, 9573, 9086])).
% 2.24/2.42 tff(9575,plain,
% 2.24/2.42 (r(s(z), z)),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[2246, 9377])).
% 2.24/2.42 tff(9576,plain,
% 2.24/2.42 (~r(s(s(s(s(z)))), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[9423, 9575, 6095])).
% 2.24/2.42 tff(9577,plain,
% 2.24/2.42 (b(s(s(s(s(z)))), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6040, 9576])).
% 2.24/2.42 tff(9578,plain,
% 2.24/2.42 (b(s(s(s(elem!1))), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[9431, 9577, 2266])).
% 2.24/2.42 tff(9579,plain,
% 2.24/2.42 (~b(s(s(elem!1)), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[9440, 9578, 1099, 1659])).
% 2.24/2.42 tff(9580,plain,
% 2.24/2.42 (r(s(s(elem!1)), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[523, 9579])).
% 2.24/2.42 tff(9581,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[7107, 183, 2246, 9580, 602])).
% 2.24/2.42 tff(9582,plain,((~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(9583,plain,
% 2.24/2.42 (~r(elem!1, z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[9582, 6095, 1099, 9552, 9536, 6])).
% 2.24/2.42 tff(9584,plain,
% 2.24/2.42 (b(elem!1, z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[1143, 9583, 1438])).
% 2.24/2.42 tff(9585,plain,
% 2.24/2.42 (~b(s(s(elem!1)), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[9387, 9584, 2362, 1099])).
% 2.24/2.42 tff(9586,plain,
% 2.24/2.42 (r(s(s(elem!1)), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[523, 9585])).
% 2.24/2.42 tff(9587,plain,
% 2.24/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(9588,plain,
% 2.24/2.42 (((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(9589,plain,
% 2.24/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), z))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[9588])).
% 2.24/2.42 tff(9590,plain,
% 2.24/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 2.24/2.42 inference(transitivity,[status(thm)],[9589, 9587])).
% 2.24/2.42 tff(9591,plain,
% 2.24/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 2.24/2.42 inference(quant_inst,[status(thm)],[])).
% 2.24/2.42 tff(9592,plain,
% 2.24/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), z))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[9591, 9590])).
% 2.24/2.42 tff(9593,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[9592, 183, 9586, 9574, 5669])).
% 2.24/2.42 tff(9594,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (elem!1 = z) | (~(s(z) = elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(9595,plain,
% 2.24/2.42 (~r(s(s(s(s(z)))), s(z))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[9594, 5669, 2362, 1099, 5401, 6, 9394, 9526])).
% 2.24/2.42 tff(9596,plain,
% 2.24/2.42 (b(s(s(s(s(z)))), s(z))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6103, 9595])).
% 2.24/2.42 tff(9597,plain,
% 2.24/2.42 (b(s(s(s(elem!1))), elem!1)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[9413, 9596, 6])).
% 2.24/2.42 tff(9598,plain,
% 2.24/2.42 (~b(elem!1, s(s(s(s(s(elem!1))))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[4864, 9597, 2362, 9086, 9134, 9394, 9124])).
% 2.24/2.42 tff(9599,plain,
% 2.24/2.42 (r(elem!1, s(s(s(s(s(elem!1))))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[5125, 9598, 9397])).
% 2.24/2.42 tff(9600,plain,
% 2.24/2.42 (~b(elem!1, s(s(s(elem!1))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[4537, 9597, 2362, 9394, 9526])).
% 2.24/2.42 tff(9601,plain,
% 2.24/2.42 (r(elem!1, s(s(s(elem!1))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[9483, 9600, 9195])).
% 2.24/2.42 tff(9602,plain,
% 2.24/2.42 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[4869, 9601, 9599])).
% 2.24/2.42 tff(9603,plain,
% 2.24/2.42 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[3693, 9602, 9124])).
% 2.24/2.42 tff(9604,plain,
% 2.24/2.42 (~b(elem!1, s(s(elem!1)))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[4983, 9526, 2362, 9394])).
% 2.24/2.42 tff(9605,plain,
% 2.24/2.42 (r(elem!1, s(s(elem!1)))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[1268, 9604, 9535])).
% 2.24/2.42 tff(9606,plain,
% 2.24/2.42 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[5295, 9601, 9605])).
% 2.24/2.42 tff(9607,plain,
% 2.24/2.42 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[4455, 9606, 9134])).
% 2.24/2.42 tff(9608,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[1667, 9607, 9603, 9526, 9548])).
% 2.24/2.42 tff(9609,plain,((~r(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), elem!1)) | (~(s(z) = elem!1)) | (~b(z, s(s(elem!1)))) | (~r(z, elem!1)) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(9610,plain,
% 2.24/2.42 (~r(s(s(s(s(s(elem!1))))), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[9609, 9079, 8750, 9375, 5365, 8755])).
% 2.24/2.42 tff(9611,plain,
% 2.24/2.42 (b(s(s(s(s(s(elem!1))))), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[1601, 9610])).
% 2.24/2.42 tff(9612,plain,
% 2.24/2.42 ((~(s(s(s(s(s(elem!1))))) = s(z))) <=> (~(s(s(s(s(s(elem!1))))) = elem!1))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[8751])).
% 2.24/2.42 tff(9613,plain,
% 2.24/2.42 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[331, 9612])).
% 2.24/2.42 tff(9614,plain,
% 2.24/2.42 (~r(s(s(s(z))), s(z))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[2274, 8750, 2232])).
% 2.24/2.42 tff(9615,plain,
% 2.24/2.42 (b(s(s(s(z))), s(z))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[52, 9614])).
% 2.24/2.42 tff(9616,plain,
% 2.24/2.42 (b(elem!1, s(s(s(z)))) <=> b(s(z), s(s(s(z))))),
% 2.24/2.42 inference(symmetry,[status(thm)],[9088])).
% 2.24/2.42 tff(9617,plain,
% 2.24/2.42 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(z))))),
% 2.24/2.42 inference(symmetry,[status(thm)],[9087])).
% 2.24/2.42 tff(9618,plain,
% 2.24/2.42 (b(elem!1, s(s(elem!1))) <=> b(s(z), s(s(s(z))))),
% 2.24/2.42 inference(transitivity,[status(thm)],[9617, 9616])).
% 2.24/2.42 tff(9619,plain,
% 2.24/2.42 (b(z, s(s(elem!1)))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[9374, 4651, 2266])).
% 2.24/2.42 tff(9620,plain,
% 2.24/2.42 (b(z, s(s(s(s(s(elem!1))))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[2487, 47, 5517, 5706])).
% 2.24/2.42 tff(9621,assumption,(b(z, s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 2.24/2.42 tff(9622,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(9623,plain,
% 2.24/2.42 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(9624,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[9623])).
% 2.24/2.43 tff(9625,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.24/2.43 inference(transitivity,[status(thm)],[9624, 9622])).
% 2.24/2.43 tff(9626,plain,
% 2.24/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.24/2.43 inference(quant_inst,[status(thm)],[])).
% 2.24/2.43 tff(9627,plain,
% 2.24/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[9626, 9625])).
% 2.24/2.43 tff(9628,plain,
% 2.24/2.43 ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[9627, 246, 2362, 1099, 9221])).
% 2.24/2.43 tff(9629,plain,
% 2.24/2.43 (~b(s(s(elem!1)), z)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[9628, 946])).
% 2.24/2.43 tff(9630,plain,
% 2.24/2.43 (r(s(s(elem!1)), z)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[523, 9629])).
% 2.24/2.43 tff(9631,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, 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(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, 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(elem!1))))), s(s(elem!1)))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(9632,plain,
% 2.24/2.43 (((~b(elem!1, z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, 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(elem!1))))), s(s(elem!1)))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(9633,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, 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(elem!1))))), s(s(elem!1))))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[9632])).
% 2.24/2.43 tff(9634,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, 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(elem!1))))), s(s(elem!1)))))),
% 2.24/2.43 inference(transitivity,[status(thm)],[9633, 9631])).
% 2.24/2.43 tff(9635,plain,
% 2.24/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 2.24/2.43 inference(quant_inst,[status(thm)],[])).
% 2.24/2.43 tff(9636,plain,
% 2.24/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[9635, 9634])).
% 2.24/2.43 tff(9637,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[9636, 246, 1051, 2362, 1099, 946, 9221, 9621])).
% 2.24/2.43 tff(9638,plain,((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.43 tff(9639,plain,
% 2.24/2.43 (~b(elem!1, z)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[9638, 946, 1099, 2362, 9221, 9621])).
% 2.24/2.43 tff(9640,plain,
% 2.24/2.43 (r(elem!1, z)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1143, 9639, 1438])).
% 2.24/2.43 tff(9641,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[7107, 183, 9640, 9630, 602])).
% 2.24/2.43 tff(9642,plain,((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (elem!1 = z) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.43 tff(9643,plain,
% 2.24/2.43 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[9642, 602, 1438, 1099, 2362, 9221, 9621])).
% 2.24/2.43 tff(9644,plain,
% 2.24/2.43 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1557, 9643, 1555])).
% 2.24/2.43 tff(9645,plain,
% 2.24/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(9646,plain,
% 2.24/2.43 (((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(9647,plain,
% 2.24/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[9646])).
% 2.24/2.43 tff(9648,plain,
% 2.24/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.24/2.43 inference(transitivity,[status(thm)],[9647, 9645])).
% 2.24/2.43 tff(9649,plain,
% 2.24/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.24/2.43 inference(quant_inst,[status(thm)],[])).
% 2.24/2.43 tff(9650,plain,
% 2.24/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[9649, 9648])).
% 2.24/2.43 tff(9651,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[9650, 183, 602, 333, 9644])).
% 2.24/2.43 tff(9652,plain,((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | (elem!1 = z) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.43 tff(9653,plain,
% 2.24/2.43 (~r(elem!1, s(s(elem!1)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[9652, 9620, 9189, 5401, 9619, 2362, 9221, 333])).
% 2.24/2.43 tff(9654,plain,
% 2.24/2.43 (b(elem!1, s(s(elem!1)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1268, 9653, 9535])).
% 2.24/2.43 tff(9655,plain,
% 2.24/2.43 (b(s(z), s(s(s(z))))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[9654, 9618])).
% 2.24/2.43 tff(9656,plain,
% 2.24/2.43 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[7450, 9655, 2003, 171, 4651])).
% 2.24/2.43 tff(9657,plain,
% 2.24/2.43 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1702, 9656])).
% 2.24/2.43 tff(9658,plain,
% 2.24/2.43 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[9657, 9162])).
% 2.24/2.43 tff(9659,plain,
% 2.24/2.43 (~b(s(s(s(elem!1))), elem!1)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[9158, 9655, 2362, 267, 3697, 6])).
% 2.24/2.43 tff(9660,plain,
% 2.24/2.43 (~b(s(s(s(s(z)))), s(z))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[9413, 9659, 6])).
% 2.24/2.43 tff(9661,plain,
% 2.24/2.43 (r(s(s(s(s(z)))), s(z))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[6103, 9660])).
% 2.24/2.43 tff(9662,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(9663,plain,
% 2.24/2.43 (((~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(9664,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1))))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[9663])).
% 2.24/2.43 tff(9665,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))))),
% 2.24/2.43 inference(transitivity,[status(thm)],[9664, 9662])).
% 2.24/2.43 tff(9666,plain,
% 2.24/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))),
% 2.24/2.43 inference(quant_inst,[status(thm)],[])).
% 2.24/2.43 tff(9667,plain,
% 2.24/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1))))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[9666, 9665])).
% 2.24/2.43 tff(9668,plain,
% 2.24/2.43 (~b(elem!1, z)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[9667, 246, 2362, 9654, 9619])).
% 2.24/2.43 tff(9669,plain,
% 2.24/2.43 (r(elem!1, z)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1143, 9668, 5401])).
% 2.24/2.43 tff(9670,plain,
% 2.24/2.43 (r(s(z), z)),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[9669, 9377])).
% 2.24/2.43 tff(9671,plain,
% 2.24/2.43 (~r(s(s(s(s(z)))), z)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[9423, 9670, 9661])).
% 2.24/2.43 tff(9672,plain,
% 2.24/2.43 (b(s(s(s(s(z)))), z)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[6040, 9671])).
% 2.24/2.43 tff(9673,plain,
% 2.24/2.43 (b(s(s(s(elem!1))), z)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[9431, 9672, 2266])).
% 2.24/2.43 tff(9674,plain,
% 2.24/2.43 (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[9345, 183, 3076, 959])).
% 2.24/2.43 tff(9675,plain,
% 2.24/2.43 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[913, 47, 785, 9674])).
% 2.24/2.43 tff(9676,plain,
% 2.24/2.43 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[5176, 959, 3076])).
% 2.24/2.43 tff(9677,plain,
% 2.24/2.43 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[3693, 9676, 775])).
% 2.24/2.43 tff(9678,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(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(elem!1))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(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(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(9679,plain,
% 2.24/2.43 (((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(9680,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(elem!1))), z))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[9679])).
% 2.24/2.43 tff(9681,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(elem!1))), z)))),
% 2.24/2.43 inference(transitivity,[status(thm)],[9680, 9678])).
% 2.24/2.43 tff(9682,plain,
% 2.24/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), z)))),
% 2.24/2.43 inference(quant_inst,[status(thm)],[])).
% 2.24/2.43 tff(9683,plain,
% 2.24/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[9682, 9681])).
% 2.24/2.43 tff(9684,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[9683, 246, 9677, 9205, 9621, 9675])).
% 2.24/2.43 tff(9685,plain,((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.43 tff(9686,plain,
% 2.24/2.43 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[9685, 9673, 9620, 9348, 9658, 9124])).
% 2.24/2.43 tff(9687,plain,
% 2.24/2.43 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1557, 9686, 9189])).
% 2.24/2.43 tff(9688,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(9689,plain,
% 2.24/2.43 (((~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(9690,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[9689])).
% 2.24/2.43 tff(9691,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.24/2.43 inference(transitivity,[status(thm)],[9690, 9688])).
% 2.24/2.43 tff(9692,plain,
% 2.24/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 2.24/2.43 inference(quant_inst,[status(thm)],[])).
% 2.24/2.43 tff(9693,plain,
% 2.24/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[9692, 9691])).
% 2.24/2.43 tff(9694,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[9693, 246, 2362, 9654, 9619, 9687, 9221])).
% 2.24/2.43 tff(9695,plain,((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~(s(z) = elem!1)) | (~b(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~b(z, s(s(s(z))))) | (~r(z, elem!1)) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.43 tff(9696,plain,
% 2.24/2.43 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[9695, 9079, 9611, 8750, 9615, 170, 9368, 5365, 9078])).
% 2.24/2.43 tff(9697,plain,
% 2.24/2.43 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[86, 9696, 9613])).
% 2.24/2.43 tff(9698,plain,
% 2.24/2.43 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 2.24/2.43 inference(monotonicity,[status(thm)],[8750])).
% 2.24/2.43 tff(9699,plain,
% 2.24/2.43 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(s(elem!1)))),
% 2.24/2.43 inference(transitivity,[status(thm)],[9698, 134])).
% 2.24/2.43 tff(9700,plain,
% 2.24/2.43 ((~(s(s(elem!1)) = s(z))) <=> (~(elem!1 = s(s(elem!1))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[9699])).
% 2.24/2.43 tff(9701,plain,
% 2.24/2.43 (~(elem!1 = s(s(elem!1)))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[113, 9700])).
% 2.24/2.43 tff(9702,plain,
% 2.24/2.43 ((s(s(s(s(s(elem!1))))) = s(s(s(z)))) <=> (s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[8756])).
% 2.24/2.43 tff(9703,plain,
% 2.24/2.43 ((~(s(s(s(s(s(elem!1))))) = s(s(s(z))))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(elem!1))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[9702])).
% 2.24/2.43 tff(9704,plain,
% 2.24/2.43 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[1622, 9703])).
% 2.24/2.43 tff(9705,plain,
% 2.24/2.43 (~b(elem!1, s(s(elem!1)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[9141, 961, 9086, 9134, 2362, 714, 9124])).
% 2.24/2.43 tff(9706,plain,
% 2.24/2.43 (r(elem!1, s(s(elem!1)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1268, 9705, 9535])).
% 2.24/2.43 tff(9707,plain,
% 2.24/2.43 (~b(elem!1, s(s(s(s(s(elem!1))))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[4864, 961, 2362, 9086, 9134, 714, 9124])).
% 2.24/2.43 tff(9708,plain,
% 2.24/2.43 (r(elem!1, s(s(s(s(s(elem!1))))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[5125, 9707, 9397])).
% 2.24/2.43 tff(9709,plain,
% 2.24/2.43 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[5165, 9708, 9706])).
% 2.24/2.43 tff(9710,plain,
% 2.24/2.43 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1557, 9709, 9189])).
% 2.24/2.43 tff(9711,plain,
% 2.24/2.43 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[9545, 9710, 2362, 714, 6])).
% 2.24/2.43 tff(9712,plain,
% 2.24/2.43 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1702, 9711])).
% 2.24/2.43 tff(9713,plain,
% 2.24/2.43 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[9446, 9712, 2266])).
% 2.24/2.43 tff(9714,plain,
% 2.24/2.43 (~b(elem!1, s(s(s(elem!1))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[4537, 9710, 2362, 714, 961])).
% 2.24/2.43 tff(9715,plain,
% 2.24/2.43 (r(elem!1, s(s(s(elem!1))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[9483, 9714, 9195])).
% 2.24/2.43 tff(9716,plain,
% 2.24/2.43 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[4869, 9715, 9708])).
% 2.24/2.43 tff(9717,plain,
% 2.24/2.43 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[3693, 9716, 9124])).
% 2.24/2.43 tff(9718,plain,
% 2.24/2.43 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[5295, 9715, 9706])).
% 2.24/2.43 tff(9719,plain,
% 2.24/2.43 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[4455, 9718, 9134])).
% 2.24/2.43 tff(9720,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1667, 9719, 9717, 9710, 9713])).
% 2.24/2.43 tff(9721,plain,((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.43 tff(9722,plain,
% 2.24/2.43 (~b(s(s(s(elem!1))), elem!1)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[9721, 2362, 714, 6])).
% 2.24/2.43 tff(9723,plain,
% 2.24/2.43 (~r(s(s(s(s(s(elem!1))))), z)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[9609, 2362, 6, 1099, 267, 202])).
% 2.24/2.43 tff(9724,plain,
% 2.24/2.43 (b(s(s(s(s(s(elem!1))))), z)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1601, 9723])).
% 2.24/2.43 tff(9725,plain,
% 2.24/2.43 (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[9345, 183, 9543, 959])).
% 2.24/2.43 tff(9726,plain,
% 2.24/2.43 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[913, 47, 9348, 9725])).
% 2.24/2.43 tff(9727,plain,
% 2.24/2.43 (~b(s(s(s(s(z)))), s(z))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[9413, 9722, 6])).
% 2.24/2.43 tff(9728,plain,
% 2.24/2.43 (r(s(s(s(s(z)))), s(z))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[6103, 9727])).
% 2.24/2.43 tff(9729,plain,
% 2.24/2.43 (~r(s(z), s(s(s(z))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[6098, 2593, 9728])).
% 2.24/2.43 tff(9730,plain,
% 2.24/2.43 (b(s(z), s(s(s(z))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1291, 9729])).
% 2.24/2.43 tff(9731,plain,
% 2.24/2.43 (b(elem!1, s(s(elem!1)))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[9730, 9089])).
% 2.24/2.43 tff(9732,plain,
% 2.24/2.43 (~b(elem!1, z)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[9667, 246, 2362, 9731, 1099])).
% 2.24/2.44 tff(9733,plain,
% 2.24/2.44 (r(elem!1, z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[1143, 9732, 1438])).
% 2.24/2.44 tff(9734,plain,
% 2.24/2.44 (r(s(z), z)),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[9733, 9377])).
% 2.24/2.44 tff(9735,plain,
% 2.24/2.44 (~r(s(s(s(s(z)))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[9423, 9734, 9728])).
% 2.24/2.44 tff(9736,plain,
% 2.24/2.44 (b(s(s(s(s(z)))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6040, 9735])).
% 2.24/2.44 tff(9737,plain,
% 2.24/2.44 (b(s(s(s(elem!1))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[9431, 9736, 2266])).
% 2.24/2.44 tff(9738,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(9739,plain,
% 2.24/2.44 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(9740,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), z))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[9739])).
% 2.24/2.44 tff(9741,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 2.24/2.44 inference(transitivity,[status(thm)],[9740, 9738])).
% 2.24/2.44 tff(9742,plain,
% 2.24/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 2.24/2.44 inference(quant_inst,[status(thm)],[])).
% 2.24/2.44 tff(9743,plain,
% 2.24/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), z))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[9742, 9741])).
% 2.24/2.44 tff(9744,plain,
% 2.24/2.44 ($false),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[9743, 246, 2362, 1099, 714, 9221, 9737, 9726])).
% 2.24/2.44 tff(9745,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~(s(z) = elem!1)) | (elem!1 = z) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.44 tff(9746,plain,
% 2.24/2.44 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[9745, 959, 1099, 714, 9724, 6, 5401, 2362])).
% 2.24/2.44 tff(9747,plain,
% 2.24/2.44 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[1702, 9746])).
% 2.24/2.44 tff(9748,plain,
% 2.24/2.44 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[9446, 9747, 2266])).
% 2.24/2.44 tff(9749,plain,
% 2.24/2.44 (~b(elem!1, s(s(elem!1)))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[9308, 9748, 6, 2362, 202, 267, 9722])).
% 2.24/2.44 tff(9750,plain,
% 2.24/2.44 (r(elem!1, s(s(elem!1)))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[1268, 9749, 9535])).
% 2.24/2.44 tff(9751,plain,
% 2.24/2.44 (~r(elem!1, s(s(s(s(s(elem!1))))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[5165, 9750, 959])).
% 2.24/2.44 tff(9752,plain,
% 2.24/2.44 (b(elem!1, s(s(s(s(s(elem!1))))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[5125, 9751, 9397])).
% 2.24/2.44 tff(9753,plain,
% 2.24/2.44 (~r(elem!1, z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[9582, 9750, 1099, 9728, 9748, 6])).
% 2.24/2.44 tff(9754,plain,
% 2.24/2.44 (b(elem!1, z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[1143, 9753, 5401])).
% 2.24/2.44 tff(9755,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(9756,plain,
% 2.24/2.44 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(9757,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1)))))))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[9756])).
% 2.24/2.44 tff(9758,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 2.24/2.44 inference(transitivity,[status(thm)],[9757, 9755])).
% 2.24/2.44 tff(9759,plain,
% 2.24/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 2.24/2.44 inference(quant_inst,[status(thm)],[])).
% 2.24/2.44 tff(9760,plain,
% 2.24/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1)))))))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[9759, 9758])).
% 2.24/2.44 tff(9761,plain,
% 2.24/2.44 ($false),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[9760, 246, 9754, 2362, 1099, 714, 9724, 9752])).
% 2.24/2.44 tff(9762,plain,((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~(s(z) = elem!1)) | (~(elem!1 = s(z))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.44 tff(9763,plain,
% 2.24/2.44 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[9762, 9079, 9375, 9697, 8750, 8755, 5365])).
% 2.24/2.44 tff(9764,plain,
% 2.24/2.44 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[1557, 9763, 9704])).
% 2.24/2.44 tff(9765,plain,
% 2.24/2.44 (~b(elem!1, s(s(elem!1)))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[4983, 9764, 9079, 9697])).
% 2.24/2.44 tff(9766,plain,
% 2.24/2.44 (r(elem!1, s(s(elem!1)))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[1268, 9765, 9701])).
% 2.24/2.44 tff(9767,plain,
% 2.24/2.44 (~b(s(s(s(elem!1))), elem!1)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[9721, 9079, 9697, 8750])).
% 2.24/2.44 tff(9768,plain,
% 2.24/2.44 (~b(s(s(s(s(z)))), s(z))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[9413, 9767, 8750])).
% 2.24/2.44 tff(9769,plain,
% 2.24/2.44 (r(s(s(s(s(z)))), s(z))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6103, 9768])).
% 2.24/2.44 tff(9770,plain,
% 2.24/2.44 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[9545, 9764, 9079, 9697, 8750])).
% 2.24/2.44 tff(9771,plain,
% 2.24/2.44 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[1702, 9770])).
% 2.24/2.44 tff(9772,plain,
% 2.24/2.44 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[9446, 9771, 8756])).
% 2.24/2.44 tff(9773,plain,
% 2.24/2.44 (~r(elem!1, z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[9582, 9772, 9375, 9769, 9766, 8750])).
% 2.24/2.44 tff(9774,plain,
% 2.24/2.44 (b(elem!1, z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[1143, 9773, 5701])).
% 2.24/2.44 tff(9775,plain,
% 2.24/2.44 (~b(elem!1, s(s(s(s(s(elem!1))))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[9760, 246, 9774, 9079, 9375, 9697, 9611])).
% 2.24/2.44 tff(9776,plain,
% 2.24/2.44 (r(elem!1, s(s(s(s(s(elem!1))))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[5125, 9775, 8754])).
% 2.24/2.44 tff(9777,plain,
% 2.24/2.44 (~b(z, s(s(s(s(s(elem!1))))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[9642, 9766, 5701, 9375, 9079, 9611, 9764])).
% 2.24/2.44 tff(9778,plain,
% 2.24/2.44 (r(z, s(s(s(s(s(elem!1))))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[2487, 47, 5706, 9777])).
% 2.24/2.44 tff(9779,plain,
% 2.24/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(9780,plain,
% 2.24/2.44 (((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(9781,plain,
% 2.24/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1)))))))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[9780])).
% 2.24/2.44 tff(9782,plain,
% 2.24/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))),
% 2.24/2.44 inference(transitivity,[status(thm)],[9781, 9779])).
% 2.24/2.44 tff(9783,plain,
% 2.24/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(z, elem!1)))),
% 2.24/2.44 inference(quant_inst,[status(thm)],[])).
% 2.24/2.44 tff(9784,plain,
% 2.24/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1)))))))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[9783, 9782])).
% 2.24/2.44 tff(9785,plain,
% 2.24/2.44 ($false),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[9784, 183, 5365, 9778, 9776])).
% 2.24/2.44 tff(9786,plain,(b(s(z), elem!1) | r(s(s(elem!1)), elem!1) | b(z, elem!1) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.44 tff(9787,plain,
% 2.24/2.44 (b(s(z), elem!1)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[9786, 54, 55, 2232])).
% 2.24/2.44 tff(9788,plain,
% 2.24/2.44 (b(s(s(s(z))), elem!1)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[9077, 171, 267, 2232, 201])).
% 2.24/2.44 tff(9789,plain,
% 2.24/2.44 (~(elem!1 = s(z))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[207, 145, 201])).
% 2.24/2.44 tff(9790,plain,
% 2.24/2.44 (b(elem!1, s(z))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[214, 9789, 8759])).
% 2.24/2.44 tff(9791,plain,
% 2.24/2.44 (~b(s(s(s(z))), s(z))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[7339, 246, 1044, 9790, 9788])).
% 2.24/2.44 tff(9792,plain,
% 2.24/2.44 (r(s(s(s(z))), s(z))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[52, 9791])).
% 2.24/2.44 tff(9793,plain,
% 2.24/2.44 (~r(z, s(s(s(z))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[438, 9792, 171])).
% 2.24/2.44 tff(9794,plain,
% 2.24/2.44 (b(z, s(s(s(z))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6165, 9793])).
% 2.24/2.44 tff(9795,plain,
% 2.24/2.44 (~r(s(s(s(z))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6464, 183, 267, 171, 9792])).
% 2.24/2.44 tff(9796,plain,
% 2.24/2.44 (b(s(s(s(z))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[995, 9795])).
% 2.24/2.44 tff(9797,plain,
% 2.24/2.44 (s(s(elem!1)) = elem!1),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[156, 145, 2232])).
% 2.24/2.44 tff(9798,plain,
% 2.24/2.44 (elem!1 = s(s(elem!1))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6867, 9797])).
% 2.24/2.44 tff(9799,plain,
% 2.24/2.44 (s(s(s(elem!1))) = s(elem!1)),
% 2.24/2.44 inference(monotonicity,[status(thm)],[9797])).
% 2.24/2.44 tff(9800,plain,
% 2.24/2.44 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[9799])).
% 2.24/2.44 tff(9801,plain,
% 2.24/2.44 (s(s(s(s(elem!1)))) = elem!1),
% 2.24/2.44 inference(transitivity,[status(thm)],[9800, 9797])).
% 2.24/2.44 tff(9802,plain,
% 2.24/2.44 (s(s(s(s(s(elem!1))))) = s(elem!1)),
% 2.24/2.44 inference(monotonicity,[status(thm)],[9801])).
% 2.24/2.44 tff(9803,plain,
% 2.24/2.44 ((s(s(s(s(s(elem!1))))) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[9802])).
% 2.24/2.44 tff(9804,plain,
% 2.24/2.44 ((~(s(s(s(s(s(elem!1))))) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[9803])).
% 2.24/2.44 tff(9805,plain,
% 2.24/2.44 (~(s(elem!1) = s(s(s(z))))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[1622, 9804])).
% 2.24/2.44 tff(9806,plain,
% 2.24/2.44 (~(s(s(s(s(z)))) = elem!1)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[2399, 9805, 9798])).
% 2.24/2.44 tff(9807,assumption,(s(s(z)) = elem!1), introduced(assumption)).
% 2.24/2.44 tff(9808,plain,
% 2.24/2.44 (s(s(z)) = s(s(elem!1))),
% 2.24/2.44 inference(transitivity,[status(thm)],[9807, 5380])).
% 2.24/2.44 tff(9809,plain,
% 2.24/2.44 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[9808])).
% 2.24/2.44 tff(9810,plain,
% 2.24/2.44 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.24/2.44 inference(symmetry,[status(thm)],[9809])).
% 2.24/2.44 tff(9811,plain,
% 2.24/2.44 (s(s(s(s(s(elem!1))))) = s(z)),
% 2.24/2.44 inference(transitivity,[status(thm)],[5861, 108, 9810, 1486])).
% 2.24/2.44 tff(9812,plain,
% 2.24/2.44 ($false),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[331, 9811])).
% 2.24/2.44 tff(9813,plain,((~(s(s(z)) = elem!1)) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.44 tff(9814,plain,
% 2.24/2.44 (~(s(s(z)) = elem!1)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[9813, 9797])).
% 2.24/2.44 tff(9815,plain,
% 2.24/2.44 (~(elem!1 = s(s(s(s(z)))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[8712, 3074])).
% 2.24/2.44 tff(9816,plain,
% 2.24/2.44 (~b(elem!1, s(s(s(s(z)))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[7175, 246, 1044, 2001, 8267])).
% 2.24/2.44 tff(9817,plain,
% 2.24/2.44 (r(elem!1, s(s(s(s(z)))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[5969, 47, 9816, 9815])).
% 2.24/2.44 tff(9818,plain,
% 2.24/2.44 (~b(s(s(s(z))), s(z))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[7339, 246, 1044, 2001, 3697])).
% 2.24/2.44 tff(9819,plain,
% 2.24/2.44 (r(s(s(s(z))), s(z))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[52, 9818])).
% 2.24/2.44 tff(9820,plain,
% 2.24/2.44 (~r(z, s(s(s(z))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[438, 9819, 171])).
% 2.24/2.44 tff(9821,plain,
% 2.24/2.44 (b(z, s(s(s(z))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6165, 9820])).
% 2.24/2.44 tff(9822,plain,
% 2.24/2.44 (~r(s(s(s(z))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6464, 183, 267, 171, 9819])).
% 2.24/2.44 tff(9823,plain,
% 2.24/2.44 (b(s(s(s(z))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[995, 9822])).
% 2.24/2.44 tff(9824,plain,
% 2.24/2.44 (~b(s(s(s(s(z)))), elem!1)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[9050, 8267, 2001, 1044])).
% 2.24/2.44 tff(9825,assumption,(~b(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 2.24/2.44 tff(9826,plain,
% 2.24/2.44 (r(s(s(s(s(z)))), elem!1)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[2442, 47, 3074, 9825])).
% 2.24/2.44 tff(9827,plain,
% 2.24/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(9828,plain,
% 2.24/2.44 (((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(9829,plain,
% 2.24/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[9828])).
% 2.24/2.44 tff(9830,plain,
% 2.24/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 2.24/2.44 inference(transitivity,[status(thm)],[9829, 9827])).
% 2.24/2.44 tff(9831,plain,
% 2.24/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 2.24/2.44 inference(quant_inst,[status(thm)],[])).
% 2.24/2.44 tff(9832,plain,
% 2.24/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[9831, 9830])).
% 2.24/2.44 tff(9833,plain,
% 2.24/2.44 ($false),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[9832, 183, 267, 7218, 9826])).
% 2.24/2.44 tff(9834,plain,((~r(s(s(s(s(z)))), z)) | (~r(z, elem!1)) | (s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.24/2.44 tff(9835,plain,
% 2.24/2.44 (~r(s(s(s(s(z)))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[9834, 9824, 3074, 267])).
% 2.24/2.44 tff(9836,plain,
% 2.24/2.44 (b(s(s(s(s(z)))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6040, 9835])).
% 2.24/2.44 tff(9837,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(9838,plain,
% 2.24/2.44 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(9839,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[9838])).
% 2.24/2.44 tff(9840,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.24/2.44 inference(transitivity,[status(thm)],[9839, 9837])).
% 2.24/2.44 tff(9841,plain,
% 2.24/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.24/2.44 inference(quant_inst,[status(thm)],[])).
% 2.24/2.44 tff(9842,plain,
% 2.24/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[9841, 9840])).
% 2.24/2.44 tff(9843,plain,
% 2.24/2.44 ($false),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[9842, 246, 4651, 2090, 1833, 8266])).
% 2.24/2.44 tff(9844,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.44 tff(9845,plain,
% 2.24/2.44 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[9844, 9836, 9823, 9821])).
% 2.24/2.44 tff(9846,plain,
% 2.24/2.44 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[1702, 9845])).
% 2.24/2.44 tff(9847,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(9848,plain,
% 2.24/2.44 (((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(9849,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z)))))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[9848])).
% 2.24/2.44 tff(9850,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 2.24/2.45 inference(transitivity,[status(thm)],[9849, 9847])).
% 2.24/2.45 tff(9851,plain,
% 2.24/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 2.24/2.45 inference(quant_inst,[status(thm)],[])).
% 2.24/2.45 tff(9852,plain,
% 2.24/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z)))))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[9851, 9850])).
% 2.24/2.45 tff(9853,plain,
% 2.24/2.45 (~b(s(z), s(s(s(z))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[9852, 246, 1044, 2001, 3697])).
% 2.24/2.45 tff(9854,plain,
% 2.24/2.45 (r(s(z), s(s(s(z))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[1291, 9853])).
% 2.24/2.45 tff(9855,plain,
% 2.24/2.45 (~r(s(z), s(s(s(s(z)))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[6088, 183, 9854, 9846])).
% 2.24/2.45 tff(9856,plain,
% 2.24/2.45 ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z)))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[6092, 47, 9855])).
% 2.24/2.45 tff(9857,plain,
% 2.24/2.45 (b(s(z), s(s(s(s(z)))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[9856, 5790])).
% 2.24/2.45 tff(9858,plain,
% 2.24/2.45 ((z = s(s(z))) <=> (s(s(z)) = z)),
% 2.24/2.45 inference(commutativity,[status(thm)],[])).
% 2.24/2.45 tff(9859,plain,
% 2.24/2.45 ((s(s(z)) = z) <=> (z = s(s(z)))),
% 2.24/2.45 inference(symmetry,[status(thm)],[9858])).
% 2.24/2.45 tff(9860,plain,
% 2.24/2.45 ((~(s(s(z)) = z)) <=> (~(z = s(s(z))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[9859])).
% 2.24/2.45 tff(9861,plain,
% 2.24/2.45 (~(z = s(s(z)))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[35, 9860])).
% 2.24/2.45 tff(9862,assumption,(b(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 2.24/2.45 tff(9863,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(9864,plain,
% 2.24/2.45 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(9865,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[9864])).
% 2.24/2.45 tff(9866,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 2.24/2.45 inference(transitivity,[status(thm)],[9865, 9863])).
% 2.24/2.45 tff(9867,plain,
% 2.24/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 2.24/2.45 inference(quant_inst,[status(thm)],[])).
% 2.24/2.45 tff(9868,plain,
% 2.24/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[9867, 9866])).
% 2.24/2.45 tff(9869,plain,
% 2.24/2.45 (~b(s(s(z)), s(z))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[9868, 246, 1044, 3457, 8267, 9862])).
% 2.24/2.45 tff(9870,plain,
% 2.24/2.45 ((s(s(z)) = s(z)) | r(s(s(z)), s(z))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[8601, 47, 9869])).
% 2.24/2.45 tff(9871,plain,
% 2.24/2.45 (r(s(s(z)), s(z))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[9870, 8591])).
% 2.24/2.45 tff(9872,plain,
% 2.24/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(z))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(9873,plain,
% 2.24/2.45 (((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(z))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(9874,plain,
% 2.24/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(z)))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[9873])).
% 2.24/2.45 tff(9875,plain,
% 2.24/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(z))))),
% 2.24/2.45 inference(transitivity,[status(thm)],[9874, 9872])).
% 2.24/2.45 tff(9876,plain,
% 2.24/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.24/2.45 inference(quant_inst,[status(thm)],[])).
% 2.24/2.45 tff(9877,plain,
% 2.24/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(z)))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[9876, 9875])).
% 2.24/2.45 tff(9878,plain,
% 2.24/2.45 (~r(s(s(s(z))), s(s(z)))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[9877, 183, 430, 9871])).
% 2.24/2.45 tff(9879,plain,
% 2.24/2.45 (b(s(s(s(z))), s(s(z)))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[8991, 47, 8374, 9878])).
% 2.24/2.45 tff(9880,plain,
% 2.24/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(9881,plain,
% 2.24/2.45 (((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(9882,plain,
% 2.24/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z)))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[9881])).
% 2.24/2.45 tff(9883,plain,
% 2.24/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 2.24/2.45 inference(transitivity,[status(thm)],[9882, 9880])).
% 2.24/2.45 tff(9884,plain,
% 2.24/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.24/2.45 inference(quant_inst,[status(thm)],[])).
% 2.24/2.45 tff(9885,plain,
% 2.24/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z)))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[9884, 9883])).
% 2.24/2.45 tff(9886,plain,
% 2.24/2.45 (~r(s(s(z)), s(s(s(z))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[9885, 183, 430, 9871])).
% 2.24/2.45 tff(9887,plain,
% 2.24/2.45 (b(s(s(z)), s(s(s(z))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[8382, 9886])).
% 2.24/2.45 tff(9888,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(9889,plain,
% 2.24/2.45 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(9890,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z))))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[9889])).
% 2.24/2.45 tff(9891,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))))),
% 2.24/2.45 inference(transitivity,[status(thm)],[9890, 9888])).
% 2.24/2.45 tff(9892,plain,
% 2.24/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))))),
% 2.24/2.45 inference(quant_inst,[status(thm)],[])).
% 2.24/2.45 tff(9893,plain,
% 2.24/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z))))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[9892, 9891])).
% 2.24/2.45 tff(9894,plain,
% 2.24/2.45 (~b(z, s(s(z)))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[9893, 246, 6456, 3457, 9887, 9879])).
% 2.24/2.45 tff(9895,plain,
% 2.24/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(9896,plain,
% 2.24/2.45 (((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z))))) <=> ((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(9897,plain,
% 2.24/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z)))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[9896])).
% 2.24/2.45 tff(9898,plain,
% 2.24/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))))),
% 2.24/2.45 inference(transitivity,[status(thm)],[9897, 9895])).
% 2.24/2.45 tff(9899,plain,
% 2.24/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))),
% 2.24/2.45 inference(quant_inst,[status(thm)],[])).
% 2.24/2.45 tff(9900,plain,
% 2.24/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z)))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[9899, 9898])).
% 2.24/2.45 tff(9901,plain,
% 2.24/2.45 (~r(z, s(s(z)))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[9900, 183, 171, 9871])).
% 2.24/2.45 tff(9902,plain,
% 2.24/2.45 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(9903,plain,
% 2.24/2.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z))))),
% 2.24/2.45 inference(quant_inst,[status(thm)],[])).
% 2.24/2.45 tff(9904,plain,
% 2.24/2.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z)))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[9903, 9902])).
% 2.24/2.45 tff(9905,plain,
% 2.24/2.45 ((z = s(s(z))) | b(z, s(s(z)))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[9904, 47, 9901])).
% 2.24/2.45 tff(9906,plain,
% 2.24/2.45 ($false),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[9905, 9894, 9861])).
% 2.24/2.45 tff(9907,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.45 tff(9908,plain,
% 2.24/2.45 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[9907, 9857, 171, 1044, 8267, 9819])).
% 2.24/2.45 tff(9909,plain,
% 2.24/2.45 (r(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[1531, 9908])).
% 2.24/2.45 tff(9910,plain,
% 2.24/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(9911,plain,
% 2.24/2.45 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1))) <=> ((~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(9912,plain,
% 2.24/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[9911])).
% 2.24/2.45 tff(9913,plain,
% 2.24/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.24/2.45 inference(transitivity,[status(thm)],[9912, 9910])).
% 2.24/2.45 tff(9914,plain,
% 2.24/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))),
% 2.24/2.45 inference(quant_inst,[status(thm)],[])).
% 2.24/2.45 tff(9915,plain,
% 2.24/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[9914, 9913])).
% 2.24/2.45 tff(9916,plain,
% 2.24/2.45 (~r(s(s(z)), elem!1)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[9915, 183, 9909, 9817])).
% 2.24/2.45 tff(9917,assumption,(~(s(s(z)) = elem!1)), introduced(assumption)).
% 2.24/2.45 tff(9918,plain,
% 2.24/2.45 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(9919,plain,
% 2.24/2.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1))),
% 2.24/2.45 inference(quant_inst,[status(thm)],[])).
% 2.24/2.45 tff(9920,plain,
% 2.24/2.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1)),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[9919, 9918])).
% 2.24/2.45 tff(9921,plain,
% 2.24/2.45 (b(s(s(z)), elem!1)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[9920, 47, 9917, 9916])).
% 2.24/2.45 tff(9922,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(9923,plain,
% 2.24/2.45 (((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(9924,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[9923])).
% 2.24/2.46 tff(9925,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 2.24/2.46 inference(transitivity,[status(thm)],[9924, 9922])).
% 2.24/2.46 tff(9926,plain,
% 2.24/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.24/2.46 inference(quant_inst,[status(thm)],[])).
% 2.24/2.46 tff(9927,plain,
% 2.24/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[9926, 9925])).
% 2.24/2.46 tff(9928,plain,
% 2.24/2.46 (~b(s(s(z)), s(s(s(z))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[9927, 246, 1044, 2001, 3697, 9921])).
% 2.24/2.46 tff(9929,plain,
% 2.24/2.46 (r(s(s(z)), s(s(s(z))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[8382, 9928])).
% 2.24/2.46 tff(9930,plain,
% 2.24/2.46 ($false),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[8354, 183, 9909, 9846, 9929])).
% 2.24/2.46 tff(9931,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (s(s(z)) = elem!1) | (~r(z, s(z))) | (s(s(s(s(z)))) = elem!1) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.46 tff(9932,plain,
% 2.24/2.46 (~b(s(s(s(s(z)))), s(z))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[9931, 9790, 1044, 9788, 9814, 171, 9806, 267])).
% 2.24/2.46 tff(9933,plain,
% 2.24/2.46 (r(s(s(s(s(z)))), s(z))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[6103, 9932])).
% 2.24/2.46 tff(9934,plain,
% 2.24/2.46 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[8491, 9933, 9792])).
% 2.24/2.46 tff(9935,plain,
% 2.24/2.46 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[1702, 9934])).
% 2.24/2.46 tff(9936,plain,
% 2.24/2.46 (~b(s(s(s(s(z)))), z)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[9844, 9935, 9796, 9794])).
% 2.24/2.46 tff(9937,plain,
% 2.24/2.46 (r(s(s(s(s(z)))), z)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[6040, 9936])).
% 2.24/2.46 tff(9938,plain,
% 2.24/2.46 ($false),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[6502, 183, 267, 171, 9933, 9937])).
% 2.24/2.46 tff(9939,plain,(b(s(s(elem!1)), elem!1) | (~r(z, elem!1)) | (~r(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.24/2.46 tff(9940,plain,
% 2.24/2.46 (b(s(s(elem!1)), elem!1)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[9939, 170, 5365, 9787, 8749, 2232])).
% 2.24/2.46 tff(9941,plain,
% 2.24/2.46 (~b(elem!1, s(z))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[3799, 9940, 8749, 9787])).
% 2.24/2.46 tff(9942,plain,
% 2.24/2.46 (elem!1 = s(z)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[214, 9941, 6376])).
% 2.24/2.46 tff(9943,plain,
% 2.24/2.46 (s(z) = elem!1),
% 2.24/2.46 inference(symmetry,[status(thm)],[9942])).
% 2.24/2.46 tff(9944,plain,
% 2.24/2.46 (b(s(z), elem!1) <=> b(elem!1, elem!1)),
% 2.24/2.46 inference(monotonicity,[status(thm)],[9943])).
% 2.24/2.46 tff(9945,plain,
% 2.24/2.46 (b(elem!1, elem!1) <=> b(s(z), elem!1)),
% 2.24/2.46 inference(symmetry,[status(thm)],[9944])).
% 2.24/2.46 tff(9946,plain,
% 2.24/2.46 ((~b(elem!1, elem!1)) <=> (~b(s(z), elem!1))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[9945])).
% 2.24/2.46 tff(9947,plain,
% 2.24/2.46 (~b(s(z), elem!1)),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[5691, 9946])).
% 2.24/2.46 tff(9948,plain,
% 2.24/2.46 ($false),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[9787, 9947])).
% 2.24/2.46 tff(9949,plain,(b(z, s(z)) | r(s(s(elem!1)), elem!1) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.24/2.46 tff(9950,plain,
% 2.24/2.46 (b(z, s(z))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[9949, 2232, 55])).
% 2.24/2.46 tff(9951,plain,
% 2.24/2.46 (~(s(z) = elem!1)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[3065, 9950, 55])).
% 2.24/2.46 tff(9952,plain,
% 2.24/2.46 (b(elem!1, s(z))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[201, 2126])).
% 2.24/2.46 tff(9953,plain,
% 2.24/2.46 (~r(s(elem!1), elem!1)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[6072, 6625, 267, 2125, 236])).
% 2.24/2.46 tff(9954,plain,
% 2.24/2.46 (b(s(s(s(z))), elem!1)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[6859, 1445, 7591, 267])).
% 2.24/2.46 tff(9955,plain,
% 2.24/2.46 (~(elem!1 = s(s(s(z))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[8772, 2125, 5806])).
% 2.24/2.46 tff(9956,plain,
% 2.24/2.46 (~b(elem!1, z)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[7290, 246, 6627, 2001, 236])).
% 2.24/2.46 tff(9957,plain,
% 2.24/2.46 (r(elem!1, z)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[1143, 9956, 5401])).
% 2.24/2.46 tff(9958,plain,
% 2.24/2.46 (b(s(s(s(s(z)))), elem!1)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[9834, 7218, 3074, 267])).
% 2.24/2.46 tff(9959,plain,
% 2.24/2.46 ($false),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[7246, 183, 2246, 7218, 5972])).
% 2.24/2.46 tff(9960,plain,((~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.46 tff(9961,plain,
% 2.24/2.46 (~r(elem!1, s(s(s(s(z)))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[9960, 7218, 2246])).
% 2.24/2.46 tff(9962,plain,
% 2.24/2.46 (b(elem!1, s(s(s(s(z)))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[5969, 47, 9961, 9815])).
% 2.24/2.46 tff(9963,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(9964,plain,
% 2.24/2.46 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(9965,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z))))))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[9964])).
% 2.24/2.46 tff(9966,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.24/2.46 inference(transitivity,[status(thm)],[9965, 9963])).
% 2.24/2.46 tff(9967,plain,
% 2.24/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.24/2.46 inference(quant_inst,[status(thm)],[])).
% 2.24/2.46 tff(9968,plain,
% 2.24/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z))))))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[9967, 9966])).
% 2.24/2.46 tff(9969,plain,
% 2.24/2.46 ($false),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[9968, 246, 3697, 1833, 9962, 9958])).
% 2.24/2.46 tff(9970,plain,((~r(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, z)) | (s(s(s(s(z)))) = elem!1) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.46 tff(9971,plain,
% 2.24/2.46 (~r(s(s(s(s(z)))), z)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[9970, 9954, 1833, 9957, 7592, 267])).
% 2.24/2.46 tff(9972,plain,
% 2.24/2.46 (b(s(s(s(s(z)))), z)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[6040, 9971])).
% 2.24/2.46 tff(9973,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(9974,plain,
% 2.24/2.46 (((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(9975,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[9974])).
% 2.24/2.46 tff(9976,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.24/2.46 inference(transitivity,[status(thm)],[9975, 9973])).
% 2.24/2.46 tff(9977,plain,
% 2.24/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.24/2.46 inference(quant_inst,[status(thm)],[])).
% 2.24/2.46 tff(9978,plain,
% 2.24/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[9977, 9976])).
% 2.24/2.46 tff(9979,plain,
% 2.24/2.46 ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[9978, 246, 2001, 236, 9954, 1833])).
% 2.24/2.46 tff(9980,plain,
% 2.24/2.46 (~b(z, s(s(s(z))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[9979, 9972])).
% 2.24/2.46 tff(9981,plain,
% 2.24/2.46 (r(z, s(s(s(z))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[6165, 9980])).
% 2.24/2.46 tff(9982,plain,
% 2.24/2.46 (~r(elem!1, s(s(s(z))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[2254, 9981, 9957])).
% 2.24/2.46 tff(9983,plain,
% 2.24/2.46 (b(elem!1, s(s(s(z))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[470, 9982, 9955])).
% 2.24/2.46 tff(9984,plain,
% 2.24/2.46 ((~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[5902, 246, 2002, 3697])).
% 2.24/2.46 tff(9985,plain,
% 2.24/2.46 (~b(s(elem!1), s(s(s(z))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[9984, 1200])).
% 2.24/2.46 tff(9986,plain,
% 2.24/2.46 (r(s(elem!1), s(s(s(z))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[1752, 47, 5896, 9985])).
% 2.24/2.46 tff(9987,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(9988,plain,
% 2.24/2.46 (((~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(9989,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[9988])).
% 2.24/2.46 tff(9990,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 2.24/2.46 inference(transitivity,[status(thm)],[9989, 9987])).
% 2.24/2.46 tff(9991,plain,
% 2.24/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))))),
% 2.24/2.46 inference(quant_inst,[status(thm)],[])).
% 2.24/2.46 tff(9992,plain,
% 2.24/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[9991, 9990])).
% 2.24/2.46 tff(9993,plain,
% 2.24/2.46 ($false),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[9992, 246, 2001, 2002, 3697, 2401])).
% 2.24/2.46 tff(9994,plain,((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.46 tff(9995,plain,
% 2.24/2.46 (~b(s(z), s(s(s(z))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[9994, 2002, 2001, 3697])).
% 2.24/2.46 tff(9996,plain,
% 2.24/2.46 (r(s(z), s(s(s(z))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[1291, 9995])).
% 2.24/2.46 tff(9997,plain,
% 2.24/2.46 (~r(s(z), s(elem!1))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[8830, 183, 9996, 9986])).
% 2.24/2.46 tff(9998,plain,
% 2.24/2.46 ((s(z) = s(elem!1)) | b(s(z), s(elem!1))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[2973, 47, 9997])).
% 2.24/2.46 tff(9999,plain,
% 2.24/2.46 (b(s(z), s(elem!1))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[9998, 6053])).
% 2.24/2.46 tff(10000,plain,
% 2.24/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(10001,plain,
% 2.24/2.46 (((~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(10002,plain,
% 2.24/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z)))))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[10001])).
% 2.24/2.46 tff(10003,plain,
% 2.24/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))))),
% 2.24/2.46 inference(transitivity,[status(thm)],[10002, 10000])).
% 2.24/2.46 tff(10004,plain,
% 2.24/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))),
% 2.24/2.46 inference(quant_inst,[status(thm)],[])).
% 2.24/2.46 tff(10005,plain,
% 2.24/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z)))))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[10004, 10003])).
% 2.24/2.46 tff(10006,plain,
% 2.24/2.46 (~r(s(elem!1), s(z))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[10005, 183, 217, 9996, 9986])).
% 2.24/2.46 tff(10007,plain,
% 2.24/2.46 ((s(elem!1) = s(z)) | b(s(elem!1), s(z))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[2989, 47, 10006])).
% 2.24/2.46 tff(10008,plain,
% 2.24/2.46 (b(s(elem!1), s(z))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[10007, 7631])).
% 2.24/2.46 tff(10009,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(10010,plain,
% 2.24/2.46 (((~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(10011,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1)))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[10010])).
% 2.24/2.46 tff(10012,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))),
% 2.24/2.46 inference(transitivity,[status(thm)],[10011, 10009])).
% 2.24/2.46 tff(10013,plain,
% 2.24/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), elem!1)))),
% 2.24/2.46 inference(quant_inst,[status(thm)],[])).
% 2.24/2.46 tff(10014,plain,
% 2.24/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1)))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[10013, 10012])).
% 2.24/2.46 tff(10015,plain,
% 2.24/2.46 ($false),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[10014, 246, 2001, 10008, 1200, 9999])).
% 2.24/2.46 tff(10016,plain,((~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~(s(s(elem!1)) = elem!1)) | (~r(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.46 tff(10017,plain,
% 2.24/2.46 (~b(s(elem!1), elem!1)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[10016, 9983, 2001, 2125, 9954, 6625])).
% 2.24/2.46 tff(10018,plain,
% 2.24/2.46 (s(elem!1) = elem!1),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[5655, 10017, 9953])).
% 2.24/2.46 tff(10019,plain,
% 2.24/2.46 (elem!1 = s(elem!1)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[3953, 10018])).
% 2.24/2.46 tff(10020,plain,
% 2.24/2.46 (s(elem!1) = elem!1),
% 2.24/2.46 inference(symmetry,[status(thm)],[10019])).
% 2.24/2.46 tff(10021,plain,
% 2.24/2.46 (r(s(z), s(elem!1)) <=> r(s(z), elem!1)),
% 2.24/2.46 inference(monotonicity,[status(thm)],[10020])).
% 2.24/2.46 tff(10022,plain,
% 2.24/2.46 (r(s(z), elem!1) <=> r(s(z), s(elem!1))),
% 2.24/2.46 inference(symmetry,[status(thm)],[10021])).
% 2.24/2.46 tff(10023,plain,
% 2.24/2.46 (r(s(z), s(elem!1))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[6625, 10022])).
% 2.24/2.46 tff(10024,plain,
% 2.24/2.46 (r(z, s(elem!1)) <=> r(z, elem!1)),
% 2.24/2.46 inference(monotonicity,[status(thm)],[10020])).
% 2.24/2.46 tff(10025,plain,
% 2.24/2.46 (r(z, elem!1) <=> r(z, s(elem!1))),
% 2.24/2.46 inference(symmetry,[status(thm)],[10024])).
% 2.24/2.46 tff(10026,plain,
% 2.24/2.46 (r(z, s(elem!1))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[267, 10025])).
% 2.24/2.46 tff(10027,plain,
% 2.24/2.46 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[7760, 8240])).
% 2.24/2.46 tff(10028,plain,
% 2.24/2.46 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(elem!1))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[10019])).
% 2.24/2.46 tff(10029,plain,
% 2.24/2.46 ((~b(s(s(s(s(z)))), elem!1)) <=> (~b(s(s(s(s(z)))), s(elem!1)))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[10028])).
% 2.24/2.46 tff(10030,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(10031,plain,
% 2.24/2.47 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(10032,plain,
% 2.24/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[10031])).
% 2.24/2.47 tff(10033,plain,
% 2.24/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.24/2.47 inference(transitivity,[status(thm)],[10032, 10030])).
% 2.24/2.47 tff(10034,plain,
% 2.24/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.24/2.47 inference(quant_inst,[status(thm)],[])).
% 2.24/2.47 tff(10035,plain,
% 2.24/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[10034, 10033])).
% 2.24/2.47 tff(10036,plain,
% 2.24/2.47 ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[10035, 246, 2001, 9954, 1833])).
% 2.24/2.47 tff(10037,plain,
% 2.24/2.47 (~b(s(s(s(s(z)))), elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[10036, 9983])).
% 2.24/2.47 tff(10038,plain,
% 2.24/2.47 (~b(s(s(s(s(z)))), s(elem!1))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[10037, 10029])).
% 2.24/2.47 tff(10039,plain,
% 2.24/2.47 (r(s(s(s(s(z)))), s(elem!1))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1728, 10038, 10027])).
% 2.24/2.47 tff(10040,plain,
% 2.24/2.47 ($false),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[8271, 10039, 10026, 6627, 10023, 236])).
% 2.24/2.47 tff(10041,plain,(b(s(z), elem!1) | (~b(z, s(z))) | (~r(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~(s(s(elem!1)) = elem!1)) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.24/2.47 tff(10042,plain,
% 2.24/2.47 (b(s(z), elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[10041, 1833, 267, 9952, 236, 2125, 2277])).
% 2.24/2.47 tff(10043,plain,
% 2.24/2.47 (~b(elem!1, z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1138, 10042, 267, 201, 236])).
% 2.24/2.47 tff(10044,plain,
% 2.24/2.47 (r(elem!1, z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1143, 10043, 5401])).
% 2.24/2.47 tff(10045,plain,
% 2.24/2.47 (~b(s(z), z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[8269, 8266, 236, 8267])).
% 2.24/2.47 tff(10046,plain,
% 2.24/2.47 (r(s(z), z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1069, 10045])).
% 2.24/2.47 tff(10047,plain,
% 2.24/2.47 (~r(s(z), elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[5432, 10046, 267])).
% 2.24/2.47 tff(10048,plain,
% 2.24/2.47 (b(s(z), elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1034, 10047, 2277])).
% 2.24/2.47 tff(10049,plain,
% 2.24/2.47 (~b(elem!1, z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1138, 10048, 267, 201, 236])).
% 2.24/2.47 tff(10050,plain,
% 2.24/2.47 (r(elem!1, z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1143, 10049, 5401])).
% 2.24/2.47 tff(10051,plain,
% 2.24/2.47 (~r(s(s(s(z))), elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[6592, 429, 267])).
% 2.24/2.47 tff(10052,plain,
% 2.24/2.47 (b(s(s(s(z))), elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[647, 10051, 3011])).
% 2.24/2.47 tff(10053,plain,
% 2.24/2.47 (~r(elem!1, s(s(s(z))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[2254, 429, 2246])).
% 2.24/2.47 tff(10054,plain,
% 2.24/2.47 (b(elem!1, s(s(s(z))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[470, 10053, 1675])).
% 2.24/2.47 tff(10055,plain,
% 2.24/2.47 (~b(s(z), s(s(s(z))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[9994, 10054, 10052, 2001])).
% 2.24/2.47 tff(10056,plain,
% 2.24/2.47 (r(s(z), s(s(s(z))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1291, 10055])).
% 2.24/2.47 tff(10057,plain,
% 2.24/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(10058,plain,
% 2.24/2.47 (((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(10059,plain,
% 2.24/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[10058])).
% 2.24/2.47 tff(10060,plain,
% 2.24/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 2.24/2.47 inference(transitivity,[status(thm)],[10059, 10057])).
% 2.24/2.47 tff(10061,plain,
% 2.24/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)))),
% 2.24/2.47 inference(quant_inst,[status(thm)],[])).
% 2.24/2.47 tff(10062,plain,
% 2.24/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[10061, 10060])).
% 2.24/2.47 tff(10063,plain,
% 2.24/2.47 ($false),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[10062, 183, 1114, 10056, 429])).
% 2.24/2.47 tff(10064,plain,((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~b(elem!1, s(z))) | (elem!1 = s(s(s(z)))) | (s(s(s(z))) = elem!1) | (~r(elem!1, z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.47 tff(10065,plain,
% 2.24/2.47 (~r(z, s(s(s(z))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[10064, 10046, 2001, 1675, 3011, 10050, 267])).
% 2.24/2.47 tff(10066,plain,
% 2.24/2.47 (b(z, s(s(s(z))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[6165, 10065])).
% 2.24/2.47 tff(10067,plain,
% 2.24/2.47 (~b(s(s(s(z))), z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[9844, 10066, 1833, 8266])).
% 2.24/2.47 tff(10068,plain,
% 2.24/2.47 (r(s(s(s(z))), z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[995, 10067])).
% 2.24/2.47 tff(10069,plain,
% 2.24/2.47 ($false),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[5411, 183, 267, 634, 997])).
% 2.24/2.47 tff(10070,plain,((~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.47 tff(10071,plain,
% 2.24/2.47 (~r(s(s(s(z))), elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[10070, 10068, 267])).
% 2.24/2.47 tff(10072,plain,
% 2.24/2.47 (b(s(s(s(z))), elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[647, 10071, 3011])).
% 2.24/2.47 tff(10073,plain,
% 2.24/2.47 ($false),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[9978, 246, 2001, 236, 10072, 10066, 1833, 8266])).
% 2.24/2.47 tff(10074,plain,((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (s(s(s(z))) = elem!1) | (~r(z, elem!1)) | (elem!1 = s(s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (s(z) = elem!1) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.47 tff(10075,plain,
% 2.24/2.47 (~b(s(s(s(s(z)))), z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[10074, 8267, 236, 1833, 3011, 267, 1675, 201, 2277, 2001])).
% 2.24/2.47 tff(10076,plain,
% 2.24/2.47 (r(s(s(s(s(z)))), z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[6040, 10075])).
% 2.24/2.47 tff(10077,plain,
% 2.24/2.47 (b(s(s(s(s(z)))), elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[9834, 10076, 3074, 267])).
% 2.24/2.47 tff(10078,plain,
% 2.24/2.47 (~b(s(z), elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[9050, 10077, 2001, 8267])).
% 2.24/2.47 tff(10079,plain,
% 2.24/2.47 (r(s(z), elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1034, 10078, 2277])).
% 2.24/2.47 tff(10080,plain,
% 2.24/2.47 (~r(s(z), z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[5432, 10079, 267])).
% 2.24/2.47 tff(10081,plain,
% 2.24/2.47 (b(s(z), z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1069, 10080])).
% 2.24/2.47 tff(10082,plain,
% 2.24/2.47 (~b(elem!1, z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[7290, 246, 10081, 2001, 236])).
% 2.24/2.47 tff(10083,plain,
% 2.24/2.47 (r(elem!1, z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1143, 10082, 5401])).
% 2.24/2.47 tff(10084,plain,
% 2.24/2.47 (~r(elem!1, s(s(s(s(z)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[9960, 10083, 10076])).
% 2.24/2.47 tff(10085,plain,
% 2.24/2.47 (b(elem!1, s(s(s(s(z)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[5969, 47, 10084, 9815])).
% 2.24/2.47 tff(10086,plain,
% 2.24/2.47 (b(s(s(s(z))), elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[6859, 10078, 2392, 267])).
% 2.24/2.47 tff(10087,plain,
% 2.24/2.47 ($false),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[9968, 246, 10086, 1833, 10085, 10077])).
% 2.24/2.47 tff(10088,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~r(z, elem!1)) | (~(elem!1 = s(s(elem!1)))) | (s(z) = elem!1) | (s(s(s(s(z)))) = elem!1) | (s(s(s(z))) = elem!1) | (elem!1 = s(s(s(z)))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.47 tff(10089,plain,
% 2.24/2.47 (~b(s(s(s(s(z)))), s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[10088, 1833, 9952, 236, 267, 7591, 2277, 7592, 5386, 9955, 201])).
% 2.24/2.47 tff(10090,plain,
% 2.24/2.47 (r(s(s(s(s(z)))), s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[6103, 10089])).
% 2.24/2.47 tff(10091,plain,
% 2.24/2.47 (~(s(s(z)) = elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[9813, 2125])).
% 2.24/2.47 tff(10092,plain,
% 2.24/2.47 (~r(s(s(s(z))), z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[10070, 634, 267])).
% 2.24/2.47 tff(10093,plain,
% 2.24/2.47 (b(s(s(s(z))), z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[995, 10092])).
% 2.24/2.47 tff(10094,plain,
% 2.24/2.47 (~b(s(s(s(s(z)))), z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[9844, 10093, 1833, 7911])).
% 2.24/2.47 tff(10095,plain,
% 2.24/2.47 (r(s(s(s(s(z)))), z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[6040, 10094])).
% 2.24/2.47 tff(10096,plain,
% 2.24/2.47 (~r(s(z), z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[9423, 10095, 6095])).
% 2.24/2.47 tff(10097,plain,
% 2.24/2.47 (b(s(z), z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1069, 10096])).
% 2.24/2.47 tff(10098,plain,
% 2.24/2.47 (~b(s(s(s(z))), s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[6174, 10097, 236, 7911])).
% 2.24/2.47 tff(10099,plain,
% 2.24/2.47 (r(s(s(s(z))), s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[52, 10098])).
% 2.24/2.47 tff(10100,plain,
% 2.24/2.47 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[8223, 10099, 6095])).
% 2.24/2.47 tff(10101,plain,
% 2.24/2.47 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[8213, 47, 8210, 10100])).
% 2.24/2.47 tff(10102,plain,
% 2.24/2.47 (~r(elem!1, s(s(s(s(z)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[9960, 10095, 2246])).
% 2.24/2.47 tff(10103,plain,
% 2.24/2.47 (b(elem!1, s(s(s(s(z)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[5969, 47, 10102, 9815])).
% 2.24/2.47 tff(10104,plain,
% 2.24/2.47 (~b(z, s(s(s(s(z)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[8791, 246, 7911, 10093, 1833])).
% 2.24/2.47 tff(10105,plain,
% 2.24/2.47 ((z = s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[2645, 47, 10104])).
% 2.24/2.47 tff(10106,plain,
% 2.24/2.47 (r(z, s(s(s(s(z)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[10105, 2635])).
% 2.24/2.47 tff(10107,plain,
% 2.24/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(10108,plain,
% 2.24/2.47 (((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(z)))) <=> ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(10109,plain,
% 2.24/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[10108])).
% 2.24/2.47 tff(10110,plain,
% 2.24/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.24/2.47 inference(transitivity,[status(thm)],[10109, 10107])).
% 2.24/2.47 tff(10111,plain,
% 2.24/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(z))))),
% 2.24/2.47 inference(quant_inst,[status(thm)],[])).
% 2.24/2.47 tff(10112,plain,
% 2.24/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[10111, 10110])).
% 2.24/2.47 tff(10113,plain,
% 2.24/2.47 (~b(s(z), s(s(s(s(z)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[10112, 246, 10097, 2001, 10093, 1833, 10103])).
% 2.24/2.47 tff(10114,plain,
% 2.24/2.47 ((s(z) = s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[6092, 47, 10113])).
% 2.24/2.47 tff(10115,plain,
% 2.24/2.47 (r(s(z), s(s(s(s(z)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[10114, 5790])).
% 2.24/2.47 tff(10116,plain,
% 2.24/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(10117,plain,
% 2.24/2.47 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(10118,plain,
% 2.24/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[10117])).
% 2.24/2.47 tff(10119,plain,
% 2.24/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 2.24/2.47 inference(transitivity,[status(thm)],[10118, 10116])).
% 2.24/2.47 tff(10120,plain,
% 2.24/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 2.24/2.47 inference(quant_inst,[status(thm)],[])).
% 2.24/2.47 tff(10121,plain,
% 2.24/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[10120, 10119])).
% 2.24/2.47 tff(10122,plain,
% 2.24/2.47 (~b(s(z), s(s(s(z))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[10121, 246, 10097, 7911, 10093])).
% 2.24/2.47 tff(10123,plain,
% 2.24/2.47 (r(s(z), s(s(s(z))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1291, 10122])).
% 2.24/2.47 tff(10124,assumption,(r(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 2.24/2.47 tff(10125,plain,
% 2.24/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(10126,plain,
% 2.24/2.47 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(10127,plain,
% 2.24/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z)))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[10126])).
% 2.24/2.47 tff(10128,plain,
% 2.24/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))),
% 2.24/2.47 inference(transitivity,[status(thm)],[10127, 10125])).
% 2.24/2.47 tff(10129,plain,
% 2.24/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 2.24/2.47 inference(quant_inst,[status(thm)],[])).
% 2.24/2.47 tff(10130,plain,
% 2.24/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z)))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[10129, 10128])).
% 2.24/2.47 tff(10131,plain,
% 2.24/2.47 (~r(s(s(z)), s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[10130, 183, 6096, 1908, 10124])).
% 2.24/2.47 tff(10132,plain,
% 2.24/2.47 ((s(s(z)) = s(z)) | b(s(s(z)), s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[8601, 47, 10131])).
% 2.24/2.47 tff(10133,plain,
% 2.24/2.47 (b(s(s(z)), s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[10132, 8591])).
% 2.24/2.47 tff(10134,plain,
% 2.24/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(10135,plain,
% 2.24/2.47 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(10136,plain,
% 2.24/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z))))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[10135])).
% 2.24/2.48 tff(10137,plain,
% 2.24/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))))),
% 2.24/2.48 inference(transitivity,[status(thm)],[10136, 10134])).
% 2.24/2.48 tff(10138,plain,
% 2.24/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))))),
% 2.24/2.48 inference(quant_inst,[status(thm)],[])).
% 2.24/2.48 tff(10139,plain,
% 2.24/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z))))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[10138, 10137])).
% 2.24/2.48 tff(10140,plain,
% 2.24/2.48 (~r(z, s(s(z)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[10139, 183, 1908, 8384])).
% 2.24/2.48 tff(10141,plain,
% 2.24/2.48 ((z = s(s(z))) | b(z, s(s(z)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[9904, 47, 10140])).
% 2.24/2.48 tff(10142,plain,
% 2.24/2.48 (b(z, s(s(z)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[10141, 9861])).
% 2.24/2.48 tff(10143,plain,
% 2.24/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(10144,plain,
% 2.24/2.48 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(10145,plain,
% 2.24/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[10144])).
% 2.24/2.48 tff(10146,plain,
% 2.24/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))),
% 2.24/2.48 inference(transitivity,[status(thm)],[10145, 10143])).
% 2.24/2.48 tff(10147,plain,
% 2.24/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))),
% 2.24/2.48 inference(quant_inst,[status(thm)],[])).
% 2.24/2.48 tff(10148,plain,
% 2.24/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[10147, 10146])).
% 2.24/2.48 tff(10149,plain,
% 2.24/2.48 (~r(s(z), s(s(z)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[10148, 183, 1908, 10124])).
% 2.24/2.48 tff(10150,plain,
% 2.24/2.48 (b(s(z), s(s(z)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[8343, 47, 8340, 10149])).
% 2.24/2.48 tff(10151,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(10152,plain,
% 2.24/2.48 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z)))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(10153,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[10152])).
% 2.24/2.48 tff(10154,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 2.24/2.48 inference(transitivity,[status(thm)],[10153, 10151])).
% 2.24/2.48 tff(10155,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))),
% 2.24/2.48 inference(quant_inst,[status(thm)],[])).
% 2.24/2.48 tff(10156,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[10155, 10154])).
% 2.24/2.48 tff(10157,plain,
% 2.24/2.48 ($false),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[10156, 246, 1056, 236, 10150, 10142, 10133])).
% 2.24/2.48 tff(10158,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.48 tff(10159,plain,
% 2.24/2.48 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[10158, 10097, 236, 10123, 10115, 10106])).
% 2.24/2.48 tff(10160,plain,
% 2.24/2.48 (b(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[1531, 10159])).
% 2.24/2.48 tff(10161,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(10162,plain,
% 2.24/2.48 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(10163,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[10162])).
% 2.24/2.48 tff(10164,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 2.24/2.48 inference(transitivity,[status(thm)],[10163, 10161])).
% 2.24/2.48 tff(10165,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 2.24/2.48 inference(quant_inst,[status(thm)],[])).
% 2.24/2.48 tff(10166,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[10165, 10164])).
% 2.24/2.48 tff(10167,plain,
% 2.24/2.48 (~b(s(s(z)), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[10166, 246, 10160, 1833, 10103, 10101])).
% 2.24/2.48 tff(10168,plain,
% 2.24/2.48 (r(s(s(z)), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[9920, 47, 9917, 10167])).
% 2.24/2.48 tff(10169,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(10170,plain,
% 2.24/2.48 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(10171,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[10170])).
% 2.24/2.48 tff(10172,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.24/2.48 inference(transitivity,[status(thm)],[10171, 10169])).
% 2.24/2.48 tff(10173,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.24/2.48 inference(quant_inst,[status(thm)],[])).
% 2.24/2.48 tff(10174,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[10173, 10172])).
% 2.24/2.48 tff(10175,plain,
% 2.24/2.48 (~b(s(s(z)), s(s(s(z))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[10174, 246, 10093, 10160, 1833, 10101])).
% 2.24/2.48 tff(10176,plain,
% 2.24/2.48 (r(s(s(z)), s(s(s(z))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[8382, 10175])).
% 2.24/2.48 tff(10177,plain,
% 2.24/2.48 (b(s(s(s(s(z)))), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[9834, 10095, 3074, 267])).
% 2.24/2.48 tff(10178,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(10179,plain,
% 2.24/2.48 (((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(10180,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[10179])).
% 2.24/2.48 tff(10181,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.24/2.48 inference(transitivity,[status(thm)],[10180, 10178])).
% 2.24/2.48 tff(10182,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.24/2.48 inference(quant_inst,[status(thm)],[])).
% 2.24/2.48 tff(10183,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[10182, 10181])).
% 2.24/2.48 tff(10184,plain,
% 2.24/2.48 (~b(elem!1, s(s(s(z))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[10183, 246, 2001, 236, 10093, 1833, 10177])).
% 2.24/2.48 tff(10185,plain,
% 2.24/2.48 (r(elem!1, s(s(s(z))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[470, 10184, 1675])).
% 2.24/2.48 tff(10186,plain,
% 2.24/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(10187,plain,
% 2.24/2.48 (((~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(10188,plain,
% 2.24/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z)))))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[10187])).
% 2.24/2.48 tff(10189,plain,
% 2.24/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))))),
% 2.24/2.48 inference(transitivity,[status(thm)],[10188, 10186])).
% 2.24/2.48 tff(10190,plain,
% 2.24/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)))),
% 2.24/2.48 inference(quant_inst,[status(thm)],[])).
% 2.24/2.48 tff(10191,plain,
% 2.24/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z)))))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[10190, 10189])).
% 2.24/2.48 tff(10192,plain,
% 2.24/2.48 ($false),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[10191, 183, 2246, 10185, 10176, 10168])).
% 2.24/2.48 tff(10193,plain,((~r(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (s(s(z)) = elem!1) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (elem!1 = s(s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (s(s(s(s(z)))) = elem!1) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.48 tff(10194,plain,
% 2.24/2.48 (~r(s(s(s(z))), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[10193, 10044, 10091, 1833, 236, 9952, 9955, 10090, 7592, 267])).
% 2.24/2.48 tff(10195,plain,
% 2.24/2.48 (b(s(s(s(z))), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[647, 10194, 5386])).
% 2.24/2.48 tff(10196,plain,
% 2.24/2.48 (~r(s(s(s(s(z)))), z)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[9970, 10195, 1833, 10044, 7592, 267])).
% 2.24/2.48 tff(10197,plain,
% 2.24/2.48 (b(s(s(s(s(z)))), z)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[6040, 10196])).
% 2.24/2.48 tff(10198,plain,
% 2.24/2.48 (~b(z, s(s(s(z))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[9978, 246, 9952, 236, 10195, 1833, 10197])).
% 2.24/2.48 tff(10199,plain,
% 2.24/2.48 (r(z, s(s(s(z))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[6165, 10198])).
% 2.24/2.48 tff(10200,plain,
% 2.24/2.48 (~b(s(z), s(s(s(z))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[9852, 246, 10042, 9952, 10195])).
% 2.24/2.48 tff(10201,plain,
% 2.24/2.48 (r(s(z), s(s(s(z))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[1291, 10200])).
% 2.24/2.48 tff(10202,plain,
% 2.24/2.48 (~r(s(z), z)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[10064, 10199, 9952, 9955, 5386, 10044, 267])).
% 2.24/2.48 tff(10203,plain,
% 2.24/2.48 (b(s(z), z)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[1069, 10202])).
% 2.24/2.48 tff(10204,plain,
% 2.24/2.48 (~r(z, s(s(z)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[3178, 183, 429, 8326])).
% 2.24/2.48 tff(10205,plain,
% 2.24/2.48 ((z = s(s(z))) | b(z, s(s(z)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[9904, 47, 10204])).
% 2.24/2.48 tff(10206,plain,
% 2.24/2.48 (b(z, s(s(z)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[10205, 9861])).
% 2.24/2.48 tff(10207,plain,
% 2.24/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(10208,plain,
% 2.24/2.48 (((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(10209,plain,
% 2.24/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z)))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[10208])).
% 2.24/2.49 tff(10210,plain,
% 2.24/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 2.24/2.49 inference(transitivity,[status(thm)],[10209, 10207])).
% 2.24/2.49 tff(10211,plain,
% 2.24/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 2.24/2.49 inference(quant_inst,[status(thm)],[])).
% 2.24/2.49 tff(10212,plain,
% 2.24/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z)))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[10211, 10210])).
% 2.24/2.49 tff(10213,plain,
% 2.24/2.49 (~r(s(s(z)), s(z))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[10212, 183, 6096, 8326])).
% 2.24/2.49 tff(10214,plain,
% 2.24/2.49 ((s(s(z)) = s(z)) | b(s(s(z)), s(z))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[8601, 47, 10213])).
% 2.24/2.49 tff(10215,plain,
% 2.24/2.49 (b(s(s(z)), s(z))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[10214, 8591])).
% 2.24/2.49 tff(10216,plain,
% 2.24/2.49 ($false),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[10156, 246, 1056, 236, 8344, 10215, 10206])).
% 2.24/2.49 tff(10217,plain,((~r(s(s(z)), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.49 tff(10218,plain,
% 2.24/2.49 (~r(s(s(z)), s(s(s(z))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[10217, 10203, 236, 10201, 10199])).
% 2.24/2.49 tff(10219,plain,
% 2.24/2.49 (b(s(s(z)), s(s(s(z))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[8382, 10218])).
% 2.24/2.49 tff(10220,plain,
% 2.24/2.49 (~r(elem!1, s(s(s(z))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[2254, 10199, 10044])).
% 2.24/2.49 tff(10221,plain,
% 2.24/2.49 (b(elem!1, s(s(s(z))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[470, 10220, 9955])).
% 2.24/2.49 tff(10222,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(10223,plain,
% 2.24/2.49 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(10224,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[10223])).
% 2.24/2.49 tff(10225,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 2.24/2.49 inference(transitivity,[status(thm)],[10224, 10222])).
% 2.24/2.49 tff(10226,plain,
% 2.24/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 2.24/2.49 inference(quant_inst,[status(thm)],[])).
% 2.24/2.49 tff(10227,plain,
% 2.24/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[10226, 10225])).
% 2.24/2.49 tff(10228,plain,
% 2.24/2.49 (~b(s(s(z)), elem!1)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[10227, 246, 9952, 10221, 10195, 10219])).
% 2.24/2.49 tff(10229,plain,
% 2.24/2.49 (r(s(s(z)), elem!1)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[9920, 47, 10091, 10228])).
% 2.24/2.49 tff(10230,plain,
% 2.24/2.49 (~b(elem!1, s(s(s(s(z)))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[5965, 246, 10221, 10195, 1833])).
% 2.24/2.49 tff(10231,plain,
% 2.24/2.49 (r(elem!1, s(s(s(s(z)))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[5969, 47, 10230, 8867])).
% 2.24/2.49 tff(10232,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(10233,plain,
% 2.24/2.49 (((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(10234,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[10233])).
% 2.24/2.49 tff(10235,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.24/2.49 inference(transitivity,[status(thm)],[10234, 10232])).
% 2.24/2.49 tff(10236,plain,
% 2.24/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.24/2.49 inference(quant_inst,[status(thm)],[])).
% 2.24/2.49 tff(10237,plain,
% 2.24/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[10236, 10235])).
% 2.24/2.49 tff(10238,plain,
% 2.24/2.49 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[10237, 246, 10221, 10195, 1833, 10219])).
% 2.24/2.49 tff(10239,plain,
% 2.24/2.49 (r(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[1531, 10238])).
% 2.24/2.49 tff(10240,plain,
% 2.24/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(10241,plain,
% 2.24/2.49 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(10242,plain,
% 2.24/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[10241])).
% 2.24/2.49 tff(10243,plain,
% 2.24/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.24/2.49 inference(transitivity,[status(thm)],[10242, 10240])).
% 2.24/2.49 tff(10244,plain,
% 2.24/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)))),
% 2.24/2.49 inference(quant_inst,[status(thm)],[])).
% 2.24/2.49 tff(10245,plain,
% 2.24/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[10244, 10243])).
% 2.24/2.49 tff(10246,plain,
% 2.24/2.49 ($false),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[10245, 183, 10044, 10239, 10231, 10229])).
% 2.24/2.49 tff(10247,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(z))) | (~r(z, elem!1)) | (~b(s(s(elem!1)), s(z))) | (~(s(s(elem!1)) = elem!1)) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.24/2.49 tff(10248,plain,
% 2.24/2.49 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[10247, 2125, 267, 201, 236, 2277])).
% 2.24/2.49 tff(10249,plain,
% 2.24/2.49 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[1702, 10248])).
% 2.24/2.49 tff(10250,plain,
% 2.24/2.49 (~b(s(z), elem!1)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[1138, 1051, 267, 201, 236])).
% 2.24/2.49 tff(10251,plain,
% 2.24/2.49 (r(s(z), elem!1)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[1034, 10250, 2277])).
% 2.24/2.49 tff(10252,plain,
% 2.24/2.49 (~r(s(z), z)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[5432, 10251, 267])).
% 2.24/2.49 tff(10253,plain,
% 2.24/2.49 (b(s(z), z)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[1069, 10252])).
% 2.24/2.49 tff(10254,plain,
% 2.24/2.49 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(10255,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z)))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[10254])).
% 2.24/2.49 tff(10256,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))))),
% 2.24/2.49 inference(transitivity,[status(thm)],[10255, 7285])).
% 2.24/2.49 tff(10257,plain,
% 2.24/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))),
% 2.24/2.49 inference(quant_inst,[status(thm)],[])).
% 2.24/2.49 tff(10258,plain,
% 2.24/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z)))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[10257, 10256])).
% 2.24/2.49 tff(10259,plain,
% 2.24/2.49 ($false),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[10258, 246, 1051, 10253, 2001, 236])).
% 2.24/2.49 tff(10260,plain,((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~r(z, elem!1)) | (s(z) = elem!1) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.49 tff(10261,plain,
% 2.24/2.49 (~b(elem!1, z)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[10260, 9952, 236, 267, 2277, 201])).
% 2.24/2.49 tff(10262,plain,
% 2.24/2.49 (r(elem!1, z)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[1143, 10261, 5401])).
% 2.24/2.49 tff(10263,plain,
% 2.24/2.49 (~r(s(elem!1), elem!1)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[6072, 217, 267, 2125, 236])).
% 2.24/2.49 tff(10264,plain,
% 2.24/2.49 (~b(s(elem!1), elem!1)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[10016, 2002, 2001, 2125, 3697, 217])).
% 2.24/2.49 tff(10265,plain,
% 2.24/2.49 (s(elem!1) = elem!1),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[5655, 10264, 10263])).
% 2.24/2.49 tff(10266,plain,
% 2.24/2.49 (elem!1 = s(elem!1)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[3953, 10265])).
% 2.24/2.49 tff(10267,plain,
% 2.24/2.49 (b(elem!1, s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[10266])).
% 2.24/2.49 tff(10268,plain,
% 2.24/2.49 (b(s(elem!1), s(s(s(z))))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[2002, 10267])).
% 2.24/2.49 tff(10269,plain,
% 2.24/2.49 (s(s(s(s(s(elem!1))))) = elem!1),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[10266, 8888])).
% 2.24/2.49 tff(10270,plain,
% 2.24/2.49 (~b(s(z), s(s(s(z))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[9994, 2002, 3697, 2001])).
% 2.24/2.49 tff(10271,plain,
% 2.24/2.49 (r(s(z), s(s(s(z))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[1291, 10270])).
% 2.24/2.49 tff(10272,plain,
% 2.24/2.49 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(elem!1))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[10266])).
% 2.24/2.49 tff(10273,plain,
% 2.24/2.49 (b(s(s(s(z))), s(elem!1))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[3697, 10272])).
% 2.24/2.49 tff(10274,plain,
% 2.24/2.49 (s(elem!1) = elem!1),
% 2.24/2.49 inference(symmetry,[status(thm)],[10266])).
% 2.24/2.49 tff(10275,plain,
% 2.24/2.49 (r(z, s(elem!1)) <=> r(z, elem!1)),
% 2.24/2.49 inference(monotonicity,[status(thm)],[10274])).
% 2.24/2.49 tff(10276,plain,
% 2.24/2.49 (r(z, elem!1) <=> r(z, s(elem!1))),
% 2.24/2.49 inference(symmetry,[status(thm)],[10275])).
% 2.24/2.49 tff(10277,plain,
% 2.24/2.49 (r(z, s(elem!1))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[267, 10276])).
% 2.24/2.49 tff(10278,plain,
% 2.24/2.49 ($false),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[8487, 10277, 10273, 236, 2593, 10271, 10269, 2125, 10268, 7994, 1056])).
% 2.24/2.49 tff(10279,plain,((~b(elem!1, s(s(s(z))))) | (~b(z, s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~(s(s(elem!1)) = elem!1)) | (~b(s(z), z)) | (~r(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.49 tff(10280,plain,
% 2.24/2.49 (~b(elem!1, s(s(s(z))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[10279, 9954, 2593, 2125, 1056, 267, 236, 2001, 6625])).
% 2.24/2.49 tff(10281,plain,
% 2.24/2.49 (r(elem!1, s(s(s(z))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[470, 10280, 9955])).
% 2.24/2.49 tff(10282,plain,
% 2.24/2.49 (~r(z, s(s(s(z))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[2254, 10281, 2246])).
% 2.24/2.49 tff(10283,plain,
% 2.24/2.49 (b(z, s(s(s(z))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[6165, 10282])).
% 2.24/2.49 tff(10284,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(10285,plain,
% 2.24/2.49 (((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(10286,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z)))))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[10285])).
% 2.24/2.49 tff(10287,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 2.24/2.49 inference(transitivity,[status(thm)],[10286, 10284])).
% 2.24/2.49 tff(10288,plain,
% 2.24/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))),
% 2.24/2.49 inference(quant_inst,[status(thm)],[])).
% 2.24/2.49 tff(10289,plain,
% 2.24/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z)))))),
% 2.24/2.50 inference(modus_ponens,[status(thm)],[10288, 10287])).
% 2.24/2.50 tff(10290,plain,
% 2.24/2.50 ($false),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[10289, 246, 1056, 2001, 236, 3697, 2401, 4651])).
% 2.24/2.50 tff(10291,plain,((~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.50 tff(10292,plain,
% 2.24/2.50 (~b(s(z), s(s(s(z))))),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[10291, 9954, 2001, 236, 1056, 10283])).
% 2.24/2.50 tff(10293,plain,
% 2.24/2.50 (r(s(z), s(s(s(z))))),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[1291, 10292])).
% 2.24/2.50 tff(10294,plain,
% 2.24/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, z)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, z)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 2.24/2.50 inference(rewrite,[status(thm)],[])).
% 2.24/2.50 tff(10295,plain,
% 2.24/2.50 (((~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(z), elem!1))) <=> ((~r(s(z), elem!1)) | (~r(elem!1, z)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 2.24/2.50 inference(rewrite,[status(thm)],[])).
% 2.24/2.50 tff(10296,plain,
% 2.24/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, z)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))))),
% 2.24/2.50 inference(monotonicity,[status(thm)],[10295])).
% 2.24/2.50 tff(10297,plain,
% 2.24/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, z)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 2.24/2.50 inference(transitivity,[status(thm)],[10296, 10294])).
% 2.24/2.50 tff(10298,plain,
% 2.24/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(z), elem!1)))),
% 2.24/2.50 inference(quant_inst,[status(thm)],[])).
% 2.24/2.50 tff(10299,plain,
% 2.24/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, z)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 2.24/2.50 inference(modus_ponens,[status(thm)],[10298, 10297])).
% 2.24/2.50 tff(10300,plain,
% 2.24/2.50 ($false),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[10299, 183, 2246, 6625, 10281, 10293])).
% 2.24/2.50 tff(10301,plain,(b(s(z), elem!1) | (~r(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~(s(s(elem!1)) = elem!1)) | (~r(z, elem!1)) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.24/2.50 tff(10302,plain,
% 2.24/2.50 (b(s(z), elem!1)),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[10301, 1056, 2001, 236, 2246, 2593, 2125, 267, 2277])).
% 2.24/2.50 tff(10303,plain,
% 2.24/2.50 (~r(s(s(s(z))), s(z))),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[9060, 634, 3074, 2001, 2593, 1044])).
% 2.24/2.50 tff(10304,plain,
% 2.24/2.50 (b(s(s(s(z))), s(z))),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[52, 10303])).
% 2.24/2.50 tff(10305,plain,
% 2.24/2.50 ($false),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[6174, 10304, 7911, 236, 1056])).
% 2.24/2.50 tff(10306,plain,((~r(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (s(s(s(s(z)))) = elem!1) | (~b(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.50 tff(10307,plain,
% 2.24/2.50 (~r(s(s(s(z))), elem!1)),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[10306, 1056, 236, 7592, 2001, 2593, 10302, 267])).
% 2.34/2.50 tff(10308,plain,
% 2.34/2.50 (b(s(s(s(z))), elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[647, 10307, 5386])).
% 2.34/2.50 tff(10309,plain,
% 2.34/2.50 (~r(s(s(s(z))), s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[8491, 6095, 2593])).
% 2.34/2.50 tff(10310,plain,
% 2.34/2.50 (b(s(s(s(z))), s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[52, 10309])).
% 2.34/2.50 tff(10311,plain,
% 2.34/2.50 (~b(z, s(s(s(z))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[6174, 10310, 236, 1056])).
% 2.34/2.50 tff(10312,plain,
% 2.34/2.50 (r(z, s(s(s(z))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[6165, 10311])).
% 2.34/2.50 tff(10313,plain,
% 2.34/2.50 (~r(s(z), s(s(s(z))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[6098, 6095, 2593])).
% 2.34/2.50 tff(10314,plain,
% 2.34/2.50 (b(s(z), s(s(s(z))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1291, 10313])).
% 2.34/2.50 tff(10315,plain,
% 2.34/2.50 (~b(elem!1, s(s(s(z))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[9994, 10314, 3697, 2001])).
% 2.34/2.50 tff(10316,plain,
% 2.34/2.50 (r(elem!1, s(s(s(z))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[470, 10315, 1675])).
% 2.34/2.50 tff(10317,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[2254, 10316, 10312, 2246])).
% 2.34/2.50 tff(10318,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, z)) | (elem!1 = s(s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(10319,plain,
% 2.34/2.50 (~r(s(s(s(s(z)))), s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[10318, 10308, 9955, 2246, 2001, 236, 1056, 2593])).
% 2.34/2.50 tff(10320,plain,
% 2.34/2.50 (b(s(s(s(s(z)))), s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[6103, 10319])).
% 2.34/2.50 tff(10321,plain,
% 2.34/2.50 (~b(s(s(s(s(z)))), elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[9050, 10320, 2001, 10302])).
% 2.34/2.50 tff(10322,plain,
% 2.34/2.50 (~b(s(s(s(s(z)))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[8269, 10320, 236, 1056])).
% 2.34/2.50 tff(10323,plain,
% 2.34/2.50 (r(s(s(s(s(z)))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[6040, 10322])).
% 2.34/2.50 tff(10324,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[9834, 10323, 10321, 7592, 267])).
% 2.34/2.50 tff(10325,plain,((~b(s(z), z)) | (~r(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~(s(s(elem!1)) = elem!1)) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(10326,plain,
% 2.34/2.50 (~b(s(z), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[10325, 9952, 267, 236, 10262, 10249, 2125, 2277])).
% 2.34/2.50 tff(10327,plain,
% 2.34/2.50 (r(s(z), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1069, 10326])).
% 2.34/2.50 tff(10328,plain,
% 2.34/2.50 (~r(s(z), elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[5432, 10327, 267])).
% 2.34/2.50 tff(10329,plain,
% 2.34/2.50 (b(s(z), elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1034, 10328, 2277])).
% 2.34/2.50 tff(10330,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[7962, 246, 1044, 2001, 236, 10304, 10093])).
% 2.34/2.50 tff(10331,plain,((~r(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~r(z, elem!1)) | (s(s(s(s(z)))) = elem!1) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(10332,plain,
% 2.34/2.50 (~r(s(s(s(z))), elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[10331, 10329, 9952, 236, 267, 7592, 10249])).
% 2.34/2.50 tff(10333,plain,
% 2.34/2.50 (b(s(s(s(z))), elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[647, 10332, 5386])).
% 2.34/2.50 tff(10334,plain,
% 2.34/2.50 (~b(s(s(s(z))), s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[7339, 246, 10329, 9952, 10333])).
% 2.34/2.50 tff(10335,plain,
% 2.34/2.50 (r(s(s(s(z))), s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[52, 10334])).
% 2.34/2.50 tff(10336,plain,
% 2.34/2.50 (~r(s(s(s(s(z)))), s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[8491, 10335, 10249])).
% 2.34/2.50 tff(10337,plain,
% 2.34/2.50 (b(s(s(s(s(z)))), s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[6103, 10336])).
% 2.34/2.50 tff(10338,plain,
% 2.34/2.50 (~b(s(s(s(s(z)))), elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[9050, 10337, 9952, 10329])).
% 2.34/2.50 tff(10339,plain,
% 2.34/2.50 (~r(s(s(s(s(z)))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[9834, 10338, 7592, 267])).
% 2.34/2.50 tff(10340,plain,
% 2.34/2.50 (b(s(s(s(s(z)))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[6040, 10339])).
% 2.34/2.50 tff(10341,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(10342,plain,
% 2.34/2.50 (((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(10343,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[10342])).
% 2.34/2.50 tff(10344,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.34/2.50 inference(transitivity,[status(thm)],[10343, 10341])).
% 2.34/2.50 tff(10345,plain,
% 2.34/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.34/2.50 inference(quant_inst,[status(thm)],[])).
% 2.34/2.50 tff(10346,plain,
% 2.34/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[10345, 10344])).
% 2.34/2.50 tff(10347,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[10346, 246, 10329, 9952, 236, 10337, 10340])).
% 2.34/2.50 tff(10348,plain,((~(s(s(elem!1)) = elem!1)) | (~b(z, s(z))) | (~r(z, elem!1)) | (s(z) = elem!1) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(10349,plain,
% 2.34/2.50 (~(s(s(elem!1)) = elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[10348, 9950, 5365, 9951, 8749])).
% 2.34/2.50 tff(10350,plain,
% 2.34/2.50 (~(elem!1 = s(s(elem!1)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[5450, 10349])).
% 2.34/2.50 tff(10351,plain,
% 2.34/2.50 (b(s(s(elem!1)), elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[156, 10349, 2232])).
% 2.34/2.50 tff(10352,plain,
% 2.34/2.50 (~(elem!1 = s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[2279, 9951])).
% 2.34/2.50 tff(10353,plain,
% 2.34/2.50 (r(elem!1, s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[214, 210, 10352])).
% 2.34/2.50 tff(10354,plain,
% 2.34/2.50 (~r(s(z), elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[5432, 1114, 267])).
% 2.34/2.50 tff(10355,plain,
% 2.34/2.50 (b(s(z), elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1034, 10354, 2277])).
% 2.34/2.50 tff(10356,plain,
% 2.34/2.50 (b(elem!1, z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1143, 6113, 5401])).
% 2.34/2.50 tff(10357,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1138, 10356, 10355, 267, 201, 236])).
% 2.34/2.50 tff(10358,plain,((~r(s(z), z)) | (~r(z, elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (s(z) = elem!1) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(10359,plain,
% 2.34/2.50 (~r(s(z), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[10358, 10353, 8749, 9950, 9951, 5365])).
% 2.34/2.50 tff(10360,plain,
% 2.34/2.50 (b(s(z), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1069, 10359])).
% 2.34/2.50 tff(10361,plain,
% 2.34/2.50 (~b(z, s(s(elem!1)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1154, 10360, 8749, 9950])).
% 2.34/2.50 tff(10362,plain,
% 2.34/2.50 (r(z, s(s(elem!1)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[264, 10361])).
% 2.34/2.50 tff(10363,plain,
% 2.34/2.50 (~r(elem!1, s(s(elem!1)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[6918, 10362, 5365])).
% 2.34/2.50 tff(10364,plain,
% 2.34/2.50 (b(elem!1, s(s(elem!1)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1268, 10363, 10350])).
% 2.34/2.50 tff(10365,plain,
% 2.34/2.50 (r(s(z), elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1034, 1445, 9951])).
% 2.34/2.50 tff(10366,plain,
% 2.34/2.50 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[5581, 10365, 5365, 9950])).
% 2.34/2.50 tff(10367,plain,
% 2.34/2.50 (~r(s(s(s(z))), elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[6629, 1445, 5365, 2232, 9950, 9951])).
% 2.34/2.50 tff(10368,plain,
% 2.34/2.50 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[5804, 9951])).
% 2.34/2.50 tff(10369,assumption,(~r(s(s(s(z))), elem!1)), introduced(assumption)).
% 2.34/2.50 tff(10370,plain,
% 2.34/2.50 (~r(s(z), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[10358, 474, 8749, 9950, 9951, 5365])).
% 2.34/2.50 tff(10371,plain,
% 2.34/2.50 (b(s(z), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1069, 10370])).
% 2.34/2.50 tff(10372,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(10373,plain,
% 2.34/2.50 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(10374,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z))))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[10373])).
% 2.34/2.50 tff(10375,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))),
% 2.34/2.50 inference(transitivity,[status(thm)],[10374, 10372])).
% 2.34/2.50 tff(10376,plain,
% 2.34/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))),
% 2.34/2.50 inference(quant_inst,[status(thm)],[])).
% 2.34/2.50 tff(10377,plain,
% 2.34/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[10376, 10375])).
% 2.34/2.50 tff(10378,plain,
% 2.34/2.50 (~b(s(s(elem!1)), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[10377, 246, 8749, 1056, 9950])).
% 2.34/2.50 tff(10379,plain,
% 2.34/2.50 (r(s(s(elem!1)), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[523, 10378])).
% 2.34/2.50 tff(10380,plain,
% 2.34/2.50 (~b(z, s(s(elem!1)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1154, 1056, 8749, 9950])).
% 2.34/2.50 tff(10381,plain,
% 2.34/2.50 (r(z, s(s(elem!1)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[264, 10380])).
% 2.34/2.50 tff(10382,plain,
% 2.34/2.50 (~r(elem!1, s(s(elem!1)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[6918, 10381, 5365])).
% 2.34/2.50 tff(10383,plain,
% 2.34/2.50 (b(elem!1, s(s(elem!1)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1268, 10382, 10350])).
% 2.34/2.50 tff(10384,plain,
% 2.34/2.50 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[7100, 1, 55, 7016, 10378, 2232])).
% 2.34/2.50 tff(10385,plain,
% 2.34/2.50 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[4983, 10384, 10351, 10383])).
% 2.34/2.50 tff(10386,plain,
% 2.34/2.50 (s(s(s(z))) = elem!1),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[647, 1, 10369])).
% 2.34/2.50 tff(10387,plain,
% 2.34/2.50 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[5623, 10386])).
% 2.34/2.50 tff(10388,plain,
% 2.34/2.50 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1557, 10387, 10385])).
% 2.34/2.50 tff(10389,plain,
% 2.34/2.50 (~r(s(s(s(s(s(elem!1))))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[5671, 10388, 10379])).
% 2.34/2.50 tff(10390,plain,
% 2.34/2.50 (b(s(s(s(s(s(elem!1))))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1601, 10389])).
% 2.34/2.50 tff(10391,plain,
% 2.34/2.50 (b(elem!1, z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1143, 7016, 5701])).
% 2.34/2.50 tff(10392,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(10393,plain,
% 2.34/2.50 (((~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(10394,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[10393])).
% 2.34/2.50 tff(10395,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.34/2.50 inference(transitivity,[status(thm)],[10394, 10392])).
% 2.34/2.50 tff(10396,plain,
% 2.34/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.34/2.50 inference(quant_inst,[status(thm)],[])).
% 2.34/2.50 tff(10397,plain,
% 2.34/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[10396, 10395])).
% 2.34/2.50 tff(10398,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[10397, 246, 10391, 1056, 9950, 10384, 10390])).
% 2.34/2.50 tff(10399,plain,(b(s(s(s(z))), elem!1) | (~b(s(z), z)) | b(z, elem!1) | r(elem!1, z) | r(s(s(elem!1)), elem!1) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(10400,plain,
% 2.34/2.50 (b(s(s(s(z))), elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[10399, 7016, 55, 10371, 2232, 10369])).
% 2.34/2.50 tff(10401,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(10402,plain,
% 2.34/2.50 (((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(10403,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1))))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[10402])).
% 2.34/2.50 tff(10404,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))),
% 2.34/2.50 inference(transitivity,[status(thm)],[10403, 10401])).
% 2.34/2.50 tff(10405,plain,
% 2.34/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.34/2.50 inference(quant_inst,[status(thm)],[])).
% 2.34/2.50 tff(10406,plain,
% 2.34/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[10405, 10404])).
% 2.34/2.50 tff(10407,plain,
% 2.34/2.50 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[10406, 246, 10391, 8749, 10351, 9950, 10400])).
% 2.34/2.50 tff(10408,plain,
% 2.34/2.50 (r(s(s(s(z))), s(s(elem!1)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[689, 10407, 10368])).
% 2.34/2.51 tff(10409,plain,
% 2.34/2.51 (~b(z, s(s(elem!1)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[1154, 10371, 8749, 9950])).
% 2.34/2.51 tff(10410,plain,
% 2.34/2.51 (r(z, s(s(elem!1)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[264, 10409])).
% 2.34/2.51 tff(10411,plain,
% 2.34/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(10412,plain,
% 2.34/2.51 (((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(s(z))), z))) <=> ((~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(10413,plain,
% 2.34/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z))))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[10412])).
% 2.34/2.51 tff(10414,plain,
% 2.34/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 2.34/2.51 inference(transitivity,[status(thm)],[10413, 10411])).
% 2.34/2.51 tff(10415,plain,
% 2.34/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)))),
% 2.34/2.51 inference(quant_inst,[status(thm)],[])).
% 2.34/2.51 tff(10416,plain,
% 2.34/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[10415, 10414])).
% 2.34/2.51 tff(10417,plain,
% 2.34/2.51 (~r(s(s(s(z))), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[10416, 183, 5365, 10410, 10408])).
% 2.34/2.51 tff(10418,plain,
% 2.34/2.51 (b(s(s(s(z))), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[995, 10417])).
% 2.34/2.51 tff(10419,plain,
% 2.34/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(10420,plain,
% 2.34/2.51 (((~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(10421,plain,
% 2.34/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1))))))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[10420])).
% 2.34/2.51 tff(10422,plain,
% 2.34/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.34/2.51 inference(transitivity,[status(thm)],[10421, 10419])).
% 2.34/2.51 tff(10423,plain,
% 2.34/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(s(s(z))))))),
% 2.34/2.51 inference(quant_inst,[status(thm)],[])).
% 2.34/2.51 tff(10424,plain,
% 2.34/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1))))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[10423, 10422])).
% 2.34/2.51 tff(10425,plain,
% 2.34/2.51 (~r(z, s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[10424, 183, 10410, 10408])).
% 2.34/2.51 tff(10426,plain,
% 2.34/2.51 (b(z, s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[6165, 10425])).
% 2.34/2.51 tff(10427,plain,
% 2.34/2.51 (~(elem!1 = s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[5785, 10400])).
% 2.34/2.51 tff(10428,plain,
% 2.34/2.51 (~b(s(s(s(z))), s(z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[6174, 10426, 9950, 10371])).
% 2.34/2.51 tff(10429,plain,
% 2.34/2.51 (r(s(s(s(z))), s(z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[52, 10428])).
% 2.34/2.51 tff(10430,plain,
% 2.34/2.51 (~r(elem!1, s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[5796, 183, 474, 10429])).
% 2.34/2.51 tff(10431,plain,
% 2.34/2.51 (b(elem!1, s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[470, 10430, 10427])).
% 2.34/2.51 tff(10432,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(10433,plain,
% 2.34/2.51 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(10434,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[10433])).
% 2.34/2.51 tff(10435,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 2.34/2.51 inference(transitivity,[status(thm)],[10434, 10432])).
% 2.34/2.51 tff(10436,plain,
% 2.34/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))),
% 2.34/2.51 inference(quant_inst,[status(thm)],[])).
% 2.34/2.51 tff(10437,plain,
% 2.34/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[10436, 10435])).
% 2.34/2.51 tff(10438,plain,
% 2.34/2.51 ($false),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[10437, 246, 10391, 10431, 10400, 10426, 10418])).
% 2.34/2.51 tff(10439,plain,(r(elem!1, z) | (~r(elem!1, s(z))) | b(z, elem!1) | r(s(s(elem!1)), elem!1) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.51 tff(10440,plain,
% 2.34/2.51 (r(elem!1, z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[10439, 10367, 55, 2232, 10353])).
% 2.34/2.51 tff(10441,plain,
% 2.34/2.51 (~b(s(s(elem!1)), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[10377, 246, 8749, 10360, 9950])).
% 2.34/2.51 tff(10442,plain,
% 2.34/2.51 (r(s(s(elem!1)), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[523, 10441])).
% 2.34/2.51 tff(10443,plain,
% 2.34/2.51 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7041, 10386])).
% 2.34/2.51 tff(10444,plain,
% 2.34/2.51 (b(s(s(elem!1)), s(elem!1))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[5757, 10386, 10443, 1, 2232, 55, 210, 10363])).
% 2.34/2.51 tff(10445,plain,
% 2.34/2.51 (~b(s(elem!1), elem!1)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7373, 10444, 10351, 10364])).
% 2.34/2.51 tff(10446,plain,
% 2.34/2.51 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[5677, 10445, 10386])).
% 2.34/2.51 tff(10447,plain,
% 2.34/2.51 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[1702, 10446])).
% 2.34/2.51 tff(10448,plain,
% 2.34/2.51 (r(s(elem!1), elem!1)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[5548, 10447, 10386])).
% 2.34/2.51 tff(10449,plain,
% 2.34/2.51 (s(s(s(s(z)))) = s(elem!1)),
% 2.34/2.51 inference(monotonicity,[status(thm)],[10386])).
% 2.34/2.51 tff(10450,plain,
% 2.34/2.51 (r(s(s(s(s(z)))), z) <=> r(s(elem!1), z)),
% 2.34/2.51 inference(monotonicity,[status(thm)],[10449])).
% 2.34/2.51 tff(10451,plain,
% 2.34/2.51 (elem!1 = s(s(s(z)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[1677, 10386])).
% 2.34/2.51 tff(10452,plain,
% 2.34/2.51 (~b(s(s(s(z))), s(z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[2297, 10451, 210])).
% 2.34/2.51 tff(10453,plain,
% 2.34/2.51 (r(s(s(s(z))), s(z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[52, 10452])).
% 2.34/2.51 tff(10454,plain,
% 2.34/2.51 (~r(s(s(s(s(z)))), s(z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[8491, 10447, 10453])).
% 2.34/2.51 tff(10455,plain,
% 2.34/2.51 (b(s(s(s(s(z)))), s(z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[6103, 10454])).
% 2.34/2.51 tff(10456,plain,
% 2.34/2.51 (~b(s(s(s(s(z)))), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[8269, 10455, 9950, 10360])).
% 2.34/2.51 tff(10457,plain,
% 2.34/2.51 (r(s(s(s(s(z)))), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[6040, 10456])).
% 2.34/2.51 tff(10458,plain,
% 2.34/2.51 (r(s(elem!1), z)),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[10457, 10450])).
% 2.34/2.51 tff(10459,plain,
% 2.34/2.51 ($false),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[5533, 183, 5365, 10458, 10448])).
% 2.34/2.51 tff(10460,plain,(b(s(s(s(z))), elem!1) | b(elem!1, s(z)) | r(s(s(elem!1)), elem!1) | b(z, elem!1) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.51 tff(10461,plain,
% 2.34/2.51 (b(s(s(s(z))), elem!1)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[10460, 10367, 2232, 55, 210])).
% 2.34/2.51 tff(10462,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(10463,plain,
% 2.34/2.51 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(10464,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1))))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[10463])).
% 2.34/2.51 tff(10465,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))),
% 2.34/2.51 inference(transitivity,[status(thm)],[10464, 10462])).
% 2.34/2.51 tff(10466,plain,
% 2.34/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.34/2.51 inference(quant_inst,[status(thm)],[])).
% 2.34/2.51 tff(10467,plain,
% 2.34/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[10466, 10465])).
% 2.34/2.51 tff(10468,plain,
% 2.34/2.51 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[10467, 246, 8749, 10351, 10364, 10461])).
% 2.34/2.51 tff(10469,plain,
% 2.34/2.51 (r(s(s(s(z))), s(s(elem!1)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[689, 10468, 10368])).
% 2.34/2.51 tff(10470,plain,
% 2.34/2.51 (~r(z, s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[10424, 183, 10362, 10469])).
% 2.34/2.51 tff(10471,plain,
% 2.34/2.51 (b(z, s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[6165, 10470])).
% 2.34/2.51 tff(10472,plain,
% 2.34/2.51 (~b(s(s(s(z))), s(z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[6174, 10471, 9950, 10360])).
% 2.34/2.51 tff(10473,plain,
% 2.34/2.51 (r(s(s(s(z))), s(z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[52, 10472])).
% 2.34/2.51 tff(10474,plain,
% 2.34/2.51 (~r(s(s(s(z))), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[10416, 183, 5365, 10362, 10469])).
% 2.34/2.51 tff(10475,plain,
% 2.34/2.51 (b(s(s(s(z))), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[995, 10474])).
% 2.34/2.51 tff(10476,plain,
% 2.34/2.51 (~(elem!1 = s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[5785, 10461])).
% 2.34/2.51 tff(10477,plain,
% 2.34/2.51 (~r(elem!1, s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[5796, 183, 10353, 10473])).
% 2.34/2.51 tff(10478,plain,
% 2.34/2.51 (b(elem!1, s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[470, 10477, 10476])).
% 2.34/2.51 tff(10479,plain,
% 2.34/2.51 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[6281, 10368])).
% 2.34/2.51 tff(10480,plain,
% 2.34/2.51 (~(s(s(elem!1)) = s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[421, 10368])).
% 2.34/2.51 tff(10481,plain,
% 2.34/2.51 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7757, 246, 10351, 10364, 10461])).
% 2.34/2.51 tff(10482,plain,
% 2.34/2.51 (r(s(s(elem!1)), s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[454, 10481, 10480])).
% 2.34/2.51 tff(10483,plain,
% 2.34/2.51 (~b(s(s(s(s(z)))), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[9844, 1833, 4651, 2090])).
% 2.34/2.51 tff(10484,plain,
% 2.34/2.51 (r(s(s(s(s(z)))), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[6040, 10483])).
% 2.34/2.51 tff(10485,plain,
% 2.34/2.51 (s(s(s(s(z)))) = elem!1),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[9970, 10484, 3697, 2246, 1833, 267])).
% 2.34/2.51 tff(10486,plain,
% 2.34/2.51 (elem!1 = s(s(s(s(z))))),
% 2.34/2.51 inference(symmetry,[status(thm)],[10485])).
% 2.34/2.51 tff(10487,assumption,(~r(s(s(s(s(s(elem!1))))), elem!1)), introduced(assumption)).
% 2.34/2.51 tff(10488,plain,
% 2.34/2.51 (r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 2.34/2.51 inference(symmetry,[status(thm)],[7158])).
% 2.34/2.51 tff(10489,plain,
% 2.34/2.51 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 2.34/2.51 inference(symmetry,[status(thm)],[7156])).
% 2.34/2.51 tff(10490,plain,
% 2.34/2.51 ((~b(elem!1, s(s(s(s(z)))))) <=> (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[10489])).
% 2.34/2.51 tff(10491,plain,
% 2.34/2.51 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[6007, 10490])).
% 2.34/2.51 tff(10492,plain,
% 2.34/2.51 (r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[1896, 10491, 1500])).
% 2.34/2.51 tff(10493,plain,
% 2.34/2.51 (r(elem!1, s(s(s(s(z)))))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[10492, 10488])).
% 2.34/2.51 tff(10494,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(10495,plain,
% 2.34/2.51 (((~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(10496,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[10495])).
% 2.34/2.51 tff(10497,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.34/2.51 inference(transitivity,[status(thm)],[10496, 10494])).
% 2.34/2.51 tff(10498,plain,
% 2.34/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.34/2.51 inference(quant_inst,[status(thm)],[])).
% 2.34/2.51 tff(10499,plain,
% 2.34/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[10498, 10497])).
% 2.34/2.51 tff(10500,plain,
% 2.34/2.51 (~b(s(s(s(s(z)))), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[10499, 246, 2002, 3697, 4651, 1833])).
% 2.34/2.51 tff(10501,plain,
% 2.34/2.51 (r(s(s(s(s(z)))), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[2424, 47, 2421, 10500])).
% 2.34/2.51 tff(10502,plain,
% 2.34/2.51 ($false),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7246, 183, 2246, 10501, 10493])).
% 2.34/2.51 tff(10503,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, z)) | (~(s(s(s(s(s(elem!1))))) = elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.51 tff(10504,plain,
% 2.34/2.51 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[10503, 1833, 2246, 3697, 4651, 2002])).
% 2.34/2.51 tff(10505,plain,
% 2.34/2.51 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[86, 10504, 10487])).
% 2.34/2.51 tff(10506,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(10507,plain,
% 2.34/2.51 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(10508,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[10507])).
% 2.34/2.51 tff(10509,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.34/2.51 inference(transitivity,[status(thm)],[10508, 10506])).
% 2.34/2.51 tff(10510,plain,
% 2.34/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 2.34/2.51 inference(quant_inst,[status(thm)],[])).
% 2.34/2.51 tff(10511,plain,
% 2.34/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[10510, 10509])).
% 2.34/2.52 tff(10512,plain,
% 2.34/2.52 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[10511, 246, 2362, 947, 3697, 10505])).
% 2.34/2.52 tff(10513,plain,
% 2.34/2.52 (r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[1626, 10512])).
% 2.34/2.52 tff(10514,plain,
% 2.34/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(10515,plain,
% 2.34/2.52 (((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(10516,plain,
% 2.34/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[10515])).
% 2.34/2.52 tff(10517,plain,
% 2.34/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 2.34/2.52 inference(transitivity,[status(thm)],[10516, 10514])).
% 2.34/2.52 tff(10518,plain,
% 2.34/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 2.34/2.52 inference(quant_inst,[status(thm)],[])).
% 2.34/2.52 tff(10519,plain,
% 2.34/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[10518, 10517])).
% 2.34/2.52 tff(10520,plain,
% 2.34/2.52 (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[10519, 183, 3886, 10513])).
% 2.34/2.52 tff(10521,plain,
% 2.34/2.52 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[4890, 10505, 2362, 947])).
% 2.34/2.52 tff(10522,plain,
% 2.34/2.52 ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[1547, 47, 10521])).
% 2.34/2.52 tff(10523,plain,
% 2.34/2.52 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[10522, 10520])).
% 2.34/2.52 tff(10524,plain,
% 2.34/2.52 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 2.34/2.52 inference(symmetry,[status(thm)],[10523])).
% 2.34/2.52 tff(10525,plain,
% 2.34/2.52 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(elem!1)))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[10524])).
% 2.34/2.52 tff(10526,plain,
% 2.34/2.52 (s(s(s(s(elem!1)))) = s(elem!1)),
% 2.34/2.52 inference(transitivity,[status(thm)],[326, 10525, 92])).
% 2.34/2.52 tff(10527,plain,
% 2.34/2.52 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(elem!1))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[10526])).
% 2.34/2.52 tff(10528,plain,
% 2.34/2.52 (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[10524])).
% 2.34/2.52 tff(10529,plain,
% 2.34/2.52 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))),
% 2.34/2.52 inference(transitivity,[status(thm)],[10528, 352, 10527, 343, 10486])).
% 2.34/2.52 tff(10530,plain,
% 2.34/2.52 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z)))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[6709, 10523, 6330])).
% 2.34/2.52 tff(10531,plain,
% 2.34/2.52 ($false),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[10530, 10529])).
% 2.34/2.52 tff(10532,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (~r(z, elem!1)) | r(s(s(s(s(s(elem!1))))), elem!1) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.52 tff(10533,plain,
% 2.34/2.52 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[10532, 10482, 10479, 10351, 10364, 10461, 10440, 5365, 10366, 10471, 10478, 10475])).
% 2.34/2.52 tff(10534,plain,
% 2.34/2.52 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[1702, 10533])).
% 2.34/2.52 tff(10535,plain,
% 2.34/2.52 (~r(s(s(s(s(z)))), s(z))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[8491, 10534, 10473])).
% 2.34/2.52 tff(10536,plain,
% 2.34/2.52 (b(s(s(s(s(z)))), s(z))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[6103, 10535])).
% 2.34/2.52 tff(10537,plain,
% 2.34/2.52 (~b(s(s(s(s(z)))), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[8269, 10536, 9950, 10360])).
% 2.34/2.52 tff(10538,plain,
% 2.34/2.52 (r(s(s(s(s(z)))), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[6040, 10537])).
% 2.34/2.52 tff(10539,plain,
% 2.34/2.52 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[7259, 10538, 10364, 10442, 10440])).
% 2.34/2.52 tff(10540,plain,
% 2.34/2.52 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[86, 10539, 10366])).
% 2.34/2.52 tff(10541,plain,
% 2.34/2.52 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[10511, 246, 10351, 10364, 10461, 10540])).
% 2.34/2.52 tff(10542,plain,
% 2.34/2.52 (r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[1626, 10541])).
% 2.34/2.52 tff(10543,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(10544,plain,
% 2.34/2.52 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(10545,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[10544])).
% 2.34/2.52 tff(10546,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 2.34/2.52 inference(transitivity,[status(thm)],[10545, 10543])).
% 2.34/2.52 tff(10547,plain,
% 2.34/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 2.34/2.52 inference(quant_inst,[status(thm)],[])).
% 2.34/2.52 tff(10548,plain,
% 2.34/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[10547, 10546])).
% 2.34/2.52 tff(10549,plain,
% 2.34/2.52 (~b(s(z), s(s(s(z))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[10548, 246, 10360, 10461, 10471, 10475])).
% 2.34/2.52 tff(10550,plain,
% 2.34/2.52 (r(s(z), s(s(s(z))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[1291, 10549])).
% 2.34/2.52 tff(10551,plain,
% 2.34/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(10552,plain,
% 2.34/2.52 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(10553,plain,
% 2.34/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(z)))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[10552])).
% 2.34/2.52 tff(10554,plain,
% 2.34/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 2.34/2.52 inference(transitivity,[status(thm)],[10553, 10551])).
% 2.34/2.52 tff(10555,plain,
% 2.34/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 2.34/2.52 inference(quant_inst,[status(thm)],[])).
% 2.34/2.52 tff(10556,plain,
% 2.34/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(z)))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[10555, 10554])).
% 2.34/2.52 tff(10557,plain,
% 2.34/2.52 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[10556, 183, 10365, 10550, 10542])).
% 2.34/2.52 tff(10558,plain,
% 2.34/2.52 (b(s(s(s(s(s(elem!1))))), s(z))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[6447, 10557])).
% 2.34/2.52 tff(10559,plain,
% 2.34/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(10560,plain,
% 2.34/2.52 (((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(10561,plain,
% 2.34/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[10560])).
% 2.34/2.52 tff(10562,plain,
% 2.34/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 2.34/2.52 inference(transitivity,[status(thm)],[10561, 10559])).
% 2.34/2.52 tff(10563,plain,
% 2.34/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 2.34/2.52 inference(quant_inst,[status(thm)],[])).
% 2.34/2.52 tff(10564,plain,
% 2.34/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[10563, 10562])).
% 2.34/2.52 tff(10565,plain,
% 2.34/2.52 (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[10564, 183, 10534, 10542])).
% 2.34/2.52 tff(10566,plain,
% 2.34/2.52 (b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[1506, 10565])).
% 2.34/2.52 tff(10567,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(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(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(10568,plain,
% 2.34/2.52 (((~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(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(elem!1))))))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(10569,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[10568])).
% 2.34/2.52 tff(10570,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 2.34/2.52 inference(transitivity,[status(thm)],[10569, 10567])).
% 2.34/2.52 tff(10571,plain,
% 2.34/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 2.34/2.52 inference(quant_inst,[status(thm)],[])).
% 2.34/2.52 tff(10572,plain,
% 2.34/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[10571, 10570])).
% 2.34/2.52 tff(10573,plain,
% 2.34/2.52 ($false),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[10572, 246, 10360, 9950, 10566, 10536, 10558])).
% 2.34/2.52 tff(10574,plain,(b(s(z), elem!1) | r(s(s(elem!1)), elem!1) | b(z, elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.52 tff(10575,plain,
% 2.34/2.52 (b(s(z), elem!1)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[10574, 210, 55, 2232])).
% 2.34/2.52 tff(10576,plain,
% 2.34/2.52 ($false),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[7124, 246, 8749, 10575, 10351, 10364])).
% 2.34/2.52 tff(10577,plain,(b(elem!1, s(z)) | b(z, elem!1) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.52 tff(10578,plain,
% 2.34/2.52 (b(elem!1, s(z))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[10577, 2232, 55])).
% 2.34/2.52 tff(10579,plain,
% 2.34/2.52 (~b(s(z), elem!1)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[3799, 10578, 8749, 10351])).
% 2.34/2.52 tff(10580,plain,
% 2.34/2.52 (r(s(z), elem!1)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[1034, 10579, 9951])).
% 2.34/2.52 tff(10581,plain,
% 2.34/2.52 (~r(s(z), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[5432, 10580, 5365])).
% 2.34/2.52 tff(10582,plain,
% 2.34/2.52 (b(s(z), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[1069, 10581])).
% 2.34/2.52 tff(10583,plain,
% 2.34/2.52 (~b(z, s(s(elem!1)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[1154, 10582, 8749, 9950])).
% 2.34/2.52 tff(10584,plain,
% 2.34/2.52 (r(z, s(s(elem!1)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[264, 10583])).
% 2.34/2.52 tff(10585,plain,
% 2.34/2.52 (~r(elem!1, s(s(elem!1)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[6918, 10584, 5365])).
% 2.34/2.52 tff(10586,plain,
% 2.34/2.52 (b(elem!1, s(s(elem!1)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[1268, 10585, 10350])).
% 2.34/2.52 tff(10587,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(10588,plain,
% 2.34/2.52 (((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(10589,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z)))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[10588])).
% 2.34/2.52 tff(10590,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))),
% 2.34/2.52 inference(transitivity,[status(thm)],[10589, 10587])).
% 2.34/2.52 tff(10591,plain,
% 2.34/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))))),
% 2.34/2.52 inference(quant_inst,[status(thm)],[])).
% 2.34/2.52 tff(10592,plain,
% 2.34/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z)))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[10591, 10590])).
% 2.34/2.52 tff(10593,plain,
% 2.34/2.52 ($false),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[10592, 246, 8749, 10582, 10578, 9950, 10586])).
% 2.34/2.52 tff(10594,plain,(r(s(s(elem!1)), elem!1) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.52 tff(10595,plain,
% 2.34/2.52 (r(s(s(elem!1)), elem!1)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[10594, 55])).
% 2.34/2.52 tff(10596,plain,
% 2.34/2.52 (~r(z, s(s(elem!1)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[275, 10595, 5365])).
% 2.34/2.52 tff(10597,plain,
% 2.34/2.52 (b(z, s(s(elem!1)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[264, 10596])).
% 2.34/2.52 tff(10598,plain,
% 2.34/2.52 (~r(s(s(elem!1)), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[1583, 10595, 5365])).
% 2.34/2.52 tff(10599,plain,
% 2.34/2.52 (b(s(s(elem!1)), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[523, 10598])).
% 2.34/2.52 tff(10600,plain,
% 2.34/2.52 ((s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(s(elem!1))))))))),
% 2.34/2.52 inference(commutativity,[status(thm)],[])).
% 2.34/2.52 tff(10601,plain,
% 2.34/2.52 ((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(z)))))),
% 2.34/2.52 inference(symmetry,[status(thm)],[10600])).
% 2.34/2.52 tff(10602,plain,
% 2.34/2.52 (s(z) = elem!1),
% 2.34/2.52 inference(symmetry,[status(thm)],[202])).
% 2.34/2.52 tff(10603,plain,
% 2.34/2.52 (r(s(z), s(s(s(s(s(elem!1)))))) <=> r(elem!1, s(s(s(s(s(elem!1))))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[10602])).
% 2.34/2.52 tff(10604,plain,
% 2.34/2.52 (r(elem!1, s(s(s(s(s(elem!1)))))) <=> r(s(z), s(s(s(s(s(elem!1))))))),
% 2.34/2.52 inference(symmetry,[status(thm)],[10603])).
% 2.34/2.52 tff(10605,plain,
% 2.34/2.52 ((s(s(s(s(s(elem!1))))) = s(z)) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 2.34/2.52 inference(monotonicity,[status(thm)],[10602])).
% 2.34/2.52 tff(10606,plain,
% 2.34/2.52 ((s(s(s(s(s(elem!1))))) = s(z)) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 2.34/2.52 inference(transitivity,[status(thm)],[10605, 124])).
% 2.34/2.52 tff(10607,plain,
% 2.34/2.52 ((~(s(s(s(s(s(elem!1))))) = s(z))) <=> (~(elem!1 = s(s(s(s(s(elem!1)))))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[10606])).
% 2.34/2.52 tff(10608,plain,
% 2.34/2.52 (~(elem!1 = s(s(s(s(s(elem!1))))))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[331, 10607])).
% 2.34/2.53 tff(10609,plain,
% 2.34/2.53 (b(s(z), s(s(s(s(s(elem!1)))))) <=> b(elem!1, s(s(s(s(s(elem!1))))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[10602])).
% 2.34/2.53 tff(10610,plain,
% 2.34/2.53 ((~b(s(z), s(s(s(s(s(elem!1))))))) <=> (~b(elem!1, s(s(s(s(s(elem!1)))))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[10609])).
% 2.34/2.53 tff(10611,plain,
% 2.34/2.53 (r(s(s(s(z))), s(z)) <=> r(s(s(elem!1)), s(z))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[3452])).
% 2.34/2.53 tff(10612,plain,
% 2.34/2.53 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(z))), s(z))),
% 2.34/2.53 inference(symmetry,[status(thm)],[10611])).
% 2.34/2.53 tff(10613,plain,
% 2.34/2.53 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(z))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[202])).
% 2.34/2.53 tff(10614,plain,
% 2.34/2.53 (r(s(s(elem!1)), s(z))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[216, 10613])).
% 2.34/2.53 tff(10615,plain,
% 2.34/2.53 (r(s(s(s(z))), s(z))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[10614, 10612])).
% 2.34/2.53 tff(10616,plain,
% 2.34/2.53 (~r(s(s(elem!1)), z)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[1583, 216, 267])).
% 2.34/2.53 tff(10617,plain,
% 2.34/2.53 (b(s(s(elem!1)), z)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[523, 10616])).
% 2.34/2.53 tff(10618,plain,
% 2.34/2.53 (~r(z, s(s(elem!1)))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[275, 216, 267])).
% 2.34/2.53 tff(10619,plain,
% 2.34/2.53 (b(z, s(s(elem!1)))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[264, 10618])).
% 2.34/2.53 tff(10620,plain,
% 2.34/2.53 (b(s(s(z)), z) <=> b(s(elem!1), z)),
% 2.34/2.53 inference(monotonicity,[status(thm)],[3455])).
% 2.34/2.53 tff(10621,plain,
% 2.34/2.53 (b(s(elem!1), z) <=> b(s(s(z)), z)),
% 2.34/2.53 inference(symmetry,[status(thm)],[10620])).
% 2.34/2.53 tff(10622,plain,
% 2.34/2.53 (r(s(elem!1), z) <=> r(s(s(z)), z)),
% 2.34/2.53 inference(monotonicity,[status(thm)],[3454])).
% 2.34/2.53 tff(10623,plain,
% 2.34/2.53 (r(s(s(z)), z) <=> r(s(elem!1), z)),
% 2.34/2.53 inference(symmetry,[status(thm)],[10622])).
% 2.34/2.53 tff(10624,plain,
% 2.34/2.53 ((~r(s(s(z)), z)) <=> (~r(s(elem!1), z))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[10623])).
% 2.34/2.53 tff(10625,plain,
% 2.34/2.53 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[3455])).
% 2.34/2.53 tff(10626,plain,
% 2.34/2.53 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 2.34/2.53 inference(symmetry,[status(thm)],[10625])).
% 2.34/2.53 tff(10627,plain,
% 2.34/2.53 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.34/2.53 inference(symmetry,[status(thm)],[3453])).
% 2.34/2.53 tff(10628,plain,
% 2.34/2.53 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[3454, 10627])).
% 2.34/2.53 tff(10629,plain,
% 2.34/2.53 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[3455])).
% 2.34/2.53 tff(10630,plain,
% 2.34/2.53 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.53 inference(transitivity,[status(thm)],[10629, 10628])).
% 2.34/2.53 tff(10631,plain,
% 2.34/2.53 ((~b(s(s(z)), s(s(s(elem!1))))) <=> (~b(s(s(z)), s(s(s(s(z))))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[10630])).
% 2.34/2.53 tff(10632,plain,
% 2.34/2.53 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[10602])).
% 2.34/2.53 tff(10633,plain,
% 2.34/2.53 ((elem!1 = s(s(s(elem!1)))) <=> (s(z) = s(s(s(elem!1))))),
% 2.34/2.53 inference(symmetry,[status(thm)],[10632])).
% 2.34/2.53 tff(10634,plain,
% 2.34/2.53 ((~(elem!1 = s(s(s(elem!1))))) <=> (~(s(z) = s(s(s(elem!1)))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[10633])).
% 2.34/2.53 tff(10635,plain,
% 2.34/2.53 ((elem!1 = s(s(s(elem!1)))) <=> (s(z) = s(s(s(s(z)))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[202, 10627])).
% 2.34/2.53 tff(10636,plain,
% 2.34/2.53 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(z))),
% 2.34/2.53 inference(transitivity,[status(thm)],[10635, 5787])).
% 2.34/2.53 tff(10637,plain,
% 2.34/2.53 ((s(s(s(s(z)))) = s(z)) <=> (elem!1 = s(s(s(elem!1))))),
% 2.34/2.53 inference(symmetry,[status(thm)],[10636])).
% 2.34/2.53 tff(10638,plain,
% 2.34/2.53 ((~(s(s(s(s(z)))) = s(z))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[10637])).
% 2.34/2.53 tff(10639,plain,
% 2.34/2.53 (~(elem!1 = s(s(s(elem!1))))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[1713, 10638])).
% 2.34/2.53 tff(10640,plain,
% 2.34/2.53 (~(s(z) = s(s(s(elem!1))))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[10639, 10634])).
% 2.34/2.53 tff(10641,plain,
% 2.34/2.53 (~b(s(s(s(elem!1))), z)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[9440, 1659, 1099, 1100])).
% 2.34/2.53 tff(10642,plain,
% 2.34/2.53 (r(s(s(s(elem!1))), z)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[3086, 47, 355, 10641])).
% 2.34/2.53 tff(10643,plain,
% 2.34/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(10644,plain,
% 2.34/2.53 (((~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(10645,plain,
% 2.34/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1)))))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[10644])).
% 2.34/2.53 tff(10646,plain,
% 2.34/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 2.34/2.53 inference(transitivity,[status(thm)],[10645, 10643])).
% 2.34/2.53 tff(10647,plain,
% 2.34/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 2.34/2.53 inference(quant_inst,[status(thm)],[])).
% 2.34/2.53 tff(10648,plain,
% 2.34/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1)))))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[10647, 10646])).
% 2.34/2.53 tff(10649,plain,
% 2.34/2.53 (~r(s(z), s(s(s(elem!1))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[10648, 183, 1114, 10642])).
% 2.34/2.53 tff(10650,plain,
% 2.34/2.53 (((~![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)))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(10651,plain,
% 2.34/2.53 ((~![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)))))),
% 2.34/2.53 inference(quant_inst,[status(thm)],[])).
% 2.34/2.53 tff(10652,plain,
% 2.34/2.53 ((~![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))))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[10651, 10650])).
% 2.34/2.53 tff(10653,plain,
% 2.34/2.53 ((s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[10652, 47, 10649])).
% 2.34/2.53 tff(10654,plain,
% 2.34/2.53 (b(s(z), s(s(s(elem!1))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[10653, 10640])).
% 2.34/2.53 tff(10655,plain,
% 2.34/2.53 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[10627])).
% 2.34/2.53 tff(10656,plain,
% 2.34/2.53 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 2.34/2.53 inference(transitivity,[status(thm)],[10655, 1825])).
% 2.34/2.53 tff(10657,plain,
% 2.34/2.53 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 2.34/2.53 inference(symmetry,[status(thm)],[10656])).
% 2.34/2.53 tff(10658,plain,
% 2.34/2.53 ((~(s(s(s(s(z)))) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[10657])).
% 2.34/2.53 tff(10659,plain,
% 2.34/2.53 (s(s(elem!1)) = s(s(s(z)))),
% 2.34/2.53 inference(symmetry,[status(thm)],[3452])).
% 2.34/2.53 tff(10660,plain,
% 2.34/2.53 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[10659])).
% 2.34/2.53 tff(10661,plain,
% 2.34/2.53 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 2.34/2.53 inference(symmetry,[status(thm)],[10660])).
% 2.34/2.53 tff(10662,plain,
% 2.34/2.53 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(s(z)))) = s(s(elem!1))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[10661])).
% 2.34/2.53 tff(10663,plain,
% 2.34/2.53 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[1697, 10662])).
% 2.34/2.53 tff(10664,plain,
% 2.34/2.53 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[10663, 10658])).
% 2.34/2.53 tff(10665,plain,
% 2.34/2.53 ((s(s(s(s(s(elem!1))))) = s(s(s(z)))) <=> (s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[3452])).
% 2.34/2.53 tff(10666,plain,
% 2.34/2.53 ((s(s(s(s(s(elem!1))))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 2.34/2.53 inference(transitivity,[status(thm)],[10665, 1535])).
% 2.34/2.53 tff(10667,plain,
% 2.34/2.53 ((~(s(s(s(s(s(elem!1))))) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(s(s(elem!1)))))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[10666])).
% 2.34/2.53 tff(10668,plain,
% 2.34/2.53 (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[1622, 10667])).
% 2.34/2.53 tff(10669,plain,
% 2.34/2.53 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(elem!1))) = s(s(s(s(s(elem!1))))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[3453])).
% 2.34/2.53 tff(10670,plain,
% 2.34/2.53 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 2.34/2.53 inference(transitivity,[status(thm)],[10669, 9120])).
% 2.34/2.53 tff(10671,plain,
% 2.34/2.53 ((~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[10670])).
% 2.34/2.53 tff(10672,plain,
% 2.34/2.53 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[1501, 10671])).
% 2.34/2.53 tff(10673,plain,
% 2.34/2.53 ((~(s(s(s(s(s(elem!1))))) = s(s(s(z))))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(elem!1))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[10665])).
% 2.34/2.53 tff(10674,plain,
% 2.34/2.53 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[1622, 10673])).
% 2.34/2.53 tff(10675,plain,
% 2.34/2.53 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[4092, 10614, 171, 10674, 1099])).
% 2.34/2.53 tff(10676,plain,
% 2.34/2.53 (b(s(s(s(s(s(elem!1))))), s(z))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[6447, 10675])).
% 2.34/2.53 tff(10677,plain,
% 2.34/2.53 ((s(s(s(elem!1))) = elem!1) <=> (elem!1 = s(s(s(elem!1))))),
% 2.34/2.53 inference(commutativity,[status(thm)],[])).
% 2.34/2.53 tff(10678,plain,
% 2.34/2.53 ((s(s(s(elem!1))) = s(z)) <=> (s(s(s(elem!1))) = elem!1)),
% 2.34/2.53 inference(monotonicity,[status(thm)],[10602])).
% 2.34/2.53 tff(10679,plain,
% 2.34/2.53 ((s(s(s(elem!1))) = s(z)) <=> (elem!1 = s(s(s(elem!1))))),
% 2.34/2.53 inference(transitivity,[status(thm)],[10678, 10677])).
% 2.34/2.53 tff(10680,plain,
% 2.34/2.53 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(z))),
% 2.34/2.53 inference(symmetry,[status(thm)],[10679])).
% 2.34/2.53 tff(10681,plain,
% 2.34/2.53 ((~(elem!1 = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(z)))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[10680])).
% 2.34/2.53 tff(10682,plain,
% 2.34/2.53 (~(s(s(s(elem!1))) = s(z))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[10639, 10681])).
% 2.34/2.53 tff(10683,plain,
% 2.34/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(10684,plain,
% 2.34/2.53 (((~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(10685,plain,
% 2.34/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z)))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[10684])).
% 2.34/2.53 tff(10686,plain,
% 2.34/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 2.34/2.53 inference(transitivity,[status(thm)],[10685, 10683])).
% 2.34/2.53 tff(10687,plain,
% 2.34/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 2.34/2.53 inference(quant_inst,[status(thm)],[])).
% 2.34/2.53 tff(10688,plain,
% 2.34/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z)))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[10687, 10686])).
% 2.34/2.53 tff(10689,plain,
% 2.34/2.53 (~r(s(s(s(elem!1))), s(z))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[10688, 183, 1114, 10642])).
% 2.34/2.53 tff(10690,plain,
% 2.34/2.53 (((~![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)))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(10691,plain,
% 2.34/2.53 ((~![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)))),
% 2.34/2.53 inference(quant_inst,[status(thm)],[])).
% 2.34/2.53 tff(10692,plain,
% 2.34/2.53 ((~![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))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[10691, 10690])).
% 2.34/2.53 tff(10693,plain,
% 2.34/2.53 ((s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[10692, 47, 10689])).
% 2.34/2.53 tff(10694,plain,
% 2.34/2.53 (b(s(s(s(elem!1))), s(z))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[10693, 10682])).
% 2.34/2.53 tff(10695,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(10696,plain,
% 2.34/2.53 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(10697,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[10696])).
% 2.34/2.53 tff(10698,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.34/2.53 inference(transitivity,[status(thm)],[10697, 10695])).
% 2.34/2.53 tff(10699,plain,
% 2.34/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.34/2.53 inference(quant_inst,[status(thm)],[])).
% 2.34/2.53 tff(10700,plain,
% 2.34/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[10699, 10698])).
% 2.34/2.53 tff(10701,plain,
% 2.34/2.53 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[10700, 246, 10654, 10694, 10676])).
% 2.34/2.53 tff(10702,plain,
% 2.34/2.53 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[3693, 10701, 10672])).
% 2.34/2.53 tff(10703,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(10704,plain,
% 2.34/2.53 (((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(10705,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[10704])).
% 2.34/2.53 tff(10706,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 2.34/2.53 inference(transitivity,[status(thm)],[10705, 10703])).
% 2.34/2.53 tff(10707,plain,
% 2.34/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 2.34/2.53 inference(quant_inst,[status(thm)],[])).
% 2.34/2.53 tff(10708,plain,
% 2.34/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[10707, 10706])).
% 2.34/2.53 tff(10709,plain,
% 2.34/2.53 (~b(z, s(s(s(elem!1))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[10708, 246, 1100, 1099, 1659])).
% 2.34/2.53 tff(10710,plain,
% 2.34/2.53 ((z = s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[9177, 47, 10709])).
% 2.34/2.53 tff(10711,plain,
% 2.34/2.53 (r(z, s(s(s(elem!1))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[10710, 5369])).
% 2.34/2.53 tff(10712,plain,
% 2.34/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~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))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~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))))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(10713,plain,
% 2.34/2.53 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), z))) <=> ((~r(z, s(z))) | (~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))))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(10714,plain,
% 2.34/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~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)))))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[10713])).
% 2.34/2.53 tff(10715,plain,
% 2.34/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~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))))))),
% 2.34/2.53 inference(transitivity,[status(thm)],[10714, 10712])).
% 2.34/2.53 tff(10716,plain,
% 2.34/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 2.34/2.53 inference(quant_inst,[status(thm)],[])).
% 2.34/2.53 tff(10717,plain,
% 2.34/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~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)))))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[10716, 10715])).
% 2.34/2.53 tff(10718,plain,
% 2.34/2.53 (~r(s(s(s(s(s(elem!1))))), z)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[10717, 183, 171, 10702, 10711])).
% 2.34/2.53 tff(10719,plain,
% 2.34/2.53 (b(s(s(s(s(s(elem!1))))), z)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[1601, 10718])).
% 2.34/2.53 tff(10720,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(10721,plain,
% 2.34/2.54 (((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(10722,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[10721])).
% 2.34/2.54 tff(10723,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 2.34/2.54 inference(transitivity,[status(thm)],[10722, 10720])).
% 2.34/2.54 tff(10724,plain,
% 2.34/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 2.34/2.54 inference(quant_inst,[status(thm)],[])).
% 2.34/2.54 tff(10725,plain,
% 2.34/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[10724, 10723])).
% 2.34/2.54 tff(10726,plain,
% 2.34/2.54 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[10725, 246, 1100, 1099, 10719])).
% 2.34/2.54 tff(10727,plain,
% 2.34/2.54 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[4488, 10726, 10702, 10668, 10664])).
% 2.34/2.54 tff(10728,plain,
% 2.34/2.54 ((s(s(s(z))) = s(s(z))) <=> (s(s(elem!1)) = s(elem!1))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[3452, 3455])).
% 2.34/2.54 tff(10729,plain,
% 2.34/2.54 ((~(s(s(s(z))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[10728])).
% 2.34/2.54 tff(10730,plain,
% 2.34/2.54 (~(s(s(elem!1)) = s(elem!1))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[8374, 10729])).
% 2.34/2.54 tff(10731,plain,
% 2.34/2.54 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(elem!1)), s(elem!1))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[3455])).
% 2.34/2.54 tff(10732,plain,
% 2.34/2.54 ((~b(s(s(elem!1)), s(s(z)))) <=> (~b(s(s(elem!1)), s(elem!1)))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[10731])).
% 2.34/2.54 tff(10733,assumption,(b(s(s(z)), s(s(s(elem!1))))), introduced(assumption)).
% 2.34/2.54 tff(10734,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(10735,plain,
% 2.34/2.54 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(10736,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z))))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[10735])).
% 2.34/2.54 tff(10737,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.34/2.54 inference(transitivity,[status(thm)],[10736, 10734])).
% 2.34/2.54 tff(10738,plain,
% 2.34/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.34/2.54 inference(quant_inst,[status(thm)],[])).
% 2.34/2.54 tff(10739,plain,
% 2.34/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z))))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[10738, 10737])).
% 2.34/2.54 tff(10740,plain,
% 2.34/2.54 ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[10739, 246, 1657, 1659])).
% 2.34/2.54 tff(10741,plain,
% 2.34/2.54 (~b(s(s(elem!1)), s(s(z)))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[10740, 10733])).
% 2.34/2.54 tff(10742,plain,
% 2.34/2.54 (~b(s(s(elem!1)), s(elem!1))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[10741, 10732])).
% 2.34/2.54 tff(10743,plain,
% 2.34/2.54 (r(s(s(elem!1)), s(elem!1))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[5644, 10742, 10730])).
% 2.34/2.54 tff(10744,plain,
% 2.34/2.54 ((elem!1 = s(elem!1)) <=> (s(z) = s(s(z)))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[202, 3454])).
% 2.34/2.54 tff(10745,plain,
% 2.34/2.54 ((s(z) = s(s(z))) <=> (elem!1 = s(elem!1))),
% 2.34/2.54 inference(symmetry,[status(thm)],[10744])).
% 2.34/2.54 tff(10746,plain,
% 2.34/2.54 ((~(s(z) = s(s(z)))) <=> (~(elem!1 = s(elem!1)))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[10745])).
% 2.34/2.54 tff(10747,plain,
% 2.34/2.54 (~(elem!1 = s(elem!1))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[8340, 10746])).
% 2.34/2.54 tff(10748,plain,
% 2.34/2.54 (b(elem!1, s(elem!1)) <=> b(s(z), s(s(z)))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[202, 3454])).
% 2.34/2.54 tff(10749,plain,
% 2.34/2.54 (b(s(z), s(s(z))) <=> b(elem!1, s(elem!1))),
% 2.34/2.54 inference(symmetry,[status(thm)],[10748])).
% 2.34/2.54 tff(10750,plain,
% 2.34/2.54 ((~b(s(z), s(s(z)))) <=> (~b(elem!1, s(elem!1)))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[10749])).
% 2.34/2.54 tff(10751,assumption,(b(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 2.34/2.54 tff(10752,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(10753,plain,
% 2.34/2.54 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(10754,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[10753])).
% 2.34/2.54 tff(10755,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.34/2.54 inference(transitivity,[status(thm)],[10754, 10752])).
% 2.34/2.54 tff(10756,plain,
% 2.34/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))))),
% 2.34/2.54 inference(quant_inst,[status(thm)],[])).
% 2.34/2.54 tff(10757,plain,
% 2.34/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[10756, 10755])).
% 2.34/2.54 tff(10758,plain,
% 2.34/2.54 ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[10757, 246, 1657, 1659, 10751])).
% 2.34/2.54 tff(10759,plain,
% 2.34/2.54 (~b(s(z), s(s(z)))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[10758, 10733])).
% 2.34/2.54 tff(10760,plain,
% 2.34/2.54 (~b(elem!1, s(elem!1))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[10759, 10750])).
% 2.34/2.54 tff(10761,plain,
% 2.34/2.54 (r(elem!1, s(elem!1))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[2864, 10760, 10747])).
% 2.34/2.54 tff(10762,plain,
% 2.34/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(10763,plain,
% 2.34/2.54 (((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(10764,plain,
% 2.34/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[10763])).
% 2.34/2.54 tff(10765,plain,
% 2.34/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.34/2.54 inference(transitivity,[status(thm)],[10764, 10762])).
% 2.34/2.54 tff(10766,plain,
% 2.34/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 2.34/2.54 inference(quant_inst,[status(thm)],[])).
% 2.34/2.54 tff(10767,plain,
% 2.34/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[10766, 10765])).
% 2.34/2.54 tff(10768,plain,
% 2.34/2.54 ($false),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[10767, 183, 216, 601, 1951])).
% 2.34/2.54 tff(10769,plain,((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.54 tff(10770,plain,
% 2.34/2.54 ($false),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[10769, 10761, 10743, 216])).
% 2.34/2.54 tff(10771,plain,((~b(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~(elem!1 = s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.54 tff(10772,plain,
% 2.34/2.54 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[10771, 10727, 202, 216, 1659, 10654])).
% 2.34/2.54 tff(10773,plain,
% 2.34/2.54 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[10772, 10631])).
% 2.34/2.54 tff(10774,plain,
% 2.34/2.54 (r(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[1531, 10773])).
% 2.34/2.54 tff(10775,plain,
% 2.34/2.54 (r(s(elem!1), s(s(s(elem!1))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[9497, 10774, 3451])).
% 2.34/2.54 tff(10776,plain,
% 2.34/2.54 (r(s(s(z)), s(s(s(elem!1))))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[10775, 10626])).
% 2.34/2.54 tff(10777,plain,
% 2.34/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(10778,plain,
% 2.34/2.54 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(z)), z))) <=> ((~r(z, s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(10779,plain,
% 2.34/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[10778])).
% 2.34/2.54 tff(10780,plain,
% 2.34/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)))),
% 2.34/2.54 inference(transitivity,[status(thm)],[10779, 10777])).
% 2.34/2.54 tff(10781,plain,
% 2.34/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(z)), z)))),
% 2.34/2.54 inference(quant_inst,[status(thm)],[])).
% 2.34/2.54 tff(10782,plain,
% 2.34/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[10781, 10780])).
% 2.34/2.54 tff(10783,plain,
% 2.34/2.54 (~r(s(s(z)), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[10782, 183, 171, 10711, 10776])).
% 2.34/2.54 tff(10784,plain,
% 2.34/2.54 (~r(s(elem!1), z)),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[10783, 10624])).
% 2.34/2.54 tff(10785,plain,
% 2.34/2.54 (b(s(elem!1), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[2581, 10784])).
% 2.34/2.54 tff(10786,plain,
% 2.34/2.54 (b(s(s(z)), z)),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[10785, 10621])).
% 2.34/2.54 tff(10787,plain,
% 2.34/2.54 ((s(s(z)) = s(s(s(s(s(elem!1)))))) <=> (s(elem!1) = s(s(s(s(s(elem!1))))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[3455])).
% 2.34/2.54 tff(10788,plain,
% 2.34/2.54 ((s(s(z)) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(elem!1))),
% 2.34/2.54 inference(transitivity,[status(thm)],[10787, 1800])).
% 2.34/2.54 tff(10789,plain,
% 2.34/2.54 ((s(s(s(s(s(elem!1))))) = s(elem!1)) <=> (s(s(z)) = s(s(s(s(s(elem!1))))))),
% 2.34/2.54 inference(symmetry,[status(thm)],[10788])).
% 2.34/2.54 tff(10790,plain,
% 2.34/2.54 ((~(s(s(s(s(s(elem!1))))) = s(elem!1))) <=> (~(s(s(z)) = s(s(s(s(s(elem!1)))))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[10789])).
% 2.34/2.54 tff(10791,plain,
% 2.34/2.54 (s(s(elem!1)) = s(s(s(z)))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[3452, 3393])).
% 2.34/2.54 tff(10792,plain,
% 2.34/2.54 (~(s(s(s(s(s(elem!1))))) = s(elem!1))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[3239, 10791])).
% 2.34/2.54 tff(10793,plain,
% 2.34/2.54 (~(s(s(z)) = s(s(s(s(s(elem!1))))))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[10792, 10790])).
% 2.34/2.54 tff(10794,plain,
% 2.34/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(10795,plain,
% 2.34/2.54 (((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(10796,plain,
% 2.34/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(s(elem!1)))))))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[10795])).
% 2.34/2.54 tff(10797,plain,
% 2.34/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 2.34/2.54 inference(transitivity,[status(thm)],[10796, 10794])).
% 2.34/2.54 tff(10798,plain,
% 2.34/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 2.34/2.54 inference(quant_inst,[status(thm)],[])).
% 2.34/2.54 tff(10799,plain,
% 2.34/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(s(elem!1)))))))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[10798, 10797])).
% 2.34/2.54 tff(10800,plain,
% 2.34/2.54 (~r(s(s(z)), s(s(s(s(s(elem!1))))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[10799, 183, 10702, 10776])).
% 2.34/2.54 tff(10801,plain,
% 2.34/2.54 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(elem!1)))))) | b(s(s(z)), s(s(s(s(s(elem!1)))))) | r(s(s(z)), s(s(s(s(s(elem!1)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(elem!1)))))) | b(s(s(z)), s(s(s(s(s(elem!1)))))) | r(s(s(z)), s(s(s(s(s(elem!1)))))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(10802,plain,
% 2.34/2.54 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(elem!1)))))) | b(s(s(z)), s(s(s(s(s(elem!1)))))) | r(s(s(z)), s(s(s(s(s(elem!1)))))))),
% 2.34/2.54 inference(quant_inst,[status(thm)],[])).
% 2.34/2.54 tff(10803,plain,
% 2.34/2.54 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(elem!1)))))) | b(s(s(z)), s(s(s(s(s(elem!1)))))) | r(s(s(z)), s(s(s(s(s(elem!1))))))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[10802, 10801])).
% 2.34/2.54 tff(10804,plain,
% 2.34/2.54 ((s(s(z)) = s(s(s(s(s(elem!1)))))) | b(s(s(z)), s(s(s(s(s(elem!1))))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[10803, 47, 10800])).
% 2.34/2.54 tff(10805,plain,
% 2.34/2.54 (b(s(s(z)), s(s(s(s(s(elem!1))))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[10804, 10793])).
% 2.34/2.54 tff(10806,plain,
% 2.34/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(elem!1))))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(10807,plain,
% 2.34/2.54 (((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(elem!1))))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(10808,plain,
% 2.34/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(elem!1)))))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[10807])).
% 2.34/2.54 tff(10809,plain,
% 2.34/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(elem!1))))))),
% 2.34/2.55 inference(transitivity,[status(thm)],[10808, 10806])).
% 2.34/2.55 tff(10810,plain,
% 2.34/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(elem!1))))))))),
% 2.34/2.55 inference(quant_inst,[status(thm)],[])).
% 2.34/2.55 tff(10811,plain,
% 2.34/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(elem!1)))))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[10810, 10809])).
% 2.34/2.55 tff(10812,plain,
% 2.34/2.55 (~r(z, s(s(s(s(s(elem!1))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[10811, 183, 10702, 10711])).
% 2.34/2.55 tff(10813,plain,
% 2.34/2.55 (b(z, s(s(s(s(s(elem!1))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[2487, 47, 10812, 5706])).
% 2.34/2.55 tff(10814,plain,
% 2.34/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), z)))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(10815,plain,
% 2.34/2.55 (((~b(z, s(s(elem!1)))) | (~b(z, 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(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), z))) <=> ((~b(z, 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(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), z)))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(10816,plain,
% 2.34/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, 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(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), z))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[10815])).
% 2.34/2.55 tff(10817,plain,
% 2.34/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, 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(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), z)))),
% 2.34/2.55 inference(transitivity,[status(thm)],[10816, 10814])).
% 2.34/2.55 tff(10818,plain,
% 2.34/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, 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(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), z)))),
% 2.34/2.55 inference(quant_inst,[status(thm)],[])).
% 2.34/2.55 tff(10819,plain,
% 2.34/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), z))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[10818, 10817])).
% 2.34/2.55 tff(10820,plain,
% 2.34/2.55 (~b(s(s(z)), z)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[10819, 246, 1099, 10719, 10813, 10805])).
% 2.34/2.55 tff(10821,plain,
% 2.34/2.55 ($false),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[10820, 10786])).
% 2.34/2.55 tff(10822,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~(elem!1 = s(z))) | (~b(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.55 tff(10823,plain,
% 2.34/2.55 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[10822, 202, 10619, 171, 216, 10617, 1114])).
% 2.34/2.55 tff(10824,plain,
% 2.34/2.55 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[9446, 10823, 3452])).
% 2.34/2.55 tff(10825,plain,
% 2.34/2.55 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[1702, 10824])).
% 2.34/2.55 tff(10826,plain,
% 2.34/2.55 (~r(s(s(s(s(z)))), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[8491, 10825, 10615])).
% 2.34/2.55 tff(10827,plain,
% 2.34/2.55 (b(s(s(s(s(z)))), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[6103, 10826])).
% 2.34/2.55 tff(10828,plain,
% 2.34/2.55 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[3068])).
% 2.34/2.55 tff(10829,plain,
% 2.34/2.55 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 2.34/2.55 inference(symmetry,[status(thm)],[10828])).
% 2.34/2.55 tff(10830,plain,
% 2.34/2.55 ((~b(s(s(s(elem!1))), s(z))) <=> (~b(s(s(s(s(z)))), s(z)))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[10829])).
% 2.34/2.55 tff(10831,assumption,(~b(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 2.34/2.55 tff(10832,plain,
% 2.34/2.55 (~b(s(s(s(s(z)))), s(z))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[10831, 10830])).
% 2.34/2.55 tff(10833,plain,
% 2.34/2.55 ($false),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[8267, 10832])).
% 2.34/2.55 tff(10834,plain,(b(s(s(s(elem!1))), s(z)) | (~b(s(s(s(s(z)))), s(z))) | (~(s(s(s(z))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.55 tff(10835,plain,
% 2.34/2.55 (b(s(s(s(elem!1))), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[10834, 10827, 3452])).
% 2.34/2.55 tff(10836,plain,
% 2.34/2.55 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[4092, 10614, 171, 10674, 10619])).
% 2.34/2.55 tff(10837,plain,
% 2.34/2.55 (b(s(s(s(s(s(elem!1))))), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[6447, 10836])).
% 2.34/2.55 tff(10838,plain,
% 2.34/2.55 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[3453, 3452])).
% 2.34/2.55 tff(10839,plain,
% 2.34/2.55 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[10825, 10838])).
% 2.34/2.55 tff(10840,plain,
% 2.34/2.55 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(s(z)))),
% 2.34/2.55 inference(symmetry,[status(thm)],[10731])).
% 2.34/2.55 tff(10841,plain,
% 2.34/2.55 (b(s(s(s(s(s(elem!1))))), s(s(z))) <=> b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[3455])).
% 2.34/2.55 tff(10842,plain,
% 2.34/2.55 (b(s(s(s(s(s(elem!1))))), s(elem!1)) <=> b(s(s(s(s(s(elem!1))))), s(s(z)))),
% 2.34/2.55 inference(symmetry,[status(thm)],[10841])).
% 2.34/2.55 tff(10843,plain,
% 2.34/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(10844,plain,
% 2.34/2.55 (((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(10845,plain,
% 2.34/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z)))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[10844])).
% 2.34/2.55 tff(10846,plain,
% 2.34/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.34/2.55 inference(transitivity,[status(thm)],[10845, 10843])).
% 2.34/2.55 tff(10847,plain,
% 2.34/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.34/2.55 inference(quant_inst,[status(thm)],[])).
% 2.34/2.55 tff(10848,plain,
% 2.34/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z)))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[10847, 10846])).
% 2.34/2.55 tff(10849,plain,
% 2.34/2.55 (~r(s(s(s(elem!1))), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[10848, 183, 1113, 3076])).
% 2.34/2.55 tff(10850,plain,
% 2.34/2.55 ((s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[10692, 47, 10849])).
% 2.34/2.55 tff(10851,plain,
% 2.34/2.55 (b(s(s(s(elem!1))), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[10850, 10682])).
% 2.34/2.55 tff(10852,plain,
% 2.34/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(10853,plain,
% 2.34/2.55 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(10854,plain,
% 2.34/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1)))))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[10853])).
% 2.34/2.55 tff(10855,plain,
% 2.34/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))),
% 2.34/2.55 inference(transitivity,[status(thm)],[10854, 10852])).
% 2.34/2.55 tff(10856,plain,
% 2.34/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))),
% 2.34/2.55 inference(quant_inst,[status(thm)],[])).
% 2.34/2.55 tff(10857,plain,
% 2.34/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1)))))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[10856, 10855])).
% 2.34/2.55 tff(10858,plain,
% 2.34/2.55 (~r(s(z), s(s(s(elem!1))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[10857, 183, 1113, 3076])).
% 2.34/2.55 tff(10859,plain,
% 2.34/2.55 ((s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[10652, 47, 10858])).
% 2.34/2.55 tff(10860,plain,
% 2.34/2.55 (b(s(z), s(s(s(elem!1))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[10859, 10640])).
% 2.34/2.55 tff(10861,plain,
% 2.34/2.55 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[10700, 246, 10860, 10851, 10676])).
% 2.34/2.55 tff(10862,plain,
% 2.34/2.55 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[3381, 10861, 3452])).
% 2.34/2.55 tff(10863,plain,
% 2.34/2.55 (r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[1897, 10862])).
% 2.34/2.55 tff(10864,plain,
% 2.34/2.55 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(z)))),
% 2.34/2.55 inference(commutativity,[status(thm)],[])).
% 2.34/2.55 tff(10865,plain,
% 2.34/2.55 ((s(s(z)) = s(s(elem!1))) <=> (s(s(z)) = s(s(s(z))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[10659])).
% 2.34/2.55 tff(10866,plain,
% 2.34/2.55 ((s(s(z)) = s(s(elem!1))) <=> (s(s(s(z))) = s(s(z)))),
% 2.34/2.55 inference(transitivity,[status(thm)],[10865, 10864])).
% 2.34/2.55 tff(10867,plain,
% 2.34/2.55 ((s(s(s(z))) = s(s(z))) <=> (s(s(z)) = s(s(elem!1)))),
% 2.34/2.55 inference(symmetry,[status(thm)],[10866])).
% 2.34/2.55 tff(10868,plain,
% 2.34/2.55 ((~(s(s(s(z))) = s(s(z)))) <=> (~(s(s(z)) = s(s(elem!1))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[10867])).
% 2.34/2.55 tff(10869,plain,
% 2.34/2.55 (~(s(s(z)) = s(s(elem!1)))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[8374, 10868])).
% 2.34/2.55 tff(10870,plain,
% 2.34/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(10871,plain,
% 2.34/2.55 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(10872,plain,
% 2.34/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[10871])).
% 2.34/2.55 tff(10873,plain,
% 2.34/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.34/2.55 inference(transitivity,[status(thm)],[10872, 10870])).
% 2.34/2.55 tff(10874,plain,
% 2.34/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))))),
% 2.34/2.55 inference(quant_inst,[status(thm)],[])).
% 2.34/2.55 tff(10875,plain,
% 2.34/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[10874, 10873])).
% 2.34/2.55 tff(10876,plain,
% 2.34/2.55 (~b(s(z), s(s(z)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[10875, 246, 10751, 8133, 10733])).
% 2.34/2.55 tff(10877,plain,
% 2.34/2.55 (~b(elem!1, s(elem!1))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[10876, 10750])).
% 2.34/2.55 tff(10878,plain,
% 2.34/2.55 (r(elem!1, s(elem!1))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[2864, 10877, 10747])).
% 2.34/2.55 tff(10879,plain,
% 2.34/2.55 (~r(s(s(elem!1)), s(elem!1))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[10769, 10878, 216])).
% 2.34/2.55 tff(10880,plain,
% 2.34/2.55 (b(s(s(elem!1)), s(elem!1))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[5644, 10879, 10730])).
% 2.34/2.55 tff(10881,plain,
% 2.34/2.55 (b(s(s(elem!1)), s(s(z)))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[10880, 10840])).
% 2.34/2.55 tff(10882,plain,
% 2.34/2.55 (b(z, s(s(z))) <=> b(z, s(elem!1))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[3455])).
% 2.34/2.55 tff(10883,plain,
% 2.34/2.55 (b(z, s(elem!1)) <=> b(z, s(s(z)))),
% 2.34/2.55 inference(symmetry,[status(thm)],[10882])).
% 2.34/2.55 tff(10884,plain,
% 2.34/2.55 (r(z, s(s(z))) <=> r(z, s(elem!1))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[3455])).
% 2.34/2.55 tff(10885,plain,
% 2.34/2.55 ((~r(z, s(s(z)))) <=> (~r(z, s(elem!1)))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[10884])).
% 2.34/2.55 tff(10886,plain,
% 2.34/2.55 (r(s(s(z)), s(z)) <=> r(s(elem!1), elem!1)),
% 2.34/2.55 inference(monotonicity,[status(thm)],[3455, 10602])).
% 2.34/2.55 tff(10887,plain,
% 2.34/2.55 (r(s(elem!1), elem!1) <=> r(s(s(z)), s(z))),
% 2.34/2.55 inference(symmetry,[status(thm)],[10886])).
% 2.34/2.55 tff(10888,plain,
% 2.34/2.55 ((s(z) = s(s(z))) <=> (s(elem!1) = elem!1)),
% 2.34/2.55 inference(transitivity,[status(thm)],[10745, 3423])).
% 2.34/2.55 tff(10889,plain,
% 2.34/2.55 ((~(s(z) = s(s(z)))) <=> (~(s(elem!1) = elem!1))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[10888])).
% 2.34/2.55 tff(10890,plain,
% 2.34/2.55 (~(s(elem!1) = elem!1)),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[8340, 10889])).
% 2.34/2.55 tff(10891,plain,
% 2.34/2.55 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(z))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[202])).
% 2.34/2.55 tff(10892,plain,
% 2.34/2.55 (b(s(elem!1), s(z)) <=> b(s(elem!1), elem!1)),
% 2.34/2.55 inference(symmetry,[status(thm)],[10891])).
% 2.34/2.55 tff(10893,plain,
% 2.34/2.55 (b(s(s(z)), s(z)) <=> b(s(elem!1), s(z))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[3455])).
% 2.34/2.55 tff(10894,plain,
% 2.34/2.55 (b(s(s(z)), s(z)) <=> b(s(elem!1), elem!1)),
% 2.34/2.55 inference(transitivity,[status(thm)],[10893, 10892])).
% 2.34/2.55 tff(10895,plain,
% 2.34/2.55 ((~b(s(s(z)), s(z))) <=> (~b(s(elem!1), elem!1))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[10894])).
% 2.34/2.55 tff(10896,plain,
% 2.34/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(10897,plain,
% 2.34/2.55 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(10898,plain,
% 2.34/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[10897])).
% 2.34/2.55 tff(10899,plain,
% 2.34/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.34/2.55 inference(transitivity,[status(thm)],[10898, 10896])).
% 2.34/2.55 tff(10900,plain,
% 2.34/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))))),
% 2.34/2.55 inference(quant_inst,[status(thm)],[])).
% 2.34/2.55 tff(10901,plain,
% 2.34/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[10900, 10899])).
% 2.34/2.55 tff(10902,plain,
% 2.34/2.55 (~b(s(s(z)), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[10901, 246, 10751, 8133, 10733])).
% 2.34/2.55 tff(10903,plain,
% 2.34/2.55 (~b(s(elem!1), elem!1)),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[10902, 10895])).
% 2.34/2.55 tff(10904,plain,
% 2.34/2.55 (r(s(elem!1), elem!1)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[5655, 10903, 10890])).
% 2.34/2.55 tff(10905,plain,
% 2.34/2.55 (r(s(s(z)), s(z))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[10904, 10887])).
% 2.34/2.55 tff(10906,plain,
% 2.34/2.55 (~r(z, s(s(z)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[9900, 183, 171, 10905])).
% 2.34/2.55 tff(10907,plain,
% 2.34/2.55 (~r(z, s(elem!1))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[10906, 10885])).
% 2.34/2.55 tff(10908,plain,
% 2.34/2.55 (b(z, s(elem!1))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[2561, 10907])).
% 2.34/2.55 tff(10909,plain,
% 2.34/2.55 (b(z, s(s(z)))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[10908, 10883])).
% 2.34/2.55 tff(10910,plain,
% 2.34/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(10911,plain,
% 2.34/2.55 (((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(10912,plain,
% 2.34/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z))))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[10911])).
% 2.34/2.56 tff(10913,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.34/2.56 inference(transitivity,[status(thm)],[10912, 10910])).
% 2.34/2.56 tff(10914,plain,
% 2.34/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))))),
% 2.34/2.56 inference(quant_inst,[status(thm)],[])).
% 2.34/2.56 tff(10915,plain,
% 2.34/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z))))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[10914, 10913])).
% 2.34/2.56 tff(10916,plain,
% 2.34/2.56 ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[10915, 246, 1099, 10733])).
% 2.34/2.56 tff(10917,plain,
% 2.34/2.56 (~b(s(s(z)), s(s(elem!1)))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[10916, 10909, 10881])).
% 2.34/2.56 tff(10918,plain,
% 2.34/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(10919,plain,
% 2.34/2.56 (((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(10920,plain,
% 2.34/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z)))))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[10919])).
% 2.34/2.56 tff(10921,plain,
% 2.34/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))))),
% 2.34/2.56 inference(transitivity,[status(thm)],[10920, 10918])).
% 2.34/2.56 tff(10922,plain,
% 2.34/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))),
% 2.34/2.56 inference(quant_inst,[status(thm)],[])).
% 2.34/2.56 tff(10923,plain,
% 2.34/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z)))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[10922, 10921])).
% 2.34/2.56 tff(10924,plain,
% 2.34/2.56 (~r(s(s(z)), s(s(elem!1)))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[10923, 183, 10614, 10905])).
% 2.34/2.56 tff(10925,plain,
% 2.34/2.56 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(10926,plain,
% 2.34/2.56 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1))))),
% 2.34/2.56 inference(quant_inst,[status(thm)],[])).
% 2.34/2.56 tff(10927,plain,
% 2.34/2.56 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1)))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[10926, 10925])).
% 2.34/2.56 tff(10928,plain,
% 2.34/2.56 ((s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1)))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[10927, 47, 10924])).
% 2.34/2.56 tff(10929,plain,
% 2.34/2.56 ($false),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[10928, 10917, 10869])).
% 2.34/2.56 tff(10930,plain,((~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~(elem!1 = s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.56 tff(10931,plain,
% 2.34/2.56 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[10930, 10860, 202, 171, 216, 1099, 10851])).
% 2.34/2.56 tff(10932,plain,
% 2.34/2.56 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[10931, 10631])).
% 2.34/2.56 tff(10933,plain,
% 2.34/2.56 (r(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[1531, 10932])).
% 2.34/2.56 tff(10934,plain,
% 2.34/2.56 (~r(s(s(s(s(s(elem!1))))), s(s(z)))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[1916, 10933, 10863])).
% 2.34/2.56 tff(10935,plain,
% 2.34/2.56 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[3257, 10934, 10791])).
% 2.34/2.56 tff(10936,plain,
% 2.34/2.56 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[1795, 10935, 10792])).
% 2.34/2.56 tff(10937,plain,
% 2.34/2.56 (b(s(s(s(s(s(elem!1))))), s(s(z)))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[10936, 10842])).
% 2.34/2.56 tff(10938,plain,
% 2.34/2.56 (r(s(elem!1), s(s(s(elem!1))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[9497, 10933, 3451])).
% 2.34/2.56 tff(10939,plain,
% 2.34/2.56 (r(s(s(z)), s(s(s(elem!1))))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[10938, 10626])).
% 2.34/2.56 tff(10940,plain,
% 2.34/2.56 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[3693, 10861, 10672])).
% 2.34/2.56 tff(10941,plain,
% 2.34/2.56 (~r(s(s(z)), s(s(s(s(s(elem!1))))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[10799, 183, 10940, 10939])).
% 2.34/2.56 tff(10942,plain,
% 2.34/2.56 ((s(s(z)) = s(s(s(s(s(elem!1)))))) | b(s(s(z)), s(s(s(s(s(elem!1))))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[10803, 47, 10941])).
% 2.34/2.56 tff(10943,plain,
% 2.34/2.56 (b(s(s(z)), s(s(s(s(s(elem!1))))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[10942, 10793])).
% 2.34/2.56 tff(10944,assumption,(b(s(s(s(s(s(elem!1))))), s(s(z)))), introduced(assumption)).
% 2.34/2.56 tff(10945,assumption,(b(s(s(z)), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 2.34/2.56 tff(10946,assumption,(b(s(z), s(s(z)))), introduced(assumption)).
% 2.34/2.56 tff(10947,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(z), s(s(z)))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(10948,plain,
% 2.34/2.56 (((~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), 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(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(z), s(s(z)))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(10949,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), 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(X1, 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(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(z), s(s(z))))))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[10948])).
% 2.34/2.56 tff(10950,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), 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(X1, 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(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(z), s(s(z)))))),
% 2.34/2.56 inference(transitivity,[status(thm)],[10949, 10947])).
% 2.34/2.56 tff(10951,plain,
% 2.34/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 2.34/2.56 inference(quant_inst,[status(thm)],[])).
% 2.34/2.56 tff(10952,plain,
% 2.34/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(z), s(s(z))))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[10951, 10950])).
% 2.34/2.56 tff(10953,plain,
% 2.34/2.56 ($false),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[10952, 246, 6875, 10946, 10945, 10944])).
% 2.34/2.56 tff(10954,plain,((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.56 tff(10955,plain,
% 2.34/2.56 (~b(s(z), s(s(z)))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[10954, 10943, 10676, 10937])).
% 2.34/2.56 tff(10956,plain,
% 2.34/2.56 (~b(elem!1, s(elem!1))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[10955, 10750])).
% 2.34/2.56 tff(10957,plain,
% 2.34/2.56 (r(elem!1, s(elem!1))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[2864, 10956, 10747])).
% 2.34/2.56 tff(10958,plain,
% 2.34/2.56 (~r(s(s(elem!1)), s(elem!1))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[10769, 10957, 216])).
% 2.34/2.56 tff(10959,plain,
% 2.34/2.56 (b(s(s(elem!1)), s(elem!1))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[5644, 10958, 10730])).
% 2.34/2.56 tff(10960,plain,
% 2.34/2.56 (b(s(s(elem!1)), s(s(z)))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[10959, 10840])).
% 2.34/2.56 tff(10961,plain,
% 2.34/2.56 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[5176, 10940, 3076])).
% 2.34/2.56 tff(10962,plain,
% 2.34/2.56 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[1557, 10961, 10674])).
% 2.34/2.56 tff(10963,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(10964,plain,
% 2.34/2.56 (((~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(10965,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z))))))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[10964])).
% 2.34/2.56 tff(10966,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.34/2.56 inference(transitivity,[status(thm)],[10965, 10963])).
% 2.34/2.56 tff(10967,plain,
% 2.34/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.34/2.56 inference(quant_inst,[status(thm)],[])).
% 2.34/2.56 tff(10968,plain,
% 2.34/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z))))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[10967, 10966])).
% 2.34/2.56 tff(10969,plain,
% 2.34/2.56 (~b(s(s(elem!1)), s(s(z)))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[10968, 246, 10962, 10943, 10937])).
% 2.34/2.56 tff(10970,plain,
% 2.34/2.56 ($false),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[10969, 10960])).
% 2.34/2.56 tff(10971,plain,((~r(s(z), s(s(elem!1)))) | (~(elem!1 = s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(z))) | (~b(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.56 tff(10972,plain,
% 2.34/2.56 (~r(s(z), s(s(elem!1)))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[10971, 202, 216, 171, 10619, 10839])).
% 2.34/2.56 tff(10973,plain,
% 2.34/2.56 (b(s(z), s(s(elem!1)))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[233, 10972])).
% 2.34/2.56 tff(10974,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(10975,plain,
% 2.34/2.56 (((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z)))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(10976,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z)))))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[10975])).
% 2.34/2.56 tff(10977,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 2.34/2.56 inference(transitivity,[status(thm)],[10976, 10974])).
% 2.34/2.56 tff(10978,plain,
% 2.34/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 2.34/2.56 inference(quant_inst,[status(thm)],[])).
% 2.34/2.56 tff(10979,plain,
% 2.34/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z)))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[10978, 10977])).
% 2.34/2.56 tff(10980,plain,
% 2.34/2.56 ($false),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[10979, 246, 1100, 1099, 235, 946, 6875])).
% 2.34/2.56 tff(10981,plain,((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.56 tff(10982,plain,
% 2.34/2.56 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[10981, 10973, 10619, 10617, 10837])).
% 2.34/2.56 tff(10983,plain,
% 2.34/2.56 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[1557, 10982, 10674])).
% 2.34/2.56 tff(10984,plain,
% 2.34/2.56 (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[9345, 183, 10839, 10983])).
% 2.34/2.56 tff(10985,plain,
% 2.34/2.56 ((~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[10669])).
% 2.34/2.56 tff(10986,plain,
% 2.34/2.56 (~(s(s(s(elem!1))) = s(s(s(s(s(elem!1))))))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[1501, 10985])).
% 2.34/2.56 tff(10987,plain,
% 2.34/2.56 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[913, 47, 10986, 10984])).
% 2.34/2.56 tff(10988,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(10989,plain,
% 2.34/2.56 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(10990,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[10989])).
% 2.34/2.56 tff(10991,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.34/2.56 inference(transitivity,[status(thm)],[10990, 10988])).
% 2.34/2.56 tff(10992,plain,
% 2.34/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.34/2.56 inference(quant_inst,[status(thm)],[])).
% 2.34/2.56 tff(10993,plain,
% 2.34/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(z)))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[10992, 10991])).
% 2.34/2.56 tff(10994,plain,
% 2.34/2.56 ((~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(z)))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[10993, 246, 10973, 10837, 10987])).
% 2.34/2.56 tff(10995,plain,
% 2.34/2.56 (~b(s(z), s(s(s(s(s(elem!1))))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[10994, 10835])).
% 2.34/2.56 tff(10996,plain,
% 2.34/2.56 (~b(elem!1, s(s(s(s(s(elem!1))))))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[10995, 10610])).
% 2.34/2.56 tff(10997,plain,
% 2.34/2.56 (r(elem!1, s(s(s(s(s(elem!1))))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[5125, 10996, 10608])).
% 2.34/2.56 tff(10998,plain,
% 2.34/2.56 (r(s(z), s(s(s(s(s(elem!1))))))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[10997, 10604])).
% 2.34/2.56 tff(10999,plain,
% 2.34/2.56 (r(elem!1, z) <=> r(s(z), z)),
% 2.34/2.56 inference(monotonicity,[status(thm)],[202])).
% 2.34/2.56 tff(11000,plain,
% 2.34/2.56 (r(s(z), z) <=> r(elem!1, z)),
% 2.34/2.56 inference(symmetry,[status(thm)],[10999])).
% 2.34/2.56 tff(11001,plain,
% 2.34/2.56 (r(elem!1, z)),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[1114, 11000])).
% 2.34/2.56 tff(11002,plain,
% 2.34/2.56 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[5176, 10983, 10839])).
% 2.34/2.56 tff(11003,plain,
% 2.34/2.56 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[3693, 11002, 10672])).
% 2.34/2.57 tff(11004,plain,
% 2.34/2.57 (r(elem!1, s(s(s(s(z))))) <=> r(s(z), s(s(s(s(z)))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[202])).
% 2.34/2.57 tff(11005,plain,
% 2.34/2.57 (r(s(z), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 2.34/2.57 inference(symmetry,[status(thm)],[11004])).
% 2.34/2.57 tff(11006,plain,
% 2.34/2.57 (r(elem!1, s(s(s(elem!1)))) <=> r(s(z), s(s(s(s(z)))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[202, 10627])).
% 2.34/2.57 tff(11007,plain,
% 2.34/2.57 (r(s(z), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[10602])).
% 2.34/2.57 tff(11008,plain,
% 2.34/2.57 (r(s(z), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(s(z)))))),
% 2.34/2.57 inference(transitivity,[status(thm)],[11007, 11006, 11005])).
% 2.34/2.57 tff(11009,plain,
% 2.34/2.57 (r(elem!1, s(s(s(elem!1)))) <=> r(s(z), s(s(s(elem!1))))),
% 2.34/2.57 inference(symmetry,[status(thm)],[11007])).
% 2.34/2.57 tff(11010,plain,
% 2.34/2.57 (b(elem!1, s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[202])).
% 2.34/2.57 tff(11011,plain,
% 2.34/2.57 (b(s(z), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.34/2.57 inference(symmetry,[status(thm)],[11010])).
% 2.34/2.57 tff(11012,plain,
% 2.34/2.57 ((~b(s(z), s(s(s(elem!1))))) <=> (~b(elem!1, s(s(s(elem!1)))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[11011])).
% 2.34/2.57 tff(11013,plain,
% 2.34/2.57 ((s(s(s(s(z)))) = s(z)) <=> (s(s(s(s(z)))) = elem!1)),
% 2.34/2.57 inference(monotonicity,[status(thm)],[10602])).
% 2.34/2.57 tff(11014,plain,
% 2.34/2.57 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[11013])).
% 2.34/2.57 tff(11015,plain,
% 2.34/2.57 (~(s(s(s(s(z)))) = elem!1)),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[1713, 11014])).
% 2.34/2.57 tff(11016,plain,
% 2.34/2.57 (b(s(s(s(s(z)))), elem!1)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[9834, 7218, 11015, 267])).
% 2.34/2.57 tff(11017,plain,
% 2.34/2.57 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[202])).
% 2.34/2.57 tff(11018,plain,
% 2.34/2.57 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(z)))), elem!1)),
% 2.34/2.57 inference(symmetry,[status(thm)],[11017])).
% 2.34/2.57 tff(11019,plain,
% 2.34/2.57 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[3453])).
% 2.34/2.57 tff(11020,plain,
% 2.34/2.57 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 2.34/2.57 inference(symmetry,[status(thm)],[11019])).
% 2.34/2.57 tff(11021,plain,
% 2.34/2.57 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(z)))), elem!1)),
% 2.34/2.57 inference(transitivity,[status(thm)],[11020, 11018])).
% 2.34/2.57 tff(11022,plain,
% 2.34/2.57 ((~b(s(s(s(elem!1))), s(z))) <=> (~b(s(s(s(s(z)))), elem!1))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[11021])).
% 2.34/2.57 tff(11023,plain,
% 2.34/2.57 (~b(s(s(s(s(z)))), elem!1)),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[10831, 11022])).
% 2.34/2.57 tff(11024,plain,
% 2.34/2.57 ($false),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[5913, 11023])).
% 2.34/2.57 tff(11025,plain,(b(s(s(s(elem!1))), s(z)) | (~b(s(s(s(s(z)))), elem!1)) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.57 tff(11026,plain,
% 2.34/2.57 (b(s(s(s(elem!1))), s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[11025, 11016, 202])).
% 2.34/2.57 tff(11027,plain,
% 2.34/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(11028,plain,
% 2.34/2.57 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(z)))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(11029,plain,
% 2.34/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[11028])).
% 2.34/2.57 tff(11030,plain,
% 2.34/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.34/2.57 inference(transitivity,[status(thm)],[11029, 11027])).
% 2.34/2.57 tff(11031,plain,
% 2.34/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 2.34/2.57 inference(quant_inst,[status(thm)],[])).
% 2.34/2.57 tff(11032,plain,
% 2.34/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[11031, 11030])).
% 2.34/2.57 tff(11033,plain,
% 2.34/2.57 (~b(s(z), s(s(s(elem!1))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[11032, 246, 235, 1658, 11026, 6875])).
% 2.34/2.57 tff(11034,plain,
% 2.34/2.57 (~b(elem!1, s(s(s(elem!1))))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[11033, 11012])).
% 2.34/2.57 tff(11035,plain,
% 2.34/2.57 (r(elem!1, s(s(s(elem!1))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[9483, 11034, 10639])).
% 2.34/2.57 tff(11036,plain,
% 2.34/2.57 (r(s(z), s(s(s(elem!1))))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[11035, 11009])).
% 2.34/2.57 tff(11037,plain,
% 2.34/2.57 (r(elem!1, s(s(s(s(z)))))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[11036, 11008])).
% 2.34/2.57 tff(11038,plain,
% 2.34/2.57 ($false),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[9961, 11037])).
% 2.34/2.57 tff(11039,plain,((~r(s(s(s(s(z)))), z)) | (~(elem!1 = s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.57 tff(11040,plain,
% 2.34/2.57 (~r(s(s(s(s(z)))), z)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[11039, 202, 10973, 11003, 10837, 267, 11001])).
% 2.34/2.57 tff(11041,plain,
% 2.34/2.57 (b(s(s(s(s(z)))), z)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[6040, 11040])).
% 2.34/2.57 tff(11042,plain,
% 2.34/2.57 (b(s(s(s(elem!1))), z)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[9431, 11041, 3452])).
% 2.34/2.57 tff(11043,plain,
% 2.34/2.57 (~b(z, s(s(s(s(s(elem!1))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[9685, 11042, 10672, 10986, 10839, 10983])).
% 2.34/2.57 tff(11044,plain,
% 2.34/2.57 (r(z, s(s(s(s(s(elem!1))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[2487, 47, 5706, 11043])).
% 2.34/2.57 tff(11045,plain,
% 2.34/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(11046,plain,
% 2.34/2.57 (((~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(11047,plain,
% 2.34/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1)))))))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[11046])).
% 2.34/2.57 tff(11048,plain,
% 2.34/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 2.34/2.57 inference(transitivity,[status(thm)],[11047, 11045])).
% 2.34/2.57 tff(11049,plain,
% 2.34/2.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(z, s(z))))),
% 2.34/2.57 inference(quant_inst,[status(thm)],[])).
% 2.34/2.57 tff(11050,plain,
% 2.34/2.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1)))))))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[11049, 11048])).
% 2.34/2.57 tff(11051,plain,
% 2.34/2.57 ($false),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[11050, 183, 171, 11044, 10998])).
% 2.34/2.57 tff(11052,plain,((~(elem!1 = s(z))) | (~r(z, s(z))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.57 tff(11053,plain,
% 2.34/2.57 (~(elem!1 = s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[11052, 1114, 5365, 10595, 170])).
% 2.34/2.57 tff(11054,plain,
% 2.34/2.57 (~(s(z) = elem!1)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[9, 11053])).
% 2.34/2.57 tff(11055,plain,
% 2.34/2.57 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[5804, 11054])).
% 2.34/2.57 tff(11056,plain,
% 2.34/2.57 (b(s(s(s(z))), s(s(elem!1)))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[689, 1647, 119])).
% 2.34/2.57 tff(11057,plain,
% 2.34/2.57 ($false),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[4659, 11056, 7911, 10617, 10093])).
% 2.34/2.57 tff(11058,plain,((~r(s(s(s(z))), elem!1)) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.57 tff(11059,plain,
% 2.34/2.57 (~r(s(s(s(z))), elem!1)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[11058, 11055, 10595, 5365])).
% 2.34/2.57 tff(11060,plain,
% 2.34/2.57 (b(s(z), elem!1)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[6422, 11053, 55, 54, 6376])).
% 2.34/2.57 tff(11061,plain,
% 2.34/2.57 (r(z, s(s(s(s(z))))) <=> r(z, s(elem!1))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[5378])).
% 2.34/2.57 tff(11062,plain,
% 2.34/2.57 ((~r(z, s(s(s(s(z)))))) <=> (~r(z, s(elem!1)))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[11061])).
% 2.34/2.57 tff(11063,plain,
% 2.34/2.57 (~(elem!1 = s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[11052, 1114, 267, 216, 171])).
% 2.34/2.57 tff(11064,plain,
% 2.34/2.57 (b(elem!1, s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[214, 11063, 8759])).
% 2.34/2.57 tff(11065,plain,
% 2.34/2.57 (r(s(elem!1), elem!1)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[5548, 1673, 2593])).
% 2.34/2.57 tff(11066,plain,
% 2.34/2.57 (~r(z, s(elem!1))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[5525, 183, 267, 11065])).
% 2.34/2.57 tff(11067,plain,
% 2.34/2.57 (b(z, s(elem!1))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[2561, 11066])).
% 2.34/2.57 tff(11068,plain,
% 2.34/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), elem!1)))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(11069,plain,
% 2.34/2.57 (((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), elem!1)))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(11070,plain,
% 2.34/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), elem!1))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[11069])).
% 2.34/2.57 tff(11071,plain,
% 2.34/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), elem!1)))),
% 2.34/2.57 inference(transitivity,[status(thm)],[11070, 11068])).
% 2.34/2.57 tff(11072,plain,
% 2.34/2.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.34/2.57 inference(quant_inst,[status(thm)],[])).
% 2.34/2.57 tff(11073,plain,
% 2.34/2.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), elem!1))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[11072, 11071])).
% 2.34/2.57 tff(11074,plain,
% 2.34/2.57 (~r(s(s(elem!1)), s(elem!1))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[11073, 183, 216, 11065])).
% 2.34/2.57 tff(11075,plain,
% 2.34/2.57 (b(s(s(elem!1)), s(elem!1))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[5644, 11074, 5641])).
% 2.34/2.57 tff(11076,plain,
% 2.34/2.57 (~(s(elem!1) = s(s(elem!1)))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[6946, 5641])).
% 2.34/2.57 tff(11077,plain,
% 2.34/2.57 (~r(s(elem!1), s(s(elem!1)))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[373, 183, 216, 11065])).
% 2.34/2.57 tff(11078,plain,
% 2.34/2.57 (b(s(elem!1), s(s(elem!1)))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[5561, 47, 11077, 11076])).
% 2.34/2.57 tff(11079,plain,
% 2.34/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(11080,plain,
% 2.34/2.57 (((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(11081,plain,
% 2.34/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1)))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[11080])).
% 2.34/2.57 tff(11082,plain,
% 2.34/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))))),
% 2.34/2.57 inference(transitivity,[status(thm)],[11081, 11079])).
% 2.34/2.57 tff(11083,plain,
% 2.34/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z)))),
% 2.34/2.57 inference(quant_inst,[status(thm)],[])).
% 2.34/2.57 tff(11084,plain,
% 2.34/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1)))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[11083, 11082])).
% 2.34/2.57 tff(11085,plain,
% 2.34/2.57 ($false),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[11084, 246, 10617, 11078, 11075, 11067])).
% 2.34/2.57 tff(11086,plain,((~(s(s(s(z))) = elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.57 tff(11087,plain,
% 2.34/2.57 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[11086, 1673, 267, 216])).
% 2.34/2.57 tff(11088,plain,
% 2.34/2.57 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[1702, 11087])).
% 2.34/2.57 tff(11089,plain,
% 2.34/2.57 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), elem!1)),
% 2.34/2.57 inference(monotonicity,[status(thm)],[1673])).
% 2.34/2.57 tff(11090,plain,
% 2.34/2.57 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.57 inference(symmetry,[status(thm)],[11089])).
% 2.34/2.57 tff(11091,plain,
% 2.34/2.57 ((~b(s(s(s(s(z)))), elem!1)) <=> (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[11090])).
% 2.34/2.57 tff(11092,plain,
% 2.34/2.57 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[9825, 11091])).
% 2.34/2.57 tff(11093,plain,
% 2.34/2.57 ($false),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[1833, 11092])).
% 2.34/2.57 tff(11094,plain,((~(s(s(s(z))) = elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | b(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.57 tff(11095,plain,
% 2.34/2.57 (b(s(s(s(s(z)))), elem!1)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[11094, 11088, 1673])).
% 2.34/2.57 tff(11096,plain,
% 2.34/2.57 (~b(s(s(s(s(z)))), s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[9050, 11095, 11064, 1044])).
% 2.34/2.57 tff(11097,plain,
% 2.34/2.57 (r(s(s(s(s(z)))), s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[6103, 11096])).
% 2.34/2.57 tff(11098,plain,
% 2.34/2.57 (~r(z, s(s(s(s(z)))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[9071, 11097, 171])).
% 2.34/2.57 tff(11099,plain,
% 2.34/2.57 (~r(z, s(elem!1))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[11098, 11062])).
% 2.34/2.57 tff(11100,plain,
% 2.34/2.57 (b(z, s(elem!1))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[2561, 11099])).
% 2.34/2.57 tff(11101,plain,
% 2.34/2.57 (b(s(elem!1), elem!1)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[5677, 11088, 1673])).
% 2.34/2.57 tff(11102,plain,
% 2.34/2.57 (b(s(s(s(s(z)))), z) <=> b(s(elem!1), z)),
% 2.34/2.57 inference(monotonicity,[status(thm)],[5378])).
% 2.34/2.57 tff(11103,plain,
% 2.34/2.57 (~r(s(s(s(s(z)))), z)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[9423, 11097, 1114])).
% 2.34/2.57 tff(11104,plain,
% 2.34/2.57 (b(s(s(s(s(z)))), z)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[6040, 11103])).
% 2.34/2.57 tff(11105,plain,
% 2.34/2.57 (b(s(elem!1), z)),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[11104, 11102])).
% 2.34/2.57 tff(11106,plain,
% 2.34/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(11107,plain,
% 2.34/2.57 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(11108,plain,
% 2.34/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[11107])).
% 2.34/2.57 tff(11109,plain,
% 2.34/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))),
% 2.34/2.57 inference(transitivity,[status(thm)],[11108, 11106])).
% 2.34/2.57 tff(11110,plain,
% 2.34/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.34/2.57 inference(quant_inst,[status(thm)],[])).
% 2.34/2.57 tff(11111,plain,
% 2.34/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[11110, 11109])).
% 2.34/2.57 tff(11112,plain,
% 2.34/2.57 (~b(s(s(elem!1)), s(elem!1))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[11111, 246, 10617, 11105, 11101, 11100])).
% 2.34/2.57 tff(11113,plain,
% 2.34/2.57 (r(s(s(elem!1)), s(elem!1))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[5644, 11112, 5641])).
% 2.34/2.57 tff(11114,plain,
% 2.34/2.57 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(elem!1 = s(elem!1)))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[5628])).
% 2.34/2.57 tff(11115,plain,
% 2.34/2.57 (~(elem!1 = s(elem!1))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[5633, 11114])).
% 2.34/2.57 tff(11116,plain,
% 2.34/2.57 (~r(elem!1, s(elem!1))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[10769, 11113, 216])).
% 2.34/2.57 tff(11117,plain,
% 2.34/2.57 (b(elem!1, s(elem!1))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[2864, 11116, 11115])).
% 2.34/2.57 tff(11118,plain,
% 2.34/2.57 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[1551, 959, 216])).
% 2.34/2.57 tff(11119,plain,
% 2.34/2.57 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[86, 11118, 69])).
% 2.34/2.57 tff(11120,plain,
% 2.34/2.57 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[1959, 959, 1951])).
% 2.34/2.57 tff(11121,plain,
% 2.34/2.57 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[1795, 11120, 3410])).
% 2.34/2.57 tff(11122,plain,
% 2.34/2.57 ($false),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[5277, 11121, 11119, 1200, 1574])).
% 2.34/2.58 tff(11123,plain,((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (s(s(s(s(s(elem!1))))) = s(elem!1)) | (s(s(s(s(s(elem!1))))) = elem!1) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.58 tff(11124,plain,
% 2.34/2.58 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[11123, 11101, 11117, 5650, 7042, 11113, 216])).
% 2.34/2.58 tff(11125,plain,
% 2.34/2.58 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[1557, 11124, 5624])).
% 2.34/2.58 tff(11126,plain,
% 2.34/2.58 ((s(z) = s(elem!1)) <=> (s(z) = s(s(s(s(z)))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[5379])).
% 2.34/2.58 tff(11127,plain,
% 2.34/2.58 ((s(z) = s(elem!1)) <=> (s(s(s(s(z)))) = s(z))),
% 2.34/2.58 inference(transitivity,[status(thm)],[11126, 5787])).
% 2.34/2.58 tff(11128,plain,
% 2.34/2.58 ((s(s(s(s(z)))) = s(z)) <=> (s(z) = s(elem!1))),
% 2.34/2.58 inference(symmetry,[status(thm)],[11127])).
% 2.34/2.58 tff(11129,plain,
% 2.34/2.58 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(z) = s(elem!1)))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[11128])).
% 2.34/2.58 tff(11130,plain,
% 2.34/2.58 (~(s(z) = s(elem!1))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[1713, 11129])).
% 2.34/2.58 tff(11131,plain,
% 2.34/2.58 (~b(s(z), s(elem!1))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[8802, 246, 1044, 11064, 11101])).
% 2.34/2.58 tff(11132,plain,
% 2.34/2.58 ((s(z) = s(elem!1)) | r(s(z), s(elem!1))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[2973, 47, 11131])).
% 2.34/2.58 tff(11133,plain,
% 2.34/2.58 (r(s(z), s(elem!1))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[11132, 11130])).
% 2.34/2.58 tff(11134,plain,
% 2.34/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(11135,plain,
% 2.34/2.58 (((~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(11136,plain,
% 2.34/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1)))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[11135])).
% 2.34/2.58 tff(11137,plain,
% 2.34/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))))),
% 2.34/2.58 inference(transitivity,[status(thm)],[11136, 11134])).
% 2.34/2.58 tff(11138,plain,
% 2.34/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))),
% 2.34/2.58 inference(quant_inst,[status(thm)],[])).
% 2.34/2.58 tff(11139,plain,
% 2.34/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1)))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[11138, 11137])).
% 2.34/2.58 tff(11140,plain,
% 2.34/2.58 (~r(s(s(elem!1)), s(z))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[11139, 183, 1114, 11113, 11133])).
% 2.34/2.58 tff(11141,plain,
% 2.34/2.58 (b(s(s(elem!1)), s(z))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[197, 11140])).
% 2.34/2.58 tff(11142,plain,
% 2.34/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(11143,plain,
% 2.34/2.58 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(11144,plain,
% 2.34/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[11143])).
% 2.34/2.58 tff(11145,plain,
% 2.34/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.34/2.58 inference(transitivity,[status(thm)],[11144, 11142])).
% 2.34/2.58 tff(11146,plain,
% 2.34/2.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.34/2.58 inference(quant_inst,[status(thm)],[])).
% 2.34/2.58 tff(11147,plain,
% 2.34/2.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[11146, 11145])).
% 2.34/2.58 tff(11148,plain,
% 2.34/2.58 ($false),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[11147, 246, 201, 1100, 1099, 946, 9221])).
% 2.34/2.58 tff(11149,plain,((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.58 tff(11150,plain,
% 2.34/2.58 (~b(s(s(s(s(s(elem!1))))), z)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[11149, 11141, 10617, 10619, 11125])).
% 2.34/2.58 tff(11151,plain,
% 2.34/2.58 (r(s(s(s(s(s(elem!1))))), z)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[1601, 11150])).
% 2.34/2.58 tff(11152,plain,
% 2.34/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(11153,plain,
% 2.34/2.58 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(11154,plain,
% 2.34/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1)))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[11153])).
% 2.34/2.58 tff(11155,plain,
% 2.34/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))))),
% 2.34/2.58 inference(transitivity,[status(thm)],[11154, 11152])).
% 2.34/2.58 tff(11156,plain,
% 2.34/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))))),
% 2.34/2.58 inference(quant_inst,[status(thm)],[])).
% 2.34/2.58 tff(11157,plain,
% 2.34/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1)))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[11156, 11155])).
% 2.34/2.58 tff(11158,plain,
% 2.34/2.58 (~r(s(z), s(s(elem!1)))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[11157, 183, 11113, 11133])).
% 2.34/2.58 tff(11159,plain,
% 2.34/2.58 (b(s(z), s(s(elem!1)))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[233, 11158])).
% 2.34/2.58 tff(11160,plain,
% 2.34/2.58 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[10981, 11125, 10619, 10617, 11159])).
% 2.34/2.58 tff(11161,plain,
% 2.34/2.58 (r(s(s(s(s(s(elem!1))))), s(z))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[6447, 11160])).
% 2.34/2.58 tff(11162,plain,
% 2.34/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(11163,plain,
% 2.34/2.58 (((~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(11164,plain,
% 2.34/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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)))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[11163])).
% 2.34/2.58 tff(11165,plain,
% 2.34/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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))))),
% 2.34/2.58 inference(transitivity,[status(thm)],[11164, 11162])).
% 2.34/2.58 tff(11166,plain,
% 2.34/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 2.34/2.58 inference(quant_inst,[status(thm)],[])).
% 2.34/2.58 tff(11167,plain,
% 2.34/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z)))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[11166, 11165])).
% 2.34/2.58 tff(11168,plain,
% 2.34/2.58 ($false),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[11167, 183, 1114, 11161, 11151])).
% 2.34/2.58 tff(11169,plain,((~(s(s(s(z))) = elem!1)) | (~r(s(z), z)) | (~r(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~r(z, s(z))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.58 tff(11170,plain,
% 2.34/2.58 (~(s(s(s(z))) = elem!1)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[11169, 1114, 10595, 11060, 170, 5365])).
% 2.34/2.58 tff(11171,plain,
% 2.34/2.58 (b(s(s(s(z))), elem!1)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[647, 11170, 11059])).
% 2.34/2.58 tff(11172,plain,
% 2.34/2.58 (b(elem!1, s(z))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[214, 11053, 6376])).
% 2.34/2.58 tff(11173,plain,
% 2.34/2.58 (~b(s(s(s(z))), s(z))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[7339, 246, 11060, 11172, 11171])).
% 2.34/2.58 tff(11174,plain,
% 2.34/2.58 (r(s(s(s(z))), s(z))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[52, 11173])).
% 2.34/2.58 tff(11175,plain,
% 2.34/2.58 (~(elem!1 = s(s(s(z))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[3013, 11170])).
% 2.34/2.58 tff(11176,plain,
% 2.34/2.58 (~(s(z) = elem!1)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[9, 11063])).
% 2.34/2.58 tff(11177,plain,
% 2.34/2.58 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[5804, 11176])).
% 2.34/2.58 tff(11178,plain,
% 2.34/2.58 (~r(s(s(s(z))), elem!1)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[11058, 11177, 216, 267])).
% 2.34/2.58 tff(11179,plain,
% 2.34/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(11180,plain,
% 2.34/2.58 (((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(11181,plain,
% 2.34/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[11180])).
% 2.34/2.58 tff(11182,plain,
% 2.34/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 2.34/2.58 inference(transitivity,[status(thm)],[11181, 11179])).
% 2.34/2.58 tff(11183,plain,
% 2.34/2.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 2.34/2.58 inference(quant_inst,[status(thm)],[])).
% 2.34/2.58 tff(11184,plain,
% 2.34/2.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[11183, 11182])).
% 2.34/2.58 tff(11185,plain,
% 2.34/2.58 ($false),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[11184, 246, 1051, 3697, 9821, 9823])).
% 2.34/2.58 tff(11186,plain,((~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~r(z, elem!1)) | (~r(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.58 tff(11187,plain,
% 2.34/2.58 (~b(s(s(s(z))), elem!1)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[11186, 1051, 267, 171, 1044, 11064])).
% 2.34/2.58 tff(11188,plain,
% 2.34/2.58 (s(s(s(z))) = elem!1),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[647, 11187, 11178])).
% 2.34/2.58 tff(11189,plain,
% 2.34/2.58 (~(s(s(elem!1)) = elem!1)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[5385, 11188])).
% 2.34/2.58 tff(11190,plain,
% 2.34/2.58 (~(s(s(elem!1)) = s(elem!1))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[5640, 11189])).
% 2.34/2.58 tff(11191,plain,
% 2.34/2.58 (s(s(s(s(z)))) = s(elem!1)),
% 2.34/2.58 inference(monotonicity,[status(thm)],[11188])).
% 2.34/2.58 tff(11192,plain,
% 2.34/2.58 (r(z, s(s(s(s(z))))) <=> r(z, s(elem!1))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[11191])).
% 2.34/2.58 tff(11193,plain,
% 2.34/2.58 ((~r(z, s(s(s(s(z)))))) <=> (~r(z, s(elem!1)))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[11192])).
% 2.34/2.58 tff(11194,plain,
% 2.34/2.58 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[11086, 11188, 267, 216])).
% 2.34/2.58 tff(11195,plain,
% 2.34/2.58 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[1702, 11194])).
% 2.34/2.58 tff(11196,plain,
% 2.34/2.58 (b(s(s(s(s(z)))), elem!1)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[11094, 11195, 11188])).
% 2.34/2.58 tff(11197,plain,
% 2.34/2.58 (~b(s(s(s(s(z)))), s(z))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[9050, 11196, 11064, 1044])).
% 2.34/2.58 tff(11198,plain,
% 2.34/2.58 (r(s(s(s(s(z)))), s(z))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[6103, 11197])).
% 2.34/2.58 tff(11199,plain,
% 2.34/2.58 (~r(z, s(s(s(s(z)))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[9071, 11198, 171])).
% 2.34/2.58 tff(11200,plain,
% 2.34/2.58 (~r(z, s(elem!1))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[11199, 11193])).
% 2.34/2.58 tff(11201,plain,
% 2.34/2.58 (b(z, s(elem!1))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[2561, 11200])).
% 2.34/2.58 tff(11202,plain,
% 2.34/2.58 (b(s(elem!1), elem!1)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[5677, 11195, 11188])).
% 2.34/2.58 tff(11203,plain,
% 2.34/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(11204,plain,
% 2.34/2.58 (((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1))))) <=> ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(11205,plain,
% 2.34/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1)))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[11204])).
% 2.34/2.58 tff(11206,plain,
% 2.34/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))))),
% 2.34/2.58 inference(transitivity,[status(thm)],[11205, 11203])).
% 2.34/2.58 tff(11207,plain,
% 2.34/2.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))),
% 2.34/2.58 inference(quant_inst,[status(thm)],[])).
% 2.34/2.58 tff(11208,plain,
% 2.34/2.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1)))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[11207, 11206])).
% 2.34/2.58 tff(11209,plain,
% 2.34/2.58 (~b(s(s(elem!1)), s(elem!1))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[11208, 246, 1051, 10617, 10619, 11202, 11201])).
% 2.34/2.58 tff(11210,plain,
% 2.34/2.58 (r(s(s(elem!1)), s(elem!1))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[5644, 11209, 11190])).
% 2.34/2.58 tff(11211,plain,
% 2.34/2.58 ((s(s(s(s(z)))) = elem!1) <=> (s(elem!1) = elem!1)),
% 2.34/2.58 inference(monotonicity,[status(thm)],[11191])).
% 2.34/2.58 tff(11212,plain,
% 2.34/2.58 ((s(s(s(s(z)))) = elem!1) <=> (elem!1 = s(elem!1))),
% 2.34/2.58 inference(transitivity,[status(thm)],[11211, 2825])).
% 2.34/2.58 tff(11213,plain,
% 2.34/2.58 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(elem!1 = s(elem!1)))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[11212])).
% 2.34/2.58 tff(11214,plain,
% 2.34/2.58 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(z)))) = elem!1)),
% 2.34/2.58 inference(monotonicity,[status(thm)],[11188])).
% 2.34/2.58 tff(11215,plain,
% 2.34/2.58 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[11214])).
% 2.34/2.58 tff(11216,plain,
% 2.34/2.58 (~(s(s(s(s(z)))) = elem!1)),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[1697, 11215])).
% 2.34/2.58 tff(11217,plain,
% 2.34/2.58 (~(elem!1 = s(elem!1))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[11216, 11213])).
% 2.34/2.58 tff(11218,plain,
% 2.34/2.58 (b(s(s(s(s(z)))), z) <=> b(s(elem!1), z)),
% 2.34/2.58 inference(monotonicity,[status(thm)],[11191])).
% 2.34/2.58 tff(11219,plain,
% 2.34/2.58 (~r(s(s(s(s(z)))), z)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[9423, 11198, 1114])).
% 2.34/2.58 tff(11220,plain,
% 2.34/2.58 (b(s(s(s(s(z)))), z)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[6040, 11219])).
% 2.34/2.58 tff(11221,plain,
% 2.34/2.58 (b(s(elem!1), z)),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[11220, 11218])).
% 2.34/2.58 tff(11222,plain,
% 2.34/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(11223,plain,
% 2.34/2.58 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(11224,plain,
% 2.34/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[11223])).
% 2.34/2.59 tff(11225,plain,
% 2.34/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))),
% 2.34/2.59 inference(transitivity,[status(thm)],[11224, 11222])).
% 2.34/2.59 tff(11226,plain,
% 2.34/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))),
% 2.34/2.59 inference(quant_inst,[status(thm)],[])).
% 2.34/2.59 tff(11227,plain,
% 2.34/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z))),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[11226, 11225])).
% 2.34/2.59 tff(11228,plain,
% 2.34/2.59 (~b(elem!1, s(elem!1))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[11227, 246, 1051, 11221, 11202, 11201])).
% 2.34/2.59 tff(11229,plain,
% 2.34/2.59 (r(elem!1, s(elem!1))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[2864, 11228, 11217])).
% 2.34/2.59 tff(11230,plain,
% 2.34/2.59 ($false),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[10769, 11229, 11210, 216])).
% 2.34/2.59 tff(11231,plain,((~b(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(z))) | (~r(s(z), z)) | (~b(s(z), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.59 tff(11232,plain,
% 2.34/2.59 (~b(elem!1, z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[11231, 1114, 170, 10595, 11060, 5365])).
% 2.34/2.59 tff(11233,plain,
% 2.34/2.59 (r(elem!1, z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[1143, 11232, 5701])).
% 2.34/2.59 tff(11234,plain,
% 2.34/2.59 (~r(z, s(s(s(z))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[10064, 11170, 1114, 11172, 11233, 11175, 5365])).
% 2.34/2.59 tff(11235,plain,
% 2.34/2.59 (b(z, s(s(s(z))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[6165, 11234])).
% 2.34/2.59 tff(11236,plain,
% 2.34/2.59 (~r(s(s(elem!1)), s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[6468, 11174, 10599, 5365, 170, 11055])).
% 2.34/2.59 tff(11237,plain,
% 2.34/2.59 (b(s(s(elem!1)), s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[197, 11236])).
% 2.34/2.59 tff(11238,plain,
% 2.34/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(11239,plain,
% 2.34/2.59 (((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z)))))) <=> ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(11240,plain,
% 2.34/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[11239])).
% 2.34/2.59 tff(11241,plain,
% 2.34/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))),
% 2.34/2.59 inference(transitivity,[status(thm)],[11240, 11238])).
% 2.34/2.59 tff(11242,plain,
% 2.34/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))))),
% 2.34/2.59 inference(quant_inst,[status(thm)],[])).
% 2.34/2.59 tff(11243,plain,
% 2.34/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1))),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[11242, 11241])).
% 2.34/2.59 tff(11244,plain,
% 2.34/2.59 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[11243, 246, 11237, 11060, 10597, 11171, 11235])).
% 2.34/2.59 tff(11245,plain,
% 2.34/2.59 (r(s(s(s(z))), s(s(elem!1)))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[689, 11244, 11055])).
% 2.34/2.59 tff(11246,plain,
% 2.34/2.59 (~(s(s(elem!1)) = s(s(s(z))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[421, 11055])).
% 2.34/2.59 tff(11247,plain,
% 2.34/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(11248,plain,
% 2.34/2.59 (((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(11249,plain,
% 2.34/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[11248])).
% 2.34/2.59 tff(11250,plain,
% 2.34/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.34/2.59 inference(transitivity,[status(thm)],[11249, 11247])).
% 2.34/2.59 tff(11251,plain,
% 2.34/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 2.34/2.59 inference(quant_inst,[status(thm)],[])).
% 2.34/2.59 tff(11252,plain,
% 2.34/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[11251, 11250])).
% 2.34/2.59 tff(11253,plain,
% 2.34/2.59 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[11252, 246, 1044, 2001, 3697, 714])).
% 2.34/2.59 tff(11254,plain,
% 2.34/2.59 (r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[1626, 11253])).
% 2.34/2.59 tff(11255,plain,
% 2.34/2.59 (r(s(s(s(s(s(elem!1))))), s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[2311, 47, 331, 6932])).
% 2.34/2.59 tff(11256,plain,
% 2.34/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(11257,plain,
% 2.34/2.59 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(11258,plain,
% 2.34/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(z)))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[11257])).
% 2.34/2.59 tff(11259,plain,
% 2.34/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 2.34/2.59 inference(transitivity,[status(thm)],[11258, 11256])).
% 2.34/2.59 tff(11260,plain,
% 2.34/2.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 2.34/2.59 inference(quant_inst,[status(thm)],[])).
% 2.34/2.59 tff(11261,plain,
% 2.34/2.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(z)))),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[11260, 11259])).
% 2.34/2.59 tff(11262,plain,
% 2.34/2.59 ($false),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[11261, 183, 1114, 9854, 11255, 11254])).
% 2.34/2.59 tff(11263,plain,((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(z), z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.59 tff(11264,plain,
% 2.34/2.59 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[11263, 11171, 1114, 11172, 11060])).
% 2.34/2.59 tff(11265,plain,
% 2.34/2.59 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[6281, 11055])).
% 2.34/2.59 tff(11266,plain,
% 2.34/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(11267,plain,
% 2.34/2.59 (((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(11268,plain,
% 2.34/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[11267])).
% 2.34/2.59 tff(11269,plain,
% 2.34/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 2.34/2.59 inference(transitivity,[status(thm)],[11268, 11266])).
% 2.34/2.59 tff(11270,plain,
% 2.34/2.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))),
% 2.34/2.59 inference(quant_inst,[status(thm)],[])).
% 2.34/2.59 tff(11271,plain,
% 2.34/2.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[11270, 11269])).
% 2.34/2.59 tff(11272,plain,
% 2.34/2.59 (~r(s(s(s(z))), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[11271, 183, 171, 430])).
% 2.34/2.59 tff(11273,plain,
% 2.34/2.59 (b(s(s(s(z))), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[995, 11272])).
% 2.34/2.59 tff(11274,plain,
% 2.34/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(11275,plain,
% 2.34/2.59 (((~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z)))))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(11276,plain,
% 2.34/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[11275])).
% 2.34/2.59 tff(11277,plain,
% 2.34/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.34/2.59 inference(transitivity,[status(thm)],[11276, 11274])).
% 2.34/2.59 tff(11278,plain,
% 2.34/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.34/2.59 inference(quant_inst,[status(thm)],[])).
% 2.34/2.59 tff(11279,plain,
% 2.34/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[11278, 11277])).
% 2.34/2.59 tff(11280,plain,
% 2.34/2.59 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[11279, 246, 1100, 1099, 11273])).
% 2.34/2.59 tff(11281,plain,
% 2.34/2.59 (r(s(s(elem!1)), s(s(s(z))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[454, 11280, 8770])).
% 2.34/2.59 tff(11282,plain,
% 2.34/2.59 (~r(z, s(s(s(z))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[438, 171, 430])).
% 2.34/2.59 tff(11283,plain,
% 2.34/2.59 ((z = s(s(s(z)))) | b(z, s(s(s(z))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[2221, 47, 11282])).
% 2.34/2.59 tff(11284,plain,
% 2.34/2.59 (b(z, s(s(s(z))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[11283, 2218])).
% 2.34/2.59 tff(11285,plain,
% 2.34/2.59 (~b(elem!1, s(s(s(z))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[10503, 11284, 7030, 2246, 1833, 3697])).
% 2.34/2.59 tff(11286,plain,
% 2.34/2.59 (r(elem!1, s(s(s(z))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[470, 11285, 1675])).
% 2.34/2.59 tff(11287,plain,
% 2.34/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(11288,plain,
% 2.34/2.59 (((~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(11289,plain,
% 2.34/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[11288])).
% 2.34/2.59 tff(11290,plain,
% 2.34/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 2.34/2.59 inference(transitivity,[status(thm)],[11289, 11287])).
% 2.34/2.59 tff(11291,plain,
% 2.34/2.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)))),
% 2.34/2.59 inference(quant_inst,[status(thm)],[])).
% 2.34/2.59 tff(11292,plain,
% 2.34/2.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[11291, 11290])).
% 2.34/2.59 tff(11293,plain,
% 2.34/2.59 ($false),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[11292, 183, 2246, 216, 11286, 11281])).
% 2.34/2.59 tff(11294,plain,((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (elem!1 = s(s(s(z)))) | (~(s(s(s(s(s(elem!1))))) = elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (s(s(elem!1)) = s(s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.59 tff(11295,plain,
% 2.34/2.59 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[11294, 1833, 216, 2246, 171, 3697, 1675, 8770, 10617, 10619, 430])).
% 2.34/2.59 tff(11296,plain,
% 2.34/2.59 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[86, 11295, 82])).
% 2.34/2.59 tff(11297,plain,
% 2.34/2.59 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[1551, 11296, 216])).
% 2.34/2.59 tff(11298,plain,
% 2.34/2.59 (~r(s(s(s(s(s(elem!1))))), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[9392, 11296, 267])).
% 2.34/2.59 tff(11299,plain,
% 2.34/2.59 (b(s(s(s(s(s(elem!1))))), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[1601, 11298])).
% 2.34/2.59 tff(11300,plain,
% 2.34/2.59 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[11149, 11299, 10617, 10619, 201])).
% 2.34/2.59 tff(11301,plain,
% 2.34/2.59 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[1557, 11300, 11297])).
% 2.34/2.59 tff(11302,plain,
% 2.34/2.59 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(elem!1)))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[11301])).
% 2.34/2.59 tff(11303,plain,
% 2.34/2.59 (s(s(s(s(elem!1)))) = s(elem!1)),
% 2.34/2.59 inference(transitivity,[status(thm)],[326, 11302, 92])).
% 2.34/2.59 tff(11304,plain,
% 2.34/2.59 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(elem!1))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[11303])).
% 2.34/2.59 tff(11305,plain,
% 2.34/2.59 (inj_0(s(elem!1)) = inj_0(s(s(s(s(elem!1)))))),
% 2.34/2.59 inference(symmetry,[status(thm)],[11304])).
% 2.34/2.59 tff(11306,plain,
% 2.34/2.59 (elem!1 = s(s(s(elem!1)))),
% 2.34/2.59 inference(transitivity,[status(thm)],[3154, 11305, 351])).
% 2.34/2.59 tff(11307,plain,
% 2.34/2.59 (~b(s(s(s(s(z)))), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[9844, 1833, 4651, 6466])).
% 2.34/2.59 tff(11308,plain,
% 2.34/2.59 (r(s(s(s(s(z)))), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[6040, 11307])).
% 2.34/2.59 tff(11309,plain,
% 2.34/2.59 (s(s(s(s(z)))) = elem!1),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[9970, 11308, 3697, 2246, 1833, 267])).
% 2.34/2.59 tff(11310,plain,
% 2.34/2.59 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = elem!1)),
% 2.34/2.59 inference(monotonicity,[status(thm)],[11309])).
% 2.34/2.59 tff(11311,plain,
% 2.34/2.59 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(elem!1))))),
% 2.34/2.59 inference(transitivity,[status(thm)],[11310, 10677])).
% 2.34/2.59 tff(11312,plain,
% 2.34/2.59 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[11311])).
% 2.34/2.59 tff(11313,plain,
% 2.34/2.59 (~(elem!1 = s(s(s(elem!1))))),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[6330, 11312])).
% 2.34/2.59 tff(11314,plain,
% 2.34/2.59 ($false),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[11313, 11306])).
% 2.34/2.59 tff(11315,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | b(s(s(s(s(s(elem!1))))), elem!1) | (~b(z, s(s(s(z))))) | (~r(z, s(z))) | (elem!1 = s(s(s(z)))) | (s(s(elem!1)) = s(s(s(z)))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.59 tff(11316,plain,
% 2.34/2.59 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[11315, 11265, 11237, 11171, 11233, 5365, 10595, 11264, 11235, 170, 11175, 11246, 11174])).
% 2.44/2.60 tff(11317,plain,
% 2.44/2.60 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[1702, 11316])).
% 2.44/2.60 tff(11318,plain,
% 2.44/2.60 (~r(s(s(s(s(z)))), s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[8491, 11317, 11174])).
% 2.44/2.60 tff(11319,plain,
% 2.44/2.60 (b(s(s(s(s(z)))), s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[6103, 11318])).
% 2.44/2.60 tff(11320,plain,
% 2.44/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(11321,plain,
% 2.44/2.60 (((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(11322,plain,
% 2.44/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[11321])).
% 2.44/2.60 tff(11323,plain,
% 2.44/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.44/2.60 inference(transitivity,[status(thm)],[11322, 11320])).
% 2.44/2.60 tff(11324,plain,
% 2.44/2.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.44/2.60 inference(quant_inst,[status(thm)],[])).
% 2.44/2.60 tff(11325,plain,
% 2.44/2.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[11324, 11323])).
% 2.44/2.60 tff(11326,plain,
% 2.44/2.60 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[11325, 246, 11237, 11060, 11172, 11319])).
% 2.44/2.60 tff(11327,plain,
% 2.44/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(11328,plain,
% 2.44/2.60 (((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(11329,plain,
% 2.44/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[11328])).
% 2.44/2.60 tff(11330,plain,
% 2.44/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.44/2.60 inference(transitivity,[status(thm)],[11329, 11327])).
% 2.44/2.60 tff(11331,plain,
% 2.44/2.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(elem!1)))))),
% 2.44/2.60 inference(quant_inst,[status(thm)],[])).
% 2.44/2.60 tff(11332,plain,
% 2.44/2.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[11331, 11330])).
% 2.44/2.60 tff(11333,plain,
% 2.44/2.60 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[11332, 246, 11237, 11172, 10597, 11171, 11235])).
% 2.44/2.60 tff(11334,plain,
% 2.44/2.60 (r(s(s(elem!1)), s(s(s(z))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[454, 11333, 11246])).
% 2.44/2.60 tff(11335,plain,
% 2.44/2.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(11336,plain,
% 2.44/2.60 (((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(11337,plain,
% 2.44/2.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[11336])).
% 2.44/2.60 tff(11338,plain,
% 2.44/2.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.44/2.60 inference(transitivity,[status(thm)],[11337, 11335])).
% 2.44/2.60 tff(11339,plain,
% 2.44/2.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.44/2.60 inference(quant_inst,[status(thm)],[])).
% 2.44/2.60 tff(11340,plain,
% 2.44/2.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[11339, 11338])).
% 2.44/2.60 tff(11341,plain,
% 2.44/2.60 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[11340, 183, 10595, 11334, 11317])).
% 2.44/2.60 tff(11342,plain,
% 2.44/2.60 ((s(s(s(s(z)))) = s(s(elem!1))) | b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[6521, 47, 11341])).
% 2.44/2.60 tff(11343,plain,
% 2.44/2.60 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[11342, 11326])).
% 2.44/2.60 tff(11344,plain,
% 2.44/2.60 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[11343])).
% 2.44/2.60 tff(11345,plain,
% 2.44/2.60 (s(s(s(z))) = s(elem!1)),
% 2.44/2.60 inference(transitivity,[status(thm)],[1492, 11344, 92])).
% 2.44/2.60 tff(11346,plain,
% 2.44/2.60 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(elem!1))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[11345])).
% 2.44/2.60 tff(11347,plain,
% 2.44/2.60 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(z))))),
% 2.44/2.60 inference(symmetry,[status(thm)],[11346])).
% 2.44/2.60 tff(11348,plain,
% 2.44/2.60 ((elem!1 = s(s(s(z)))) <=> (elem!1 = s(elem!1))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[11345])).
% 2.44/2.60 tff(11349,plain,
% 2.44/2.60 ((~(elem!1 = s(s(s(z))))) <=> (~(elem!1 = s(elem!1)))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[11348])).
% 2.44/2.60 tff(11350,plain,
% 2.44/2.60 (~(elem!1 = s(elem!1))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[11175, 11349])).
% 2.44/2.60 tff(11351,plain,
% 2.44/2.60 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(z)))))),
% 2.44/2.60 inference(symmetry,[status(thm)],[11344])).
% 2.44/2.60 tff(11352,plain,
% 2.44/2.60 (s(elem!1) = s(s(s(z)))),
% 2.44/2.60 inference(transitivity,[status(thm)],[108, 11351, 1491])).
% 2.44/2.60 tff(11353,plain,
% 2.44/2.60 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[11352])).
% 2.44/2.60 tff(11354,plain,
% 2.44/2.60 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.44/2.60 inference(symmetry,[status(thm)],[11353])).
% 2.44/2.60 tff(11355,plain,
% 2.44/2.60 (r(s(elem!1), s(s(elem!1)))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[11245, 11354])).
% 2.44/2.60 tff(11356,plain,
% 2.44/2.60 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[11345])).
% 2.44/2.60 tff(11357,plain,
% 2.44/2.60 (s(s(z)) = elem!1),
% 2.44/2.60 inference(transitivity,[status(thm)],[25, 11356, 343])).
% 2.44/2.60 tff(11358,plain,
% 2.44/2.60 (r(s(s(z)), s(s(s(s(z))))) <=> r(elem!1, s(s(elem!1)))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[11357, 11343])).
% 2.44/2.60 tff(11359,plain,
% 2.44/2.60 (~b(s(z), s(s(s(z))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[9852, 246, 11060, 11172, 11171])).
% 2.44/2.60 tff(11360,plain,
% 2.44/2.60 (r(s(z), s(s(s(z))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[1291, 11359])).
% 2.44/2.60 tff(11361,plain,
% 2.44/2.60 (~r(s(z), s(s(s(s(z)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[6088, 183, 11360, 11317])).
% 2.44/2.60 tff(11362,plain,
% 2.44/2.60 ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[6092, 47, 11361])).
% 2.44/2.60 tff(11363,plain,
% 2.44/2.60 (b(s(z), s(s(s(s(z)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[11362, 5790])).
% 2.44/2.60 tff(11364,plain,
% 2.44/2.60 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[9907, 11363, 170, 11060, 11319, 11174])).
% 2.44/2.60 tff(11365,plain,
% 2.44/2.60 (r(s(s(z)), s(s(s(s(z)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[1531, 11364])).
% 2.44/2.60 tff(11366,plain,
% 2.44/2.60 (r(elem!1, s(s(elem!1)))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[11365, 11358])).
% 2.44/2.60 tff(11367,plain,
% 2.44/2.60 (~r(elem!1, s(elem!1))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[1215, 183, 11366, 11355])).
% 2.44/2.60 tff(11368,plain,
% 2.44/2.60 (b(elem!1, s(elem!1))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[2864, 11367, 11350])).
% 2.44/2.60 tff(11369,plain,
% 2.44/2.60 (b(elem!1, s(s(s(z))))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[11368, 11347])).
% 2.44/2.60 tff(11370,plain,
% 2.44/2.60 (~r(s(s(s(z))), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[6464, 183, 5365, 170, 11174])).
% 2.44/2.60 tff(11371,plain,
% 2.44/2.60 (b(s(s(s(z))), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[995, 11370])).
% 2.44/2.60 tff(11372,plain,
% 2.44/2.60 ((s(s(z)) = s(s(s(s(z))))) <=> (elem!1 = s(s(elem!1)))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[11357, 11343])).
% 2.44/2.60 tff(11373,plain,
% 2.44/2.60 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(elem!1)) = elem!1)),
% 2.44/2.60 inference(transitivity,[status(thm)],[11372, 133])).
% 2.44/2.60 tff(11374,plain,
% 2.44/2.60 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(elem!1)) = elem!1))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[11373])).
% 2.44/2.60 tff(11375,plain,
% 2.44/2.60 (~(s(s(elem!1)) = elem!1)),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[1526, 11374])).
% 2.44/2.60 tff(11376,plain,
% 2.44/2.60 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[86, 69, 82])).
% 2.44/2.60 tff(11377,plain,
% 2.44/2.60 (~r(s(s(s(s(s(elem!1))))), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[5470, 183, 267, 11376])).
% 2.44/2.60 tff(11378,plain,
% 2.44/2.60 (b(s(s(s(s(s(elem!1))))), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[1601, 11377])).
% 2.44/2.60 tff(11379,plain,
% 2.44/2.60 (~r(s(s(elem!1)), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[1581, 183, 267, 216])).
% 2.44/2.60 tff(11380,plain,
% 2.44/2.60 (b(s(s(elem!1)), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[523, 11379])).
% 2.44/2.60 tff(11381,plain,
% 2.44/2.60 (((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(11382,plain,
% 2.44/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[11381])).
% 2.44/2.60 tff(11383,plain,
% 2.44/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.44/2.60 inference(transitivity,[status(thm)],[11382, 4085])).
% 2.44/2.60 tff(11384,plain,
% 2.44/2.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.44/2.60 inference(quant_inst,[status(thm)],[])).
% 2.44/2.60 tff(11385,plain,
% 2.44/2.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[11384, 11383])).
% 2.44/2.60 tff(11386,plain,
% 2.44/2.60 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[11385, 246, 11380, 10619, 11378])).
% 2.44/2.60 tff(11387,plain,
% 2.44/2.60 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[339, 183, 216, 11376])).
% 2.44/2.60 tff(11388,plain,
% 2.44/2.60 ((s(s(s(s(s(elem!1))))) = s(s(elem!1))) | b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[361, 47, 11387])).
% 2.44/2.60 tff(11389,plain,
% 2.44/2.60 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[11388, 11386])).
% 2.44/2.60 tff(11390,plain,
% 2.44/2.60 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(elem!1)))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[11389])).
% 2.44/2.60 tff(11391,plain,
% 2.44/2.60 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(elem!1))))))),
% 2.44/2.60 inference(symmetry,[status(thm)],[11390])).
% 2.44/2.60 tff(11392,plain,
% 2.44/2.60 (s(elem!1) = s(s(s(s(elem!1))))),
% 2.44/2.60 inference(transitivity,[status(thm)],[108, 11391, 325])).
% 2.44/2.60 tff(11393,plain,
% 2.44/2.60 (inj_0(s(elem!1)) = inj_0(s(s(s(s(elem!1)))))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[11392])).
% 2.44/2.60 tff(11394,plain,
% 2.44/2.60 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(elem!1))),
% 2.44/2.60 inference(symmetry,[status(thm)],[11393])).
% 2.44/2.60 tff(11395,plain,
% 2.44/2.60 (s(s(s(elem!1))) = elem!1),
% 2.44/2.60 inference(transitivity,[status(thm)],[352, 11394, 343])).
% 2.44/2.60 tff(11396,plain,
% 2.44/2.60 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), elem!1)),
% 2.44/2.60 inference(monotonicity,[status(thm)],[11395])).
% 2.44/2.60 tff(11397,plain,
% 2.44/2.60 (b(s(z), elem!1) <=> b(s(z), s(s(s(elem!1))))),
% 2.44/2.60 inference(symmetry,[status(thm)],[11396])).
% 2.44/2.60 tff(11398,plain,
% 2.44/2.60 (b(s(z), s(s(s(elem!1))))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[1044, 11397])).
% 2.44/2.60 tff(11399,plain,
% 2.44/2.60 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 2.44/2.60 inference(symmetry,[status(thm)],[11389])).
% 2.44/2.60 tff(11400,plain,
% 2.44/2.60 ((s(elem!1) = s(s(elem!1))) <=> (s(elem!1) = s(s(s(s(s(elem!1))))))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[11399])).
% 2.44/2.60 tff(11401,plain,
% 2.44/2.60 ((s(elem!1) = s(s(elem!1))) <=> (s(s(s(s(s(elem!1))))) = s(elem!1))),
% 2.44/2.60 inference(transitivity,[status(thm)],[11400, 1800])).
% 2.44/2.60 tff(11402,plain,
% 2.44/2.60 ((s(s(s(s(s(elem!1))))) = s(elem!1)) <=> (s(elem!1) = s(s(elem!1)))),
% 2.44/2.60 inference(symmetry,[status(thm)],[11401])).
% 2.44/2.60 tff(11403,plain,
% 2.44/2.60 ((~(s(s(s(s(s(elem!1))))) = s(elem!1))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[11402])).
% 2.44/2.60 tff(11404,plain,
% 2.44/2.60 (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[11389])).
% 2.44/2.60 tff(11405,plain,
% 2.44/2.60 (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(elem!1))))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[11404])).
% 2.44/2.60 tff(11406,plain,
% 2.44/2.60 (s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(elem!1)))))))),
% 2.44/2.60 inference(symmetry,[status(thm)],[11405])).
% 2.44/2.60 tff(11407,plain,
% 2.44/2.60 (s(elem!1) = s(s(s(s(s(s(s(elem!1)))))))),
% 2.44/2.60 inference(transitivity,[status(thm)],[108, 11391, 325, 11406])).
% 2.44/2.60 tff(11408,plain,
% 2.44/2.60 ((s(s(s(s(s(elem!1))))) = s(elem!1)) <=> (s(s(elem!1)) = s(s(s(s(s(s(s(elem!1))))))))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[11389, 11407])).
% 2.44/2.60 tff(11409,plain,
% 2.44/2.60 ((s(s(elem!1)) = s(s(s(s(s(s(s(elem!1)))))))) <=> (s(s(s(s(s(elem!1))))) = s(elem!1))),
% 2.44/2.60 inference(symmetry,[status(thm)],[11408])).
% 2.44/2.60 tff(11410,plain,
% 2.44/2.60 ((~(s(s(elem!1)) = s(s(s(s(s(s(s(elem!1))))))))) <=> (~(s(s(s(s(s(elem!1))))) = s(elem!1)))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[11409])).
% 2.44/2.60 tff(11411,plain,
% 2.44/2.60 (~(s(s(elem!1)) = s(s(s(s(s(s(s(elem!1))))))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[579, 69])).
% 2.44/2.60 tff(11412,plain,
% 2.44/2.60 (~(s(s(s(s(s(elem!1))))) = s(elem!1))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[11411, 11410])).
% 2.44/2.60 tff(11413,plain,
% 2.44/2.60 (~(s(elem!1) = s(s(elem!1)))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[11412, 11403])).
% 2.44/2.60 tff(11414,assumption,(~r(elem!1, s(elem!1))), introduced(assumption)).
% 2.44/2.60 tff(11415,plain,
% 2.44/2.60 ((s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))) <=> (elem!1 = s(s(elem!1)))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[11395, 11389])).
% 2.44/2.60 tff(11416,plain,
% 2.44/2.60 ((s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))) <=> (s(s(elem!1)) = elem!1)),
% 2.44/2.60 inference(transitivity,[status(thm)],[11415, 133])).
% 2.44/2.60 tff(11417,plain,
% 2.44/2.60 ((s(s(elem!1)) = elem!1) <=> (s(s(s(elem!1))) = s(s(s(s(s(elem!1))))))),
% 2.44/2.60 inference(symmetry,[status(thm)],[11416])).
% 2.44/2.60 tff(11418,plain,
% 2.44/2.60 ((~(s(s(elem!1)) = elem!1)) <=> (~(s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[11417])).
% 2.44/2.60 tff(11419,plain,
% 2.44/2.60 (~(s(s(s(elem!1))) = s(s(s(s(s(elem!1))))))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[199, 11418])).
% 2.44/2.60 tff(11420,plain,
% 2.44/2.60 (s(s(s(elem!1))) = s(elem!1)),
% 2.44/2.60 inference(transitivity,[status(thm)],[352, 349, 343, 3189])).
% 2.44/2.60 tff(11421,plain,
% 2.44/2.60 (inj_0(s(s(s(elem!1)))) = inj_0(s(elem!1))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[11420])).
% 2.44/2.60 tff(11422,plain,
% 2.44/2.60 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 2.44/2.60 inference(symmetry,[status(thm)],[11421])).
% 2.44/2.60 tff(11423,plain,
% 2.44/2.60 (s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))),
% 2.44/2.60 inference(transitivity,[status(thm)],[352, 349, 11422, 103, 6295])).
% 2.44/2.60 tff(11424,plain,
% 2.44/2.60 ($false),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[785, 11423])).
% 2.44/2.60 tff(11425,plain,((~(elem!1 = s(elem!1))) | (s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))) | (~(s(s(s(s(s(elem!1))))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.60 tff(11426,plain,
% 2.44/2.60 (~(elem!1 = s(elem!1))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[11425, 11419, 11389])).
% 2.44/2.60 tff(11427,plain,
% 2.44/2.60 (b(elem!1, s(elem!1))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[2864, 11426, 11414])).
% 2.44/2.60 tff(11428,plain,
% 2.44/2.60 (b(elem!1, s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[6283])).
% 2.44/2.60 tff(11429,plain,
% 2.44/2.60 (b(s(s(s(elem!1))), s(elem!1))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[1574, 11428])).
% 2.44/2.60 tff(11430,plain,
% 2.44/2.60 ($false),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[3659, 11429])).
% 2.44/2.60 tff(11431,plain,((~b(elem!1, s(elem!1))) | b(s(s(s(elem!1))), s(elem!1)) | (~(s(s(s(s(s(elem!1))))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.60 tff(11432,plain,
% 2.44/2.60 (b(s(s(s(elem!1))), s(elem!1))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[11431, 11427, 11389])).
% 2.44/2.60 tff(11433,plain,
% 2.44/2.60 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[11395])).
% 2.44/2.60 tff(11434,plain,
% 2.44/2.60 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 2.44/2.60 inference(symmetry,[status(thm)],[11433])).
% 2.44/2.60 tff(11435,plain,
% 2.44/2.60 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[2002, 11434])).
% 2.44/2.60 tff(11436,plain,
% 2.44/2.60 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(s(z))), elem!1)),
% 2.44/2.60 inference(monotonicity,[status(thm)],[11395])).
% 2.44/2.60 tff(11437,plain,
% 2.44/2.60 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 2.44/2.60 inference(symmetry,[status(thm)],[11436])).
% 2.44/2.60 tff(11438,plain,
% 2.44/2.60 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[3697, 11437])).
% 2.44/2.60 tff(11439,assumption,(b(s(s(s(elem!1))), s(s(s(z))))), introduced(assumption)).
% 2.44/2.60 tff(11440,plain,
% 2.44/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(11441,plain,
% 2.44/2.60 (((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(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(z))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(11442,plain,
% 2.44/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[11441])).
% 2.44/2.61 tff(11443,plain,
% 2.44/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.44/2.61 inference(transitivity,[status(thm)],[11442, 11440])).
% 2.44/2.61 tff(11444,plain,
% 2.44/2.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(11445,plain,
% 2.44/2.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[11444, 11443])).
% 2.44/2.61 tff(11446,plain,
% 2.44/2.61 ($false),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[11445, 246, 1937, 11439, 8030, 8299])).
% 2.44/2.61 tff(11447,plain,((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.61 tff(11448,plain,
% 2.44/2.61 (~b(s(elem!1), s(s(s(z))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[11447, 11438, 11435, 11432])).
% 2.44/2.61 tff(11449,plain,
% 2.44/2.61 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[8641])).
% 2.44/2.61 tff(11450,plain,
% 2.44/2.61 (s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))),
% 2.44/2.61 inference(transitivity,[status(thm)],[11449, 6295])).
% 2.44/2.61 tff(11451,plain,
% 2.44/2.61 ($false),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[1501, 11450])).
% 2.44/2.61 tff(11452,plain,((~(s(elem!1) = s(s(s(z))))) | (~(s(s(s(s(s(elem!1))))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.61 tff(11453,plain,
% 2.44/2.61 (~(s(elem!1) = s(s(s(z))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[11452, 11389])).
% 2.44/2.61 tff(11454,plain,
% 2.44/2.61 (r(s(elem!1), s(s(s(z))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[1754, 11453, 11448])).
% 2.44/2.61 tff(11455,plain,
% 2.44/2.61 (r(s(s(s(s(s(elem!1))))), s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[11389])).
% 2.44/2.61 tff(11456,plain,
% 2.44/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(11457,plain,
% 2.44/2.61 (((~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(11458,plain,
% 2.44/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[11457])).
% 2.44/2.61 tff(11459,plain,
% 2.44/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.44/2.61 inference(transitivity,[status(thm)],[11458, 11456])).
% 2.44/2.61 tff(11460,plain,
% 2.44/2.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(11461,plain,
% 2.44/2.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[11460, 11459])).
% 2.44/2.61 tff(11462,plain,
% 2.44/2.61 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[11461, 246, 11380, 10619, 2090, 11378])).
% 2.44/2.61 tff(11463,plain,
% 2.44/2.61 (r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[1626, 11462])).
% 2.44/2.61 tff(11464,plain,
% 2.44/2.61 (r(s(s(elem!1)), s(s(s(z))))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[11463, 11455])).
% 2.44/2.61 tff(11465,plain,
% 2.44/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(11466,plain,
% 2.44/2.61 (((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(11467,plain,
% 2.44/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z)))))))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[11466])).
% 2.44/2.61 tff(11468,plain,
% 2.44/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))))),
% 2.44/2.61 inference(transitivity,[status(thm)],[11467, 11465])).
% 2.44/2.61 tff(11469,plain,
% 2.44/2.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(11470,plain,
% 2.44/2.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z)))))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[11469, 11468])).
% 2.44/2.61 tff(11471,plain,
% 2.44/2.61 (~r(s(elem!1), s(s(elem!1)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[11470, 183, 11464, 11454])).
% 2.44/2.61 tff(11472,plain,
% 2.44/2.61 ((s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[5561, 47, 11471])).
% 2.44/2.61 tff(11473,plain,
% 2.44/2.61 (b(s(elem!1), s(s(elem!1)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[11472, 11413])).
% 2.44/2.61 tff(11474,plain,
% 2.44/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(11475,plain,
% 2.44/2.61 (((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(11476,plain,
% 2.44/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[11475])).
% 2.44/2.61 tff(11477,plain,
% 2.44/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.44/2.61 inference(transitivity,[status(thm)],[11476, 11474])).
% 2.44/2.61 tff(11478,plain,
% 2.44/2.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(11479,plain,
% 2.44/2.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[11478, 11477])).
% 2.44/2.61 tff(11480,plain,
% 2.44/2.61 (~r(s(z), s(s(elem!1)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[11479, 183, 6096, 11464])).
% 2.44/2.61 tff(11481,plain,
% 2.44/2.61 (b(s(z), s(s(elem!1)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[233, 11480])).
% 2.44/2.61 tff(11482,plain,
% 2.44/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(11483,plain,
% 2.44/2.61 (((~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(11484,plain,
% 2.44/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[11483])).
% 2.44/2.61 tff(11485,plain,
% 2.44/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.44/2.61 inference(transitivity,[status(thm)],[11484, 11482])).
% 2.44/2.61 tff(11486,plain,
% 2.44/2.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(11487,plain,
% 2.44/2.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[11486, 11485])).
% 2.44/2.61 tff(11488,plain,
% 2.44/2.61 (~r(s(s(elem!1)), s(z))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[11487, 183, 1114, 6096, 11464])).
% 2.44/2.61 tff(11489,plain,
% 2.44/2.61 (b(s(s(elem!1)), s(z))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[197, 11488])).
% 2.44/2.61 tff(11490,plain,
% 2.44/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(11491,plain,
% 2.44/2.61 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(11492,plain,
% 2.44/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z)))))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[11491])).
% 2.44/2.61 tff(11493,plain,
% 2.44/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))))),
% 2.44/2.61 inference(transitivity,[status(thm)],[11492, 11490])).
% 2.44/2.61 tff(11494,plain,
% 2.44/2.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(11495,plain,
% 2.44/2.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z)))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[11494, 11493])).
% 2.44/2.61 tff(11496,plain,
% 2.44/2.61 (~b(s(elem!1), s(z))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[11495, 246, 11489, 11481, 11473, 11398])).
% 2.44/2.61 tff(11497,plain,
% 2.44/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(11498,plain,
% 2.44/2.61 (((~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(11499,plain,
% 2.44/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z)))))))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[11498])).
% 2.44/2.61 tff(11500,plain,
% 2.44/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))))),
% 2.44/2.61 inference(transitivity,[status(thm)],[11499, 11497])).
% 2.44/2.61 tff(11501,plain,
% 2.44/2.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(11502,plain,
% 2.44/2.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z)))))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[11501, 11500])).
% 2.44/2.61 tff(11503,plain,
% 2.44/2.61 (~r(s(elem!1), s(z))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[11502, 183, 1114, 6096, 11454])).
% 2.44/2.61 tff(11504,plain,
% 2.44/2.61 ((s(elem!1) = s(z)) | b(s(elem!1), s(z))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[2989, 47, 11503])).
% 2.44/2.61 tff(11505,plain,
% 2.44/2.61 (s(elem!1) = s(z)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[11504, 11496])).
% 2.44/2.61 tff(11506,plain,
% 2.44/2.61 (s(z) = s(elem!1)),
% 2.44/2.61 inference(symmetry,[status(thm)],[11505])).
% 2.44/2.61 tff(11507,plain,
% 2.44/2.61 (inj_0(s(z)) = inj_0(s(elem!1))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[11506])).
% 2.44/2.61 tff(11508,plain,
% 2.44/2.61 (inj_0(s(elem!1)) = inj_0(s(z))),
% 2.44/2.61 inference(symmetry,[status(thm)],[11507])).
% 2.44/2.61 tff(11509,plain,
% 2.44/2.61 (s(s(s(elem!1))) = z),
% 2.44/2.61 inference(transitivity,[status(thm)],[352, 11394, 11508, 20])).
% 2.44/2.61 tff(11510,plain,
% 2.44/2.61 ($false),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[355, 11509])).
% 2.44/2.61 tff(11511,plain,((s(s(s(s(s(elem!1))))) = elem!1) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | r(elem!1, s(elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (s(s(elem!1)) = elem!1) | (~b(s(s(s(z))), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | b(s(s(s(s(s(elem!1))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.61 tff(11512,plain,
% 2.44/2.61 (s(s(s(s(s(elem!1))))) = elem!1),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[11511, 11369, 11060, 11367, 11171, 1114, 11360, 11375, 11371, 10595, 5365, 11264])).
% 2.44/2.62 tff(11513,plain,
% 2.44/2.62 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[7198])).
% 2.44/2.62 tff(11514,plain,
% 2.44/2.62 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(elem!1)))))))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.44/2.62 inference(symmetry,[status(thm)],[11513])).
% 2.44/2.62 tff(11515,assumption,(~(s(s(s(s(z)))) = s(s(s(s(s(s(s(elem!1))))))))), introduced(assumption)).
% 2.44/2.62 tff(11516,plain,
% 2.44/2.62 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[7198])).
% 2.44/2.62 tff(11517,plain,
% 2.44/2.62 ((~r(s(s(s(s(z)))), s(s(elem!1)))) <=> (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(elem!1)))))))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[11516])).
% 2.44/2.62 tff(11518,assumption,(~b(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 2.44/2.62 tff(11519,plain,
% 2.44/2.62 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[1701, 8207, 11518])).
% 2.44/2.62 tff(11520,plain,
% 2.44/2.62 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[11340, 183, 216, 3886, 11519])).
% 2.44/2.62 tff(11521,plain,
% 2.44/2.62 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[11520, 11517])).
% 2.44/2.62 tff(11522,plain,
% 2.44/2.62 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(s(elem!1)))))))) | r(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(z)))) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(s(elem!1)))))))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(11523,plain,
% 2.44/2.62 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(s(elem!1)))))))))),
% 2.44/2.62 inference(quant_inst,[status(thm)],[])).
% 2.44/2.62 tff(11524,plain,
% 2.44/2.62 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[11523, 11522])).
% 2.44/2.62 tff(11525,plain,
% 2.44/2.62 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[11524, 47])).
% 2.44/2.62 tff(11526,plain,
% 2.44/2.62 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[11525, 11521, 11515])).
% 2.44/2.62 tff(11527,plain,
% 2.44/2.62 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[11526, 11514])).
% 2.44/2.62 tff(11528,plain,
% 2.44/2.62 (~r(s(s(s(s(z)))), z)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[6502, 183, 267, 171, 6095])).
% 2.44/2.62 tff(11529,plain,
% 2.44/2.62 (b(s(s(s(s(z)))), z)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[2424, 47, 2421, 11528])).
% 2.44/2.62 tff(11530,plain,
% 2.44/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(11531,plain,
% 2.44/2.62 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(11532,plain,
% 2.44/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[11531])).
% 2.44/2.62 tff(11533,plain,
% 2.44/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.44/2.62 inference(transitivity,[status(thm)],[11532, 11530])).
% 2.44/2.62 tff(11534,plain,
% 2.44/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.44/2.62 inference(quant_inst,[status(thm)],[])).
% 2.44/2.62 tff(11535,plain,
% 2.44/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[11534, 11533])).
% 2.44/2.62 tff(11536,plain,
% 2.44/2.62 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[11535, 183, 633, 430, 6095])).
% 2.44/2.62 tff(11537,plain,
% 2.44/2.62 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[1701, 11536, 8207])).
% 2.44/2.62 tff(11538,plain,
% 2.44/2.62 ($false),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[10499, 246, 2002, 3697, 11284, 11537, 11529])).
% 2.44/2.62 tff(11539,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (s(s(s(s(z)))) = s(s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~r(z, elem!1)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.62 tff(11540,plain,
% 2.44/2.62 (~r(s(s(s(s(z)))), s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[11539, 8207, 3697, 2002, 633, 430, 267, 171])).
% 2.44/2.62 tff(11541,plain,
% 2.44/2.62 (b(s(s(s(s(z)))), s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[2411, 47, 1713, 11540])).
% 2.44/2.62 tff(11542,plain,
% 2.44/2.62 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[11325, 246, 201, 1044, 2001, 11541])).
% 2.44/2.62 tff(11543,plain,
% 2.44/2.62 ($false),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[11542, 11527])).
% 2.44/2.62 tff(11544,plain,((s(s(s(s(z)))) = s(s(s(z)))) | (~(s(s(s(s(s(elem!1))))) = elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (s(s(s(s(z)))) = s(s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))) | b(s(s(s(s(z)))), s(s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~r(z, elem!1)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.62 tff(11545,plain,
% 2.44/2.62 ((~(s(s(s(s(s(elem!1))))) = elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (s(s(s(s(z)))) = s(s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))) | b(s(s(s(s(z)))), s(s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~r(z, elem!1)) | (~r(z, s(z)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[11544, 1697])).
% 2.44/2.62 tff(11546,plain,
% 2.44/2.62 (s(s(s(s(z)))) = s(s(s(s(s(s(s(elem!1)))))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[11545, 11512, 10595, 11334, 11237, 11060, 11172, 11316, 11171, 11369, 11245, 11174, 5365, 170])).
% 2.44/2.62 tff(11547,plain,
% 2.44/2.62 (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(z))))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[11546, 10601])).
% 2.44/2.62 tff(11548,plain,
% 2.44/2.62 (~(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(z)))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[7214, 11512])).
% 2.44/2.62 tff(11549,plain,
% 2.44/2.62 ($false),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[11548, 11547])).
% 2.44/2.62 tff(11550,plain,((~r(s(z), z)) | b(z, elem!1) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.62 tff(11551,plain,
% 2.44/2.62 (~r(s(z), z)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[11550, 54, 55])).
% 2.44/2.62 tff(11552,plain,
% 2.44/2.62 (b(s(z), z)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[1069, 11551])).
% 2.44/2.62 tff(11553,plain,
% 2.44/2.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(11554,plain,
% 2.44/2.62 (((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(11555,plain,
% 2.44/2.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1))))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[11554])).
% 2.44/2.62 tff(11556,plain,
% 2.44/2.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))))),
% 2.44/2.62 inference(transitivity,[status(thm)],[11555, 11553])).
% 2.44/2.62 tff(11557,plain,
% 2.44/2.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 2.44/2.62 inference(quant_inst,[status(thm)],[])).
% 2.44/2.62 tff(11558,plain,
% 2.44/2.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1))))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[11557, 11556])).
% 2.44/2.62 tff(11559,plain,
% 2.44/2.62 (~b(s(s(elem!1)), s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[11558, 246, 11552, 10599, 10597])).
% 2.44/2.62 tff(11560,plain,
% 2.44/2.62 (r(s(s(elem!1)), s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[197, 11559])).
% 2.44/2.62 tff(11561,plain,
% 2.44/2.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1)))) | (~b(s(z), s(s(elem!1)))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(11562,plain,
% 2.44/2.62 (((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(11563,plain,
% 2.44/2.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1)))) | (~b(s(z), s(s(elem!1))))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[11562])).
% 2.44/2.62 tff(11564,plain,
% 2.44/2.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1)))) | (~b(s(z), s(s(elem!1)))))),
% 2.44/2.62 inference(transitivity,[status(thm)],[11563, 11561])).
% 2.44/2.62 tff(11565,plain,
% 2.44/2.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))),
% 2.44/2.62 inference(quant_inst,[status(thm)],[])).
% 2.44/2.62 tff(11566,plain,
% 2.44/2.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1))))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[11565, 11564])).
% 2.44/2.62 tff(11567,plain,
% 2.44/2.62 (~b(s(z), s(s(elem!1)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[11566, 246, 11552, 10599, 10597])).
% 2.44/2.62 tff(11568,plain,
% 2.44/2.62 (r(s(z), s(s(elem!1)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[233, 11567])).
% 2.44/2.62 tff(11569,plain,
% 2.44/2.62 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.62 inference(symmetry,[status(thm)],[10838])).
% 2.44/2.62 tff(11570,plain,
% 2.44/2.62 ((~r(s(s(s(elem!1))), s(s(elem!1)))) <=> (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[11569])).
% 2.44/2.62 tff(11571,plain,
% 2.44/2.62 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[10971, 202, 216, 171, 1099, 1113])).
% 2.44/2.62 tff(11572,plain,
% 2.44/2.62 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[11571, 11570])).
% 2.44/2.62 tff(11573,plain,
% 2.44/2.62 ($false),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[2593, 11572])).
% 2.44/2.62 tff(11574,plain,((~(elem!1 = s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(z))) | (~b(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.62 tff(11575,plain,
% 2.44/2.62 (~(elem!1 = s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[11574, 2593, 10595, 170, 10597, 11568])).
% 2.44/2.62 tff(11576,plain,
% 2.44/2.62 (~(s(z) = elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[9, 11575])).
% 2.44/2.62 tff(11577,plain,
% 2.44/2.62 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[5804, 11576])).
% 2.44/2.62 tff(11578,plain,
% 2.44/2.62 (~r(s(s(s(z))), s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[6468, 11577, 10599, 5365, 170, 11560])).
% 2.44/2.62 tff(11579,plain,
% 2.44/2.62 (b(s(s(s(z))), s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[52, 11578])).
% 2.44/2.62 tff(11580,plain,
% 2.44/2.62 (~(s(s(s(z))) = elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[11086, 2593, 5365, 10595])).
% 2.44/2.62 tff(11581,plain,
% 2.44/2.62 (~r(s(s(s(z))), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[11058, 11577, 10595, 5365])).
% 2.44/2.62 tff(11582,plain,
% 2.44/2.62 (b(s(s(s(z))), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[647, 11581, 11580])).
% 2.44/2.62 tff(11583,plain,
% 2.44/2.62 (b(elem!1, s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[214, 11575, 6376])).
% 2.44/2.62 tff(11584,plain,
% 2.44/2.62 (b(s(z), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[6422, 11575, 55, 54, 6376])).
% 2.44/2.62 tff(11585,plain,
% 2.44/2.62 ($false),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[7747, 246, 11584, 11583, 11582, 11579])).
% 2.44/2.62 tff(11586,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | b(z, elem!1) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.62 tff(11587,plain,
% 2.44/2.62 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[11586, 54, 55])).
% 2.44/2.62 tff(11588,plain,
% 2.44/2.62 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[1702, 11587])).
% 2.44/2.62 tff(11589,plain,
% 2.44/2.62 (~(s(z) = elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[121, 119])).
% 2.44/2.62 tff(11590,plain,
% 2.44/2.62 (~(elem!1 = s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[2279, 11589])).
% 2.44/2.62 tff(11591,plain,
% 2.44/2.62 (b(elem!1, s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[214, 11590, 8759])).
% 2.44/2.62 tff(11592,plain,
% 2.44/2.62 (~(s(s(elem!1)) = elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[2130, 11591, 2124])).
% 2.44/2.62 tff(11593,plain,
% 2.44/2.62 (~(s(s(elem!1)) = s(elem!1))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[5640, 11592])).
% 2.44/2.62 tff(11594,plain,
% 2.44/2.62 (~r(s(s(s(z))), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[11058, 119, 216, 267])).
% 2.44/2.62 tff(11595,plain,
% 2.44/2.62 (~r(s(s(s(z))), s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[6468, 119, 10617, 267, 171, 2133])).
% 2.44/2.62 tff(11596,plain,
% 2.44/2.62 (b(s(s(s(z))), s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[52, 11595])).
% 2.44/2.62 tff(11597,plain,
% 2.44/2.62 (b(s(z), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[1034, 11589, 8757])).
% 2.44/2.62 tff(11598,plain,
% 2.44/2.62 (~b(s(s(s(z))), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[7747, 246, 11597, 11591, 11596])).
% 2.44/2.62 tff(11599,plain,
% 2.44/2.62 (s(s(s(z))) = elem!1),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[647, 11598, 11594])).
% 2.44/2.62 tff(11600,plain,
% 2.44/2.62 (s(s(s(s(z)))) = s(elem!1)),
% 2.44/2.62 inference(monotonicity,[status(thm)],[11599])).
% 2.44/2.62 tff(11601,plain,
% 2.44/2.62 (s(elem!1) = s(s(s(s(z))))),
% 2.44/2.62 inference(symmetry,[status(thm)],[11600])).
% 2.44/2.62 tff(11602,plain,
% 2.44/2.62 (r(s(elem!1), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[11601])).
% 2.44/2.62 tff(11603,plain,
% 2.44/2.62 (r(s(s(s(s(z)))), s(z)) <=> r(s(elem!1), s(z))),
% 2.44/2.62 inference(symmetry,[status(thm)],[11602])).
% 2.44/2.62 tff(11604,plain,
% 2.44/2.62 (b(s(s(s(s(z)))), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[11094, 11599, 1833])).
% 2.44/2.62 tff(11605,plain,
% 2.44/2.62 (~b(s(s(s(s(z)))), s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[9050, 11604, 11591, 11597])).
% 2.44/2.62 tff(11606,plain,
% 2.44/2.62 (r(s(s(s(s(z)))), s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[6103, 11605])).
% 2.44/2.62 tff(11607,plain,
% 2.44/2.62 (r(s(elem!1), s(z))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[11606, 11603])).
% 2.44/2.62 tff(11608,plain,
% 2.44/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(11609,plain,
% 2.44/2.62 (((~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(11610,plain,
% 2.44/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1)))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[11609])).
% 2.44/2.62 tff(11611,plain,
% 2.44/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.44/2.62 inference(transitivity,[status(thm)],[11610, 11608])).
% 2.44/2.62 tff(11612,plain,
% 2.44/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.44/2.62 inference(quant_inst,[status(thm)],[])).
% 2.44/2.62 tff(11613,plain,
% 2.44/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1)))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[11612, 11611])).
% 2.44/2.62 tff(11614,plain,
% 2.44/2.62 (~r(s(s(elem!1)), s(elem!1))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[11613, 183, 2133, 11607])).
% 2.44/2.62 tff(11615,plain,
% 2.44/2.62 (b(s(s(elem!1)), s(elem!1))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[5644, 11614, 11593])).
% 2.44/2.62 tff(11616,plain,
% 2.44/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(11617,plain,
% 2.44/2.62 (((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, elem!1)) | (~r(s(elem!1), z))) <=> ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(11618,plain,
% 2.44/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[11617])).
% 2.44/2.62 tff(11619,plain,
% 2.44/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 2.44/2.62 inference(transitivity,[status(thm)],[11618, 11616])).
% 2.44/2.62 tff(11620,plain,
% 2.44/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 2.44/2.62 inference(quant_inst,[status(thm)],[])).
% 2.44/2.62 tff(11621,plain,
% 2.44/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[11620, 11619])).
% 2.44/2.62 tff(11622,plain,
% 2.44/2.62 (~r(s(elem!1), z)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[11621, 183, 267, 171, 11607])).
% 2.44/2.62 tff(11623,plain,
% 2.44/2.62 (b(s(elem!1), z)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[2581, 11622])).
% 2.44/2.62 tff(11624,plain,
% 2.44/2.62 (r(z, s(s(s(s(z))))) <=> r(z, s(elem!1))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[11600])).
% 2.44/2.62 tff(11625,plain,
% 2.44/2.62 ((~r(z, s(s(s(s(z)))))) <=> (~r(z, s(elem!1)))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[11624])).
% 2.44/2.62 tff(11626,plain,
% 2.44/2.62 (~r(z, s(s(s(s(z)))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[9071, 11606, 171])).
% 2.44/2.62 tff(11627,plain,
% 2.44/2.62 (~r(z, s(elem!1))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[11626, 11625])).
% 2.44/2.62 tff(11628,plain,
% 2.44/2.62 (b(z, s(elem!1))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[2561, 11627])).
% 2.44/2.62 tff(11629,plain,
% 2.44/2.62 (b(s(elem!1), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[5677, 11599, 1833])).
% 2.44/2.62 tff(11630,plain,
% 2.44/2.62 ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[11111, 246, 10617, 11629, 11628])).
% 2.44/2.62 tff(11631,plain,
% 2.44/2.62 ($false),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[11630, 11623, 11615])).
% 2.44/2.62 tff(11632,plain,((s(s(s(z))) = s(s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | b(s(s(elem!1)), s(z)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.62 tff(11633,plain,
% 2.44/2.62 (s(s(s(z))) = s(s(elem!1))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[11632, 170, 5365, 11588, 11559, 10595])).
% 2.44/2.62 tff(11634,plain,
% 2.44/2.62 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[9446, 11633, 11588])).
% 2.44/2.62 tff(11635,plain,
% 2.44/2.62 (~b(z, s(s(s(elem!1))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[10708, 246, 10599, 10597, 11634])).
% 2.44/2.62 tff(11636,plain,
% 2.44/2.62 ((z = s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[9177, 47, 11635])).
% 2.44/2.62 tff(11637,plain,
% 2.44/2.62 (r(z, s(s(s(elem!1))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[11636, 5369])).
% 2.44/2.62 tff(11638,plain,
% 2.44/2.62 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[11633])).
% 2.44/2.62 tff(11639,plain,
% 2.44/2.62 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(elem!1))) = s(s(s(s(s(elem!1))))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[11638])).
% 2.44/2.62 tff(11640,plain,
% 2.44/2.62 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 2.44/2.62 inference(transitivity,[status(thm)],[11639, 9120])).
% 2.44/2.62 tff(11641,plain,
% 2.44/2.62 ((~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[11640])).
% 2.44/2.62 tff(11642,plain,
% 2.44/2.62 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[1501, 11641])).
% 2.44/2.62 tff(11643,plain,
% 2.44/2.62 (s(z) = elem!1),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[5804, 11633])).
% 2.44/2.62 tff(11644,plain,
% 2.44/2.62 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.44/2.62 inference(symmetry,[status(thm)],[11638])).
% 2.44/2.62 tff(11645,plain,
% 2.44/2.62 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(s(z)))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[11644])).
% 2.44/2.62 tff(11646,plain,
% 2.44/2.62 (r(z, s(s(s(s(z)))))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[11637, 11645])).
% 2.44/2.62 tff(11647,plain,
% 2.44/2.62 (~r(s(s(s(s(z)))), s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[9071, 11646, 170])).
% 2.44/2.62 tff(11648,plain,
% 2.44/2.62 (b(s(s(s(s(z)))), s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[6103, 11647])).
% 2.44/2.62 tff(11649,plain,
% 2.44/2.62 (b(s(s(s(elem!1))), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[9413, 11648, 11643])).
% 2.44/2.62 tff(11650,plain,
% 2.44/2.62 (elem!1 = s(z)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[9, 11643])).
% 2.44/2.62 tff(11651,plain,
% 2.44/2.62 (~b(s(s(s(z))), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[5773, 11650, 11559])).
% 2.44/2.62 tff(11652,plain,
% 2.44/2.62 (~b(s(s(elem!1)), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[5568, 11651, 11633])).
% 2.44/2.62 tff(11653,plain,
% 2.44/2.62 (~b(s(s(elem!1)), s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[207, 202, 145])).
% 2.44/2.62 tff(11654,plain,
% 2.44/2.62 (r(s(s(elem!1)), s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[197, 11653])).
% 2.44/2.62 tff(11655,plain,
% 2.44/2.62 (r(s(s(s(z))), s(z))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[11654, 10612])).
% 2.44/2.62 tff(11656,plain,
% 2.44/2.62 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(z))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[202])).
% 2.44/2.62 tff(11657,plain,
% 2.44/2.62 ((~r(s(s(s(z))), elem!1)) <=> (~r(s(s(s(z))), s(z)))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[11656])).
% 2.44/2.63 tff(11658,plain,
% 2.44/2.63 (~r(s(s(s(z))), s(z))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[10369, 11657])).
% 2.44/2.63 tff(11659,plain,
% 2.44/2.63 ($false),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[11658, 11655])).
% 2.44/2.63 tff(11660,plain,((~(elem!1 = s(z))) | r(s(s(s(z))), elem!1) | b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.63 tff(11661,plain,
% 2.44/2.63 (r(s(s(s(z))), elem!1)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[11660, 11652, 11650])).
% 2.44/2.63 tff(11662,plain,
% 2.44/2.63 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[5485, 11661, 5365])).
% 2.44/2.63 tff(11663,plain,
% 2.44/2.63 ((s(s(s(s(s(elem!1))))) = s(z)) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 2.44/2.63 inference(monotonicity,[status(thm)],[11643])).
% 2.44/2.63 tff(11664,plain,
% 2.44/2.63 ((~(s(s(s(s(s(elem!1))))) = s(z))) <=> (~(s(s(s(s(s(elem!1))))) = elem!1))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[11663])).
% 2.44/2.63 tff(11665,plain,
% 2.44/2.63 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[331, 11664])).
% 2.44/2.63 tff(11666,plain,
% 2.44/2.63 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[86, 11665, 11662])).
% 2.44/2.63 tff(11667,plain,
% 2.44/2.63 (b(s(z), z) <=> b(elem!1, z)),
% 2.44/2.63 inference(monotonicity,[status(thm)],[11643])).
% 2.44/2.63 tff(11668,plain,
% 2.44/2.63 (b(elem!1, z)),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[11552, 11667])).
% 2.44/2.63 tff(11669,plain,
% 2.44/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(11670,plain,
% 2.44/2.63 (((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(11671,plain,
% 2.44/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[11670])).
% 2.44/2.63 tff(11672,plain,
% 2.44/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.44/2.63 inference(transitivity,[status(thm)],[11671, 11669])).
% 2.44/2.63 tff(11673,plain,
% 2.44/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.44/2.63 inference(quant_inst,[status(thm)],[])).
% 2.44/2.63 tff(11674,plain,
% 2.44/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[11673, 11672])).
% 2.44/2.63 tff(11675,plain,
% 2.44/2.63 ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[11674, 246, 11668, 10597, 11666, 11634])).
% 2.44/2.63 tff(11676,plain,
% 2.44/2.63 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[11675, 11649])).
% 2.44/2.63 tff(11677,plain,
% 2.44/2.63 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[3693, 11676, 11642])).
% 2.44/2.63 tff(11678,plain,
% 2.44/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, 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))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, 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))))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(11679,plain,
% 2.44/2.63 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), z))) <=> ((~r(z, 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))))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(11680,plain,
% 2.44/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, 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)))))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[11679])).
% 2.44/2.63 tff(11681,plain,
% 2.44/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, 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))))))),
% 2.44/2.63 inference(transitivity,[status(thm)],[11680, 11678])).
% 2.44/2.63 tff(11682,plain,
% 2.44/2.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 2.44/2.63 inference(quant_inst,[status(thm)],[])).
% 2.44/2.63 tff(11683,plain,
% 2.44/2.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, 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)))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[11682, 11681])).
% 2.44/2.63 tff(11684,plain,
% 2.44/2.63 (~r(s(s(s(s(s(elem!1))))), z)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[11683, 183, 5365, 11677, 11637])).
% 2.44/2.63 tff(11685,plain,
% 2.44/2.63 (b(s(s(s(s(s(elem!1))))), z)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[1601, 11684])).
% 2.44/2.63 tff(11686,plain,
% 2.44/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(11687,plain,
% 2.44/2.63 (((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(11688,plain,
% 2.44/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[11687])).
% 2.44/2.63 tff(11689,plain,
% 2.44/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.44/2.63 inference(transitivity,[status(thm)],[11688, 11686])).
% 2.44/2.63 tff(11690,plain,
% 2.44/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.44/2.63 inference(quant_inst,[status(thm)],[])).
% 2.44/2.63 tff(11691,plain,
% 2.44/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[11690, 11689])).
% 2.44/2.63 tff(11692,plain,
% 2.44/2.63 ($false),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[11691, 246, 11668, 10599, 10597, 11666, 11685])).
% 2.44/2.63 tff(11693,plain,(b(z, s(z)) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.63 tff(11694,plain,
% 2.44/2.63 (b(z, s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[11693, 55])).
% 2.44/2.63 tff(11695,plain,
% 2.44/2.63 (~(s(z) = elem!1)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[3065, 11694, 55])).
% 2.44/2.63 tff(11696,plain,
% 2.44/2.63 (~(elem!1 = s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[2279, 11695])).
% 2.44/2.63 tff(11697,plain,
% 2.44/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(11698,plain,
% 2.44/2.63 (((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(11699,plain,
% 2.44/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z)))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[11698])).
% 2.44/2.63 tff(11700,plain,
% 2.44/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))))),
% 2.44/2.63 inference(transitivity,[status(thm)],[11699, 11697])).
% 2.44/2.63 tff(11701,plain,
% 2.44/2.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 2.44/2.63 inference(quant_inst,[status(thm)],[])).
% 2.44/2.63 tff(11702,plain,
% 2.44/2.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z)))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[11701, 11700])).
% 2.44/2.63 tff(11703,plain,
% 2.44/2.63 ($false),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[11702, 183, 173, 216, 474])).
% 2.44/2.63 tff(11704,plain,((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.63 tff(11705,plain,
% 2.44/2.63 (~r(s(s(elem!1)), s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[11704, 474, 216])).
% 2.44/2.63 tff(11706,plain,
% 2.44/2.63 (b(s(s(elem!1)), s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[197, 11705])).
% 2.44/2.63 tff(11707,plain,
% 2.44/2.63 (~b(s(z), z)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[1154, 11706, 10619, 236])).
% 2.44/2.63 tff(11708,plain,
% 2.44/2.63 (~r(s(z), z)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[10358, 11706, 474, 236, 2277, 267])).
% 2.44/2.63 tff(11709,plain,
% 2.44/2.63 ($false),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[1069, 11708, 11707])).
% 2.44/2.63 tff(11710,plain,((~r(elem!1, s(z))) | (~b(z, s(z))) | (s(z) = elem!1) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.63 tff(11711,plain,
% 2.44/2.63 (~r(elem!1, s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[11710, 11694, 11695, 5365, 10595])).
% 2.44/2.63 tff(11712,plain,
% 2.44/2.63 (b(elem!1, s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[214, 11711, 11696])).
% 2.44/2.63 tff(11713,plain,
% 2.44/2.63 (~b(s(z), z)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[1154, 201, 1099, 236])).
% 2.44/2.63 tff(11714,plain,
% 2.44/2.63 (r(s(z), z)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[1069, 11713])).
% 2.44/2.63 tff(11715,plain,
% 2.44/2.63 (~r(s(z), elem!1)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[5432, 11714, 267])).
% 2.44/2.63 tff(11716,plain,
% 2.44/2.63 (b(s(z), elem!1)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[1034, 11715, 2277])).
% 2.44/2.63 tff(11717,plain,
% 2.44/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(11718,plain,
% 2.44/2.63 (((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(11719,plain,
% 2.44/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z)))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[11718])).
% 2.44/2.63 tff(11720,plain,
% 2.44/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))))),
% 2.44/2.63 inference(transitivity,[status(thm)],[11719, 11717])).
% 2.44/2.63 tff(11721,plain,
% 2.44/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))),
% 2.44/2.63 inference(quant_inst,[status(thm)],[])).
% 2.44/2.63 tff(11722,plain,
% 2.44/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z)))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[11721, 11720])).
% 2.44/2.63 tff(11723,plain,
% 2.44/2.63 ($false),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[11722, 246, 201, 11716, 2001, 1100, 236])).
% 2.44/2.63 tff(11724,plain,((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (s(z) = elem!1) | (~r(z, elem!1)) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.63 tff(11725,plain,
% 2.44/2.63 (~b(s(s(elem!1)), s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[11724, 11712, 10599, 11694, 11695, 5365, 10597])).
% 2.44/2.63 tff(11726,plain,
% 2.44/2.63 (r(s(s(elem!1)), s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[197, 11725])).
% 2.44/2.63 tff(11727,plain,
% 2.44/2.63 (~r(elem!1, s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[11710, 236, 2277, 267, 216])).
% 2.44/2.63 tff(11728,plain,
% 2.44/2.63 (b(elem!1, s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[214, 11727, 2339])).
% 2.44/2.63 tff(11729,plain,
% 2.44/2.63 ($false),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[2139, 183, 173, 217, 216])).
% 2.44/2.63 tff(11730,plain,((~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.63 tff(11731,plain,
% 2.44/2.63 (~r(s(z), elem!1)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[11730, 173, 216])).
% 2.44/2.63 tff(11732,plain,
% 2.44/2.63 (b(s(z), elem!1)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[1034, 11731, 2277])).
% 2.44/2.63 tff(11733,plain,
% 2.44/2.63 (~b(s(z), s(elem!1))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[8802, 246, 11732, 11728, 11101])).
% 2.44/2.63 tff(11734,plain,
% 2.44/2.63 ((s(z) = s(elem!1)) | r(s(z), s(elem!1))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[2973, 47, 11733])).
% 2.44/2.63 tff(11735,plain,
% 2.44/2.63 (r(s(z), s(elem!1))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[11734, 11130])).
% 2.44/2.63 tff(11736,plain,
% 2.44/2.63 (~b(s(s(s(s(z)))), s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[9050, 11732, 11728, 11095])).
% 2.44/2.63 tff(11737,plain,
% 2.44/2.63 (r(s(s(s(s(z)))), s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[6103, 11736])).
% 2.44/2.63 tff(11738,plain,
% 2.44/2.63 (b(s(elem!1), z) <=> b(s(s(s(s(z)))), z)),
% 2.44/2.63 inference(symmetry,[status(thm)],[11102])).
% 2.44/2.63 tff(11739,plain,
% 2.44/2.63 ((~b(s(elem!1), z)) <=> (~b(s(s(s(s(z)))), z))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[11738])).
% 2.44/2.63 tff(11740,plain,
% 2.44/2.63 (r(s(elem!1), s(z))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[11737, 6949])).
% 2.44/2.63 tff(11741,plain,
% 2.44/2.63 (~r(s(s(elem!1)), s(elem!1))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[11613, 183, 173, 11740])).
% 2.44/2.63 tff(11742,plain,
% 2.44/2.63 (b(s(s(elem!1)), s(elem!1))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[5644, 11741, 5641])).
% 2.44/2.63 tff(11743,plain,
% 2.44/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(11744,plain,
% 2.44/2.63 (((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(11745,plain,
% 2.44/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[11744])).
% 2.44/2.63 tff(11746,plain,
% 2.44/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 2.44/2.63 inference(transitivity,[status(thm)],[11745, 11743])).
% 2.44/2.63 tff(11747,plain,
% 2.44/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.44/2.63 inference(quant_inst,[status(thm)],[])).
% 2.44/2.63 tff(11748,plain,
% 2.44/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[11747, 11746])).
% 2.44/2.63 tff(11749,plain,
% 2.44/2.63 ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[11748, 246, 11732, 10617, 236, 11101])).
% 2.44/2.63 tff(11750,plain,
% 2.44/2.63 (~b(s(elem!1), z)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[11749, 11742])).
% 2.44/2.63 tff(11751,plain,
% 2.44/2.63 (~b(s(s(s(s(z)))), z)),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[11750, 11739])).
% 2.44/2.63 tff(11752,plain,
% 2.44/2.63 (r(s(s(s(s(z)))), z)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[6040, 11751])).
% 2.44/2.63 tff(11753,plain,
% 2.44/2.63 (~r(s(z), z)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[9423, 11752, 11737])).
% 2.44/2.63 tff(11754,plain,
% 2.44/2.63 (b(s(z), z)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[1069, 11753])).
% 2.44/2.63 tff(11755,plain,
% 2.44/2.63 (~r(s(s(s(s(s(elem!1))))), z)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[9392, 333, 267])).
% 2.44/2.63 tff(11756,plain,
% 2.44/2.63 (b(s(s(s(s(s(elem!1))))), z)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[1601, 11755])).
% 2.44/2.63 tff(11757,plain,
% 2.44/2.63 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[1557, 1552, 1555])).
% 2.44/2.63 tff(11758,plain,
% 2.44/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(11759,plain,
% 2.44/2.64 (((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(11760,plain,
% 2.44/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[11759])).
% 2.44/2.64 tff(11761,plain,
% 2.44/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.44/2.64 inference(transitivity,[status(thm)],[11760, 11758])).
% 2.44/2.64 tff(11762,plain,
% 2.44/2.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.44/2.64 inference(quant_inst,[status(thm)],[])).
% 2.44/2.64 tff(11763,plain,
% 2.44/2.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[11762, 11761])).
% 2.44/2.64 tff(11764,plain,
% 2.44/2.64 ($false),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[11763, 246, 1056, 10617, 236, 11757, 11756])).
% 2.44/2.64 tff(11765,plain,((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.64 tff(11766,plain,
% 2.44/2.64 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[11765, 11754, 236, 5624, 267, 216])).
% 2.44/2.64 tff(11767,plain,
% 2.44/2.64 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[86, 11766, 7042])).
% 2.44/2.64 tff(11768,plain,
% 2.44/2.64 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[6883, 11767, 236, 11728, 11754])).
% 2.44/2.64 tff(11769,plain,
% 2.44/2.64 (r(s(s(s(s(s(elem!1))))), s(z))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[6447, 11768])).
% 2.44/2.64 tff(11770,plain,
% 2.44/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1)))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(11771,plain,
% 2.44/2.64 (((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1)))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(11772,plain,
% 2.44/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1))))))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[11771])).
% 2.44/2.64 tff(11773,plain,
% 2.44/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1)))))),
% 2.44/2.64 inference(transitivity,[status(thm)],[11772, 11770])).
% 2.44/2.64 tff(11774,plain,
% 2.44/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))))),
% 2.44/2.64 inference(quant_inst,[status(thm)],[])).
% 2.44/2.64 tff(11775,plain,
% 2.44/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1))))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[11774, 11773])).
% 2.44/2.64 tff(11776,plain,
% 2.44/2.64 (~r(s(elem!1), s(s(elem!1)))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[11775, 183, 173, 11740])).
% 2.44/2.64 tff(11777,plain,
% 2.44/2.64 (b(s(elem!1), s(s(elem!1)))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[5561, 47, 11776, 11076])).
% 2.44/2.64 tff(11778,plain,
% 2.44/2.64 (r(s(elem!1), z)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[2581, 11750])).
% 2.44/2.64 tff(11779,plain,
% 2.44/2.64 (~b(elem!1, z)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[1135, 246, 11732, 11728, 236])).
% 2.44/2.64 tff(11780,plain,
% 2.44/2.64 (r(elem!1, z)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[1143, 11779, 5401])).
% 2.44/2.64 tff(11781,plain,
% 2.44/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(11782,plain,
% 2.44/2.64 (((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(11783,plain,
% 2.44/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z))))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[11782])).
% 2.44/2.64 tff(11784,plain,
% 2.44/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)))),
% 2.44/2.64 inference(transitivity,[status(thm)],[11783, 11781])).
% 2.44/2.64 tff(11785,plain,
% 2.44/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))))),
% 2.44/2.64 inference(quant_inst,[status(thm)],[])).
% 2.44/2.64 tff(11786,plain,
% 2.44/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[11785, 11784])).
% 2.44/2.64 tff(11787,plain,
% 2.44/2.64 (~r(elem!1, s(elem!1))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[11786, 183, 11780, 11778])).
% 2.44/2.64 tff(11788,plain,
% 2.44/2.64 (b(elem!1, s(elem!1))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[2864, 11787, 11115])).
% 2.44/2.64 tff(11789,plain,
% 2.44/2.64 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[3612, 11767, 11742, 11788, 11777])).
% 2.44/2.64 tff(11790,plain,
% 2.44/2.64 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[1795, 11789, 5650])).
% 2.44/2.64 tff(11791,plain,
% 2.44/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(11792,plain,
% 2.44/2.64 (((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z)))) <=> ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(11793,plain,
% 2.44/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1))))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[11792])).
% 2.44/2.64 tff(11794,plain,
% 2.44/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 2.44/2.64 inference(transitivity,[status(thm)],[11793, 11791])).
% 2.44/2.64 tff(11795,plain,
% 2.44/2.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))),
% 2.44/2.64 inference(quant_inst,[status(thm)],[])).
% 2.44/2.64 tff(11796,plain,
% 2.44/2.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[11795, 11794])).
% 2.44/2.64 tff(11797,plain,
% 2.44/2.64 (~b(s(z), s(s(elem!1)))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[11796, 246, 11732, 236, 10619, 11742, 11101])).
% 2.44/2.64 tff(11798,plain,
% 2.44/2.64 (r(s(z), s(s(elem!1)))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[233, 11797])).
% 2.44/2.64 tff(11799,plain,
% 2.44/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(z), s(elem!1))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(11800,plain,
% 2.44/2.64 (((~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(z)))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(z), s(elem!1))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(11801,plain,
% 2.44/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(z), s(elem!1)))))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[11800])).
% 2.44/2.64 tff(11802,plain,
% 2.44/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(z), s(elem!1))))),
% 2.44/2.64 inference(transitivity,[status(thm)],[11801, 11799])).
% 2.44/2.64 tff(11803,plain,
% 2.44/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 2.44/2.64 inference(quant_inst,[status(thm)],[])).
% 2.44/2.64 tff(11804,plain,
% 2.44/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(z), s(elem!1)))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[11803, 11802])).
% 2.44/2.64 tff(11805,plain,
% 2.44/2.64 ($false),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[11804, 183, 11798, 11790, 11769, 11735])).
% 2.44/2.64 tff(11806,plain,((~r(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~(s(s(s(z))) = elem!1)) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.64 tff(11807,plain,
% 2.44/2.64 (~(s(s(s(z))) = elem!1)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[11806, 11726, 5365, 10595, 11694, 11695])).
% 2.44/2.64 tff(11808,plain,
% 2.44/2.64 (~(elem!1 = s(s(s(z))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[3013, 11807])).
% 2.44/2.64 tff(11809,plain,
% 2.44/2.64 (~r(s(z), elem!1)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[11730, 11726, 10595])).
% 2.44/2.64 tff(11810,plain,
% 2.44/2.64 (b(s(z), elem!1)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[1034, 11809, 11695])).
% 2.44/2.64 tff(11811,plain,
% 2.44/2.64 (~b(elem!1, z)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[1135, 246, 11810, 11712, 11694])).
% 2.44/2.64 tff(11812,plain,
% 2.44/2.64 (r(elem!1, z)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[1143, 11811, 5701])).
% 2.44/2.64 tff(11813,plain,
% 2.44/2.64 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[5804, 11695])).
% 2.44/2.64 tff(11814,plain,
% 2.44/2.64 (~(s(s(elem!1)) = s(s(s(z))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[421, 11813])).
% 2.44/2.64 tff(11815,plain,
% 2.44/2.64 (~r(s(s(s(z))), elem!1)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[11058, 11813, 10595, 5365])).
% 2.44/2.64 tff(11816,plain,
% 2.44/2.64 (b(s(s(s(z))), elem!1)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[647, 11807, 11815])).
% 2.44/2.64 tff(11817,plain,
% 2.44/2.64 (~b(s(s(s(z))), s(z))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[7339, 246, 11810, 11712, 11816])).
% 2.44/2.64 tff(11818,plain,
% 2.44/2.64 (r(s(s(s(z))), s(z))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[52, 11817])).
% 2.44/2.64 tff(11819,plain,
% 2.44/2.64 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[7762, 11818, 11726])).
% 2.44/2.64 tff(11820,plain,
% 2.44/2.64 (b(s(s(elem!1)), s(s(s(z))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[454, 11819, 11814])).
% 2.44/2.64 tff(11821,plain,
% 2.44/2.64 (~b(z, s(s(s(z))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[7313, 246, 11712, 10599, 11694, 11816, 11820])).
% 2.44/2.64 tff(11822,plain,
% 2.44/2.64 (r(z, s(s(s(z))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[6165, 11821])).
% 2.44/2.64 tff(11823,plain,
% 2.44/2.64 (~r(s(z), z)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[10064, 11822, 11807, 11712, 11812, 11808, 5365])).
% 2.44/2.64 tff(11824,plain,
% 2.44/2.64 (b(s(z), z)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[1069, 11823])).
% 2.44/2.64 tff(11825,plain,
% 2.44/2.64 (~r(elem!1, s(s(s(z))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[2254, 11822, 11812])).
% 2.44/2.64 tff(11826,plain,
% 2.44/2.64 (b(elem!1, s(s(s(z))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[470, 11825, 11808])).
% 2.44/2.64 tff(11827,plain,
% 2.44/2.64 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[4248, 183, 11726, 11818])).
% 2.44/2.64 tff(11828,plain,
% 2.44/2.64 (b(s(s(s(z))), s(s(elem!1)))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[689, 11827, 11813])).
% 2.44/2.64 tff(11829,plain,
% 2.44/2.64 (~b(s(z), s(s(s(z))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[9852, 246, 11810, 11712, 11816])).
% 2.44/2.64 tff(11830,plain,
% 2.44/2.64 (r(s(z), s(s(s(z))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[1291, 11829])).
% 2.44/2.64 tff(11831,plain,
% 2.44/2.64 (~(s(s(elem!1)) = elem!1)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[2130, 11725, 11712])).
% 2.44/2.64 tff(11832,plain,
% 2.44/2.64 (~(elem!1 = s(s(elem!1)))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[5450, 11831])).
% 2.44/2.64 tff(11833,plain,
% 2.44/2.64 (~b(elem!1, s(s(elem!1)))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[4335, 11828, 10599, 11816, 11712, 11694])).
% 2.44/2.64 tff(11834,plain,
% 2.44/2.64 (r(elem!1, s(s(elem!1)))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[1268, 11833, 11832])).
% 2.44/2.64 tff(11835,plain,
% 2.44/2.64 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[6281, 11813])).
% 2.44/2.64 tff(11836,plain,
% 2.44/2.64 ((~(s(s(elem!1)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(elem!1))))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[1825])).
% 2.44/2.64 tff(11837,plain,
% 2.44/2.64 (r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.44/2.64 inference(symmetry,[status(thm)],[7216])).
% 2.44/2.64 tff(11838,plain,
% 2.44/2.64 ((~b(s(s(elem!1)), s(s(s(s(z)))))) <=> (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z))))))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[7199])).
% 2.44/2.64 tff(11839,plain,
% 2.44/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(11840,plain,
% 2.44/2.64 (((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(11841,plain,
% 2.44/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[11840])).
% 2.44/2.64 tff(11842,plain,
% 2.44/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.44/2.64 inference(transitivity,[status(thm)],[11841, 11839])).
% 2.44/2.64 tff(11843,plain,
% 2.44/2.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.44/2.64 inference(quant_inst,[status(thm)],[])).
% 2.44/2.64 tff(11844,plain,
% 2.44/2.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[11843, 11842])).
% 2.44/2.64 tff(11845,plain,
% 2.44/2.64 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[11844, 246, 2002, 3697, 963, 1833])).
% 2.44/2.64 tff(11846,plain,
% 2.44/2.64 (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z)))))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[11845, 11838])).
% 2.44/2.64 tff(11847,plain,
% 2.44/2.64 (r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z)))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[7230, 11846, 7215])).
% 2.44/2.64 tff(11848,plain,
% 2.44/2.64 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[11847, 11837])).
% 2.44/2.64 tff(11849,plain,
% 2.44/2.64 (r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[1897, 10491])).
% 2.44/2.64 tff(11850,plain,
% 2.44/2.64 (r(elem!1, s(s(s(s(z)))))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[11849, 10488])).
% 2.44/2.64 tff(11851,plain,
% 2.44/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(11852,plain,
% 2.44/2.64 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(11853,plain,
% 2.44/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[11852])).
% 2.44/2.64 tff(11854,plain,
% 2.44/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.44/2.65 inference(transitivity,[status(thm)],[11853, 11851])).
% 2.44/2.65 tff(11855,plain,
% 2.44/2.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), elem!1)))),
% 2.44/2.65 inference(quant_inst,[status(thm)],[])).
% 2.44/2.65 tff(11856,plain,
% 2.44/2.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[11855, 11854])).
% 2.44/2.65 tff(11857,plain,
% 2.44/2.65 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[11856, 183, 216, 11850])).
% 2.44/2.65 tff(11858,plain,
% 2.44/2.65 ($false),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[11857, 11848])).
% 2.44/2.65 tff(11859,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~(s(s(s(s(s(elem!1))))) = elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.65 tff(11860,plain,
% 2.44/2.65 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[11859, 1833, 216, 2002, 3697, 963])).
% 2.44/2.65 tff(11861,assumption,(s(s(elem!1)) = s(s(s(s(z))))), introduced(assumption)).
% 2.44/2.65 tff(11862,plain,
% 2.44/2.65 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(z)))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[11861])).
% 2.44/2.65 tff(11863,plain,
% 2.44/2.65 (s(elem!1) = s(s(s(z)))),
% 2.44/2.65 inference(transitivity,[status(thm)],[108, 11862, 1491])).
% 2.44/2.65 tff(11864,plain,
% 2.44/2.65 (r(s(s(s(s(s(elem!1))))), s(elem!1)) <=> r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[11863])).
% 2.44/2.65 tff(11865,plain,
% 2.44/2.65 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 2.44/2.65 inference(symmetry,[status(thm)],[11862])).
% 2.44/2.65 tff(11866,plain,
% 2.44/2.65 (s(s(s(z))) = s(elem!1)),
% 2.44/2.65 inference(transitivity,[status(thm)],[1492, 11865, 92])).
% 2.44/2.65 tff(11867,plain,
% 2.44/2.65 ((s(s(s(s(s(elem!1))))) = s(s(s(z)))) <=> (s(s(s(s(s(elem!1))))) = s(elem!1))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[11866])).
% 2.44/2.65 tff(11868,plain,
% 2.44/2.65 ((~(s(s(s(s(s(elem!1))))) = s(s(s(z))))) <=> (~(s(s(s(s(s(elem!1))))) = s(elem!1)))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[11867])).
% 2.44/2.65 tff(11869,plain,
% 2.44/2.65 (~(s(s(s(s(s(elem!1))))) = s(elem!1))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[1622, 11868])).
% 2.44/2.65 tff(11870,plain,
% 2.44/2.65 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[11861])).
% 2.44/2.65 tff(11871,plain,
% 2.44/2.65 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.44/2.65 inference(symmetry,[status(thm)],[11870])).
% 2.44/2.65 tff(11872,plain,
% 2.44/2.65 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[11866, 11861])).
% 2.44/2.65 tff(11873,plain,
% 2.44/2.65 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.44/2.65 inference(transitivity,[status(thm)],[11872, 11871])).
% 2.44/2.65 tff(11874,plain,
% 2.44/2.65 (b(s(elem!1), s(s(elem!1)))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[4327, 11873])).
% 2.44/2.65 tff(11875,plain,
% 2.44/2.65 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(z))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[11863])).
% 2.44/2.65 tff(11876,plain,
% 2.44/2.65 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(elem!1))),
% 2.44/2.65 inference(symmetry,[status(thm)],[11875])).
% 2.44/2.65 tff(11877,plain,
% 2.44/2.65 (b(elem!1, s(elem!1))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[2002, 11876])).
% 2.44/2.65 tff(11878,plain,
% 2.44/2.65 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(s(z)))), s(elem!1))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[11861])).
% 2.44/2.65 tff(11879,plain,
% 2.44/2.65 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 2.44/2.65 inference(symmetry,[status(thm)],[11878])).
% 2.44/2.65 tff(11880,plain,
% 2.44/2.65 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[11863])).
% 2.44/2.65 tff(11881,plain,
% 2.44/2.65 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 2.44/2.65 inference(symmetry,[status(thm)],[11880])).
% 2.44/2.65 tff(11882,plain,
% 2.44/2.65 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(elem!1)), s(elem!1))),
% 2.44/2.65 inference(transitivity,[status(thm)],[11881, 11879])).
% 2.44/2.65 tff(11883,plain,
% 2.44/2.65 (b(s(s(elem!1)), s(elem!1))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[1833, 11882])).
% 2.44/2.65 tff(11884,plain,
% 2.44/2.65 ((s(s(s(s(s(elem!1))))) = s(s(elem!1))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(s(z)))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[11861])).
% 2.44/2.65 tff(11885,plain,
% 2.44/2.65 ((s(s(s(s(s(elem!1))))) = s(s(elem!1))) <=> (s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))),
% 2.44/2.65 inference(transitivity,[status(thm)],[11884, 1483])).
% 2.44/2.65 tff(11886,plain,
% 2.44/2.65 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.44/2.65 inference(symmetry,[status(thm)],[11885])).
% 2.44/2.65 tff(11887,plain,
% 2.44/2.65 ((~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(elem!1))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[11886])).
% 2.44/2.65 tff(11888,plain,
% 2.44/2.65 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[1501, 11887])).
% 2.44/2.65 tff(11889,plain,
% 2.44/2.65 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[11765, 11888, 236, 1056, 267, 216])).
% 2.44/2.65 tff(11890,plain,
% 2.44/2.65 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[86, 11889, 69])).
% 2.44/2.65 tff(11891,plain,
% 2.44/2.65 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[3612, 11890, 11883, 11877, 11874])).
% 2.44/2.65 tff(11892,plain,
% 2.44/2.65 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[1795, 11891, 11869])).
% 2.44/2.65 tff(11893,plain,
% 2.44/2.65 (r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[11892, 11864])).
% 2.44/2.65 tff(11894,plain,
% 2.44/2.65 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[6883, 11890, 236, 2001, 1056])).
% 2.44/2.65 tff(11895,plain,
% 2.44/2.65 (r(s(s(s(s(s(elem!1))))), s(z))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[6447, 11894])).
% 2.44/2.65 tff(11896,plain,
% 2.44/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(11897,plain,
% 2.44/2.65 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(z)))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(11898,plain,
% 2.44/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(z)))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[11897])).
% 2.44/2.65 tff(11899,plain,
% 2.44/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 2.44/2.65 inference(transitivity,[status(thm)],[11898, 11896])).
% 2.44/2.65 tff(11900,plain,
% 2.44/2.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 2.44/2.65 inference(quant_inst,[status(thm)],[])).
% 2.44/2.65 tff(11901,plain,
% 2.44/2.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(z)))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[11900, 11899])).
% 2.44/2.65 tff(11902,plain,
% 2.44/2.65 ($false),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[11901, 183, 6096, 11895, 11893])).
% 2.44/2.65 tff(11903,plain,((~(s(s(elem!1)) = s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (s(s(s(s(s(elem!1))))) = elem!1) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.65 tff(11904,plain,
% 2.44/2.65 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[11903, 11860, 236, 2001, 1056, 6096, 267, 216, 4327, 2002, 1833])).
% 2.44/2.65 tff(11905,plain,
% 2.44/2.65 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[11904, 11836])).
% 2.44/2.65 tff(11906,plain,
% 2.44/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(11907,plain,
% 2.44/2.65 (((~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(11908,plain,
% 2.44/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[11907])).
% 2.44/2.65 tff(11909,plain,
% 2.44/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.44/2.65 inference(transitivity,[status(thm)],[11908, 11906])).
% 2.44/2.65 tff(11910,plain,
% 2.44/2.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.44/2.65 inference(quant_inst,[status(thm)],[])).
% 2.44/2.65 tff(11911,plain,
% 2.44/2.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[11910, 11909])).
% 2.44/2.65 tff(11912,plain,
% 2.44/2.65 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[11911, 246, 2002, 3697, 963, 1833])).
% 2.44/2.65 tff(11913,plain,
% 2.44/2.65 ((s(s(s(s(z)))) = s(s(elem!1))) | r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[6521, 47, 11912])).
% 2.44/2.65 tff(11914,plain,
% 2.44/2.65 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[11913, 11905])).
% 2.44/2.65 tff(11915,plain,
% 2.44/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(11916,plain,
% 2.44/2.65 (((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(11917,plain,
% 2.44/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[11916])).
% 2.44/2.65 tff(11918,plain,
% 2.44/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.44/2.65 inference(transitivity,[status(thm)],[11917, 11915])).
% 2.44/2.65 tff(11919,plain,
% 2.44/2.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.44/2.65 inference(quant_inst,[status(thm)],[])).
% 2.44/2.65 tff(11920,plain,
% 2.44/2.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[11919, 11918])).
% 2.44/2.65 tff(11921,plain,
% 2.44/2.65 (~r(elem!1, s(s(s(s(z)))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[11920, 183, 602, 11914])).
% 2.44/2.65 tff(11922,plain,
% 2.44/2.65 (elem!1 = s(s(s(s(z))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[6008, 11921])).
% 2.44/2.65 tff(11923,plain,
% 2.44/2.65 (s(s(s(s(z)))) = elem!1),
% 2.44/2.65 inference(symmetry,[status(thm)],[11922])).
% 2.44/2.65 tff(11924,plain,
% 2.44/2.65 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(z))), elem!1)),
% 2.44/2.65 inference(monotonicity,[status(thm)],[11923])).
% 2.44/2.65 tff(11925,plain,
% 2.44/2.65 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 2.44/2.65 inference(symmetry,[status(thm)],[11924])).
% 2.44/2.65 tff(11926,plain,
% 2.44/2.65 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[3697, 11925])).
% 2.44/2.65 tff(11927,plain,
% 2.44/2.65 (b(s(s(s(s(s(elem!1))))), elem!1) <=> b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[11922])).
% 2.44/2.65 tff(11928,plain,
% 2.44/2.65 ((~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(elem!1))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[1534])).
% 2.44/2.65 tff(11929,plain,
% 2.44/2.65 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(elem!1)))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[3813])).
% 2.44/2.65 tff(11930,plain,
% 2.44/2.65 (s(s(s(s(elem!1)))) = s(elem!1)),
% 2.44/2.65 inference(transitivity,[status(thm)],[326, 11929, 92])).
% 2.44/2.65 tff(11931,plain,
% 2.44/2.65 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(elem!1))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[11930])).
% 2.44/2.65 tff(11932,plain,
% 2.44/2.65 (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[3813])).
% 2.44/2.65 tff(11933,plain,
% 2.44/2.65 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))),
% 2.44/2.65 inference(transitivity,[status(thm)],[11932, 352, 11931, 343, 8709])).
% 2.44/2.65 tff(11934,plain,
% 2.44/2.65 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z)))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[6709, 3812, 6330])).
% 2.44/2.65 tff(11935,plain,
% 2.44/2.65 ($false),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[11934, 11933])).
% 2.44/2.65 tff(11936,plain,((~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))) | (~(elem!1 = s(s(s(s(z)))))) | (s(s(s(elem!1))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.65 tff(11937,plain,
% 2.44/2.65 (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[11936, 11922, 6330])).
% 2.44/2.65 tff(11938,plain,
% 2.44/2.65 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[11937, 11928])).
% 2.44/2.65 tff(11939,plain,
% 2.44/2.65 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[11765, 11938, 236, 1056, 267, 216])).
% 2.44/2.65 tff(11940,plain,
% 2.44/2.65 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[86, 11939, 11860])).
% 2.44/2.65 tff(11941,plain,
% 2.44/2.65 (b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[11940, 11927])).
% 2.44/2.65 tff(11942,plain,
% 2.44/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(11943,plain,
% 2.44/2.65 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))) <=> ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(11944,plain,
% 2.44/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[11943])).
% 2.44/2.65 tff(11945,plain,
% 2.44/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 2.44/2.65 inference(transitivity,[status(thm)],[11944, 11942])).
% 2.44/2.65 tff(11946,plain,
% 2.44/2.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 2.44/2.65 inference(quant_inst,[status(thm)],[])).
% 2.44/2.65 tff(11947,plain,
% 2.44/2.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[11946, 11945])).
% 2.44/2.65 tff(11948,plain,
% 2.44/2.65 ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[11947, 246, 11941, 1833])).
% 2.44/2.65 tff(11949,plain,
% 2.44/2.65 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[11948, 11926])).
% 2.44/2.65 tff(11950,plain,
% 2.44/2.65 (r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[1626, 11949])).
% 2.44/2.65 tff(11951,plain,
% 2.44/2.65 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[6883, 11940, 236, 2001, 1056])).
% 2.44/2.65 tff(11952,plain,
% 2.44/2.65 (r(s(s(s(s(s(elem!1))))), s(z))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[6447, 11951])).
% 2.44/2.65 tff(11953,plain,
% 2.44/2.65 ($false),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[6767, 183, 430, 11952, 11950])).
% 2.44/2.65 tff(11954,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.65 tff(11955,plain,
% 2.44/2.65 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[11954, 11818, 11816, 11694, 11712, 11824, 5365, 10595, 11835, 11834, 11830, 11828, 11826, 11820])).
% 2.44/2.65 tff(11956,plain,
% 2.44/2.65 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[1702, 11955])).
% 2.44/2.65 tff(11957,plain,
% 2.44/2.65 (~r(s(s(s(s(z)))), s(z))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[8491, 11956, 11818])).
% 2.44/2.65 tff(11958,plain,
% 2.44/2.65 (b(s(s(s(s(z)))), s(z))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[6103, 11957])).
% 2.44/2.65 tff(11959,plain,
% 2.44/2.65 (~b(s(s(s(s(z)))), z)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[8269, 11958, 11694, 11824])).
% 2.44/2.65 tff(11960,plain,
% 2.44/2.65 (r(s(s(s(s(z)))), z)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[6040, 11959])).
% 2.44/2.65 tff(11961,plain,
% 2.44/2.65 ($false),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[8737, 183, 5365, 11822, 11956, 11960])).
% 2.44/2.65 tff(11962,plain,(b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.65 tff(11963,plain,
% 2.44/2.65 (b(z, elem!1) <=> b(z, s(z))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[202])).
% 2.44/2.65 tff(11964,plain,
% 2.44/2.65 (b(z, s(z)) <=> b(z, elem!1)),
% 2.44/2.65 inference(symmetry,[status(thm)],[11963])).
% 2.44/2.65 tff(11965,plain,
% 2.44/2.65 ((~b(z, s(z))) <=> (~b(z, elem!1))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[11964])).
% 2.44/2.65 tff(11966,plain,
% 2.44/2.65 (~b(z, elem!1)),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[54, 11965])).
% 2.44/2.65 tff(11967,plain,
% 2.44/2.65 ($false),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[2239, 11966])).
% 2.44/2.65 tff(11968,plain,((~(elem!1 = s(z))) | (~b(z, elem!1)) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.65 tff(11969,plain,
% 2.44/2.65 ((~(elem!1 = s(z))) | b(z, s(z))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[11968, 11962])).
% 2.44/2.65 tff(11970,plain,
% 2.44/2.65 (~(elem!1 = s(z))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[11969, 54])).
% 2.44/2.65 tff(11971,plain,
% 2.44/2.65 (~(s(z) = elem!1)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[9, 11970])).
% 2.44/2.65 tff(11972,plain,
% 2.44/2.65 (r(z, s(s(elem!1)))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[264, 259])).
% 2.44/2.65 tff(11973,plain,
% 2.44/2.65 (~r(s(z), s(s(elem!1)))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[6407, 11972, 171])).
% 2.44/2.66 tff(11974,plain,
% 2.44/2.66 (b(s(z), s(s(elem!1)))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[233, 11973])).
% 2.44/2.66 tff(11975,plain,
% 2.44/2.66 (b(z, s(s(elem!1))) <=> b(z, elem!1)),
% 2.44/2.66 inference(monotonicity,[status(thm)],[2125])).
% 2.44/2.66 tff(11976,plain,
% 2.44/2.66 (b(z, elem!1) <=> b(z, s(s(elem!1)))),
% 2.44/2.66 inference(symmetry,[status(thm)],[11975])).
% 2.44/2.66 tff(11977,plain,
% 2.44/2.66 (b(z, s(s(elem!1)))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[2239, 11976])).
% 2.44/2.66 tff(11978,plain,
% 2.44/2.66 ($false),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[259, 11977])).
% 2.44/2.66 tff(11979,plain,((~(s(s(elem!1)) = elem!1)) | b(z, s(s(elem!1))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.66 tff(11980,plain,
% 2.44/2.66 ((~(s(s(elem!1)) = elem!1)) | b(z, s(s(elem!1)))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[11979, 11962])).
% 2.44/2.66 tff(11981,plain,
% 2.44/2.66 (~(s(s(elem!1)) = elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[11980, 259])).
% 2.44/2.66 tff(11982,plain,
% 2.44/2.66 (~(s(s(elem!1)) = s(elem!1))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[5640, 11981])).
% 2.44/2.66 tff(11983,plain,
% 2.44/2.66 (~(elem!1 = s(s(elem!1)))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[5450, 11981])).
% 2.44/2.66 tff(11984,plain,
% 2.44/2.66 (b(s(s(elem!1)), elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[156, 11981, 2232])).
% 2.44/2.66 tff(11985,plain,
% 2.44/2.66 (r(elem!1, s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[214, 210, 3])).
% 2.44/2.66 tff(11986,plain,
% 2.44/2.66 (b(z, elem!1) <=> b(z, z)),
% 2.44/2.66 inference(monotonicity,[status(thm)],[1038])).
% 2.44/2.66 tff(11987,plain,
% 2.44/2.66 (b(z, z) <=> b(z, elem!1)),
% 2.44/2.66 inference(symmetry,[status(thm)],[11986])).
% 2.44/2.66 tff(11988,plain,
% 2.44/2.66 ((~b(z, z)) <=> (~b(z, elem!1))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[11987])).
% 2.44/2.66 tff(11989,plain,
% 2.44/2.66 ((~![X: $i] : (~b(X, X))) | (~b(z, z))),
% 2.44/2.66 inference(quant_inst,[status(thm)],[])).
% 2.44/2.66 tff(11990,plain,
% 2.44/2.66 (~b(z, z)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[11989, 5689])).
% 2.44/2.66 tff(11991,plain,
% 2.44/2.66 (~b(z, elem!1)),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[11990, 11988])).
% 2.44/2.66 tff(11992,plain,
% 2.44/2.66 ($false),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[2239, 11991])).
% 2.44/2.66 tff(11993,plain,((~(elem!1 = z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.66 tff(11994,plain,
% 2.44/2.66 (~(elem!1 = z)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[11993, 11962])).
% 2.44/2.66 tff(11995,plain,
% 2.44/2.66 (~r(s(s(elem!1)), s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[191, 171, 172])).
% 2.44/2.66 tff(11996,plain,
% 2.44/2.66 (b(s(s(elem!1)), s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[197, 11995])).
% 2.44/2.66 tff(11997,plain,
% 2.44/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(11998,plain,
% 2.44/2.66 (((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(11999,plain,
% 2.44/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z)))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[11998])).
% 2.44/2.66 tff(12000,plain,
% 2.44/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 2.44/2.66 inference(transitivity,[status(thm)],[11999, 11997])).
% 2.44/2.66 tff(12001,plain,
% 2.44/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 2.44/2.66 inference(quant_inst,[status(thm)],[])).
% 2.44/2.66 tff(12002,plain,
% 2.44/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z)))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[12001, 12000])).
% 2.44/2.66 tff(12003,plain,
% 2.44/2.66 ($false),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[12002, 246, 2239, 2353, 11996, 1044, 2362])).
% 2.44/2.66 tff(12004,plain,((~r(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (elem!1 = z) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.66 tff(12005,plain,
% 2.44/2.66 ((~r(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(z)))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[12004, 11994, 11962])).
% 2.44/2.66 tff(12006,plain,
% 2.44/2.66 (~b(s(z), elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[12005, 11985, 171, 2362, 172])).
% 2.44/2.66 tff(12007,plain,
% 2.44/2.66 (~r(elem!1, z)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[2351, 11985, 171])).
% 2.44/2.66 tff(12008,plain,
% 2.44/2.66 (b(elem!1, z) | r(elem!1, z)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[1143, 11994])).
% 2.44/2.66 tff(12009,plain,
% 2.44/2.66 (b(elem!1, z)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[12008, 12007])).
% 2.44/2.66 tff(12010,plain,
% 2.44/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(12011,plain,
% 2.44/2.66 (((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z)))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(12012,plain,
% 2.44/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[12011])).
% 2.44/2.66 tff(12013,plain,
% 2.44/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.44/2.66 inference(transitivity,[status(thm)],[12012, 12010])).
% 2.44/2.66 tff(12014,plain,
% 2.44/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))),
% 2.44/2.66 inference(quant_inst,[status(thm)],[])).
% 2.44/2.66 tff(12015,plain,
% 2.44/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[12014, 12013])).
% 2.44/2.66 tff(12016,plain,
% 2.44/2.66 (~b(z, s(s(s(z))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[12015, 246, 11962, 1051, 3697])).
% 2.44/2.66 tff(12017,plain,
% 2.44/2.66 (r(z, s(s(s(z))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[6165, 12016])).
% 2.44/2.66 tff(12018,plain,
% 2.44/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(12019,plain,
% 2.44/2.66 (((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(12020,plain,
% 2.44/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[12019])).
% 2.44/2.66 tff(12021,plain,
% 2.44/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)))),
% 2.44/2.66 inference(transitivity,[status(thm)],[12020, 12018])).
% 2.44/2.66 tff(12022,plain,
% 2.44/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.44/2.66 inference(quant_inst,[status(thm)],[])).
% 2.44/2.66 tff(12023,plain,
% 2.44/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[12022, 12021])).
% 2.44/2.66 tff(12024,plain,
% 2.44/2.66 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[12023, 246, 11962, 1051, 2362, 3697])).
% 2.44/2.66 tff(12025,plain,
% 2.44/2.66 (r(s(s(s(z))), s(s(elem!1)))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[689, 12024, 119])).
% 2.44/2.66 tff(12026,plain,
% 2.44/2.66 ($false),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[10424, 183, 266, 12025, 12017])).
% 2.44/2.66 tff(12027,plain,((~b(s(s(s(z))), elem!1)) | (~r(z, s(s(elem!1)))) | (s(s(s(z))) = s(s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.66 tff(12028,plain,
% 2.44/2.66 (~b(s(s(s(z))), elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[12027, 12009, 7736, 266, 2362])).
% 2.44/2.66 tff(12029,plain,
% 2.44/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(12030,plain,
% 2.44/2.66 (((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(12031,plain,
% 2.44/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[12030])).
% 2.44/2.66 tff(12032,plain,
% 2.44/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 2.44/2.66 inference(transitivity,[status(thm)],[12031, 12029])).
% 2.44/2.66 tff(12033,plain,
% 2.44/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.44/2.66 inference(quant_inst,[status(thm)],[])).
% 2.44/2.66 tff(12034,plain,
% 2.44/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[12033, 12032])).
% 2.44/2.66 tff(12035,plain,
% 2.44/2.66 (~b(s(s(elem!1)), s(elem!1))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[12034, 246, 11962, 1051, 2362, 1200])).
% 2.44/2.66 tff(12036,plain,
% 2.44/2.66 (r(s(s(elem!1)), s(elem!1))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[5644, 12035, 5642])).
% 2.44/2.66 tff(12037,plain,
% 2.44/2.66 (~b(s(elem!1), z)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[2961, 246, 11962, 1051, 1200])).
% 2.44/2.66 tff(12038,plain,
% 2.44/2.66 (r(s(elem!1), z)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[2581, 12037])).
% 2.44/2.66 tff(12039,plain,
% 2.44/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(12040,plain,
% 2.44/2.66 (((~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(12041,plain,
% 2.44/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[12040])).
% 2.44/2.66 tff(12042,plain,
% 2.44/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)))),
% 2.44/2.66 inference(transitivity,[status(thm)],[12041, 12039])).
% 2.44/2.66 tff(12043,plain,
% 2.44/2.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.44/2.66 inference(quant_inst,[status(thm)],[])).
% 2.44/2.66 tff(12044,plain,
% 2.44/2.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[12043, 12042])).
% 2.44/2.66 tff(12045,plain,
% 2.44/2.66 ($false),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[12044, 183, 172, 12038, 12036])).
% 2.44/2.66 tff(12046,plain,((~b(s(elem!1), elem!1)) | (~r(s(s(elem!1)), z)) | (s(s(elem!1)) = s(elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.66 tff(12047,plain,
% 2.44/2.66 (~b(s(elem!1), elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[12046, 12009, 5642, 172, 2362])).
% 2.44/2.66 tff(12048,plain,
% 2.44/2.66 (~r(s(s(elem!1)), s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[191, 172, 171])).
% 2.44/2.66 tff(12049,plain,
% 2.44/2.66 (b(s(s(elem!1)), s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[197, 12048])).
% 2.44/2.66 tff(12050,plain,
% 2.44/2.66 (r(s(z), elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[1034, 12006, 10])).
% 2.44/2.66 tff(12051,plain,
% 2.44/2.66 (~b(s(s(s(z))), elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[12027, 1051, 119, 266, 2362])).
% 2.44/2.66 tff(12052,plain,
% 2.44/2.66 ((~b(s(s(elem!1)), elem!1)) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[2388, 11962])).
% 2.44/2.66 tff(12053,plain,
% 2.44/2.66 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[12052, 5624, 2362, 1051])).
% 2.44/2.66 tff(12054,plain,
% 2.44/2.66 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[5677, 1673, 5267])).
% 2.44/2.66 tff(12055,plain,
% 2.44/2.66 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[1702, 12054])).
% 2.44/2.66 tff(12056,plain,
% 2.44/2.66 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[3545, 2628, 217])).
% 2.44/2.66 tff(12057,plain,
% 2.44/2.66 (s(s(s(s(s(elem!1))))) = elem!1),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[86, 12056, 82])).
% 2.44/2.66 tff(12058,plain,
% 2.44/2.66 (s(s(s(s(s(s(elem!1)))))) = s(elem!1)),
% 2.44/2.66 inference(monotonicity,[status(thm)],[12057])).
% 2.44/2.66 tff(12059,plain,
% 2.44/2.66 (s(s(s(s(s(s(s(elem!1))))))) = s(s(elem!1))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[12058])).
% 2.44/2.66 tff(12060,plain,
% 2.44/2.66 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(elem!1)))))))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[12059])).
% 2.44/2.66 tff(12061,plain,
% 2.44/2.66 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(s(elem!1))))))))),
% 2.44/2.66 inference(symmetry,[status(thm)],[12060])).
% 2.44/2.66 tff(12062,plain,
% 2.44/2.66 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(z)))))),
% 2.44/2.66 inference(transitivity,[status(thm)],[12061, 10601])).
% 2.44/2.66 tff(12063,plain,
% 2.44/2.66 (~r(s(z), s(s(elem!1)))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[6407, 266, 171])).
% 2.44/2.66 tff(12064,plain,
% 2.44/2.66 (b(s(z), s(s(elem!1)))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[233, 12063])).
% 2.44/2.66 tff(12065,plain,
% 2.44/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(12066,plain,
% 2.44/2.66 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(12067,plain,
% 2.44/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z)))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[12066])).
% 2.44/2.66 tff(12068,plain,
% 2.44/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))))),
% 2.44/2.66 inference(transitivity,[status(thm)],[12067, 12065])).
% 2.44/2.66 tff(12069,plain,
% 2.44/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.44/2.66 inference(quant_inst,[status(thm)],[])).
% 2.44/2.66 tff(12070,plain,
% 2.44/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z)))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[12069, 12068])).
% 2.44/2.66 tff(12071,plain,
% 2.44/2.66 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[12070, 246, 201, 12064, 2003])).
% 2.44/2.66 tff(12072,plain,
% 2.44/2.66 (r(s(s(s(z))), s(s(elem!1)))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[689, 12071, 119])).
% 2.44/2.66 tff(12073,plain,
% 2.44/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(12074,plain,
% 2.44/2.66 (((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(12075,plain,
% 2.44/2.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z))))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[12074])).
% 2.44/2.67 tff(12076,plain,
% 2.44/2.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 2.44/2.67 inference(transitivity,[status(thm)],[12075, 12073])).
% 2.44/2.67 tff(12077,plain,
% 2.44/2.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))),
% 2.44/2.67 inference(quant_inst,[status(thm)],[])).
% 2.44/2.67 tff(12078,plain,
% 2.44/2.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[12077, 12076])).
% 2.44/2.67 tff(12079,plain,
% 2.44/2.67 (~r(s(s(s(z))), z)),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[12078, 183, 171, 266, 12072])).
% 2.44/2.67 tff(12080,plain,
% 2.44/2.67 (b(s(s(s(z))), z)),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[995, 12079])).
% 2.44/2.67 tff(12081,plain,
% 2.44/2.67 (~r(z, s(s(s(z))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[10424, 183, 266, 12072])).
% 2.44/2.67 tff(12082,plain,
% 2.44/2.67 (b(z, s(s(s(z))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[6165, 12081])).
% 2.44/2.67 tff(12083,plain,
% 2.44/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(12084,plain,
% 2.44/2.67 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(12085,plain,
% 2.44/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[12084])).
% 2.44/2.67 tff(12086,plain,
% 2.44/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.44/2.67 inference(transitivity,[status(thm)],[12085, 12083])).
% 2.44/2.67 tff(12087,plain,
% 2.44/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))),
% 2.44/2.67 inference(quant_inst,[status(thm)],[])).
% 2.44/2.67 tff(12088,plain,
% 2.44/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[12087, 12086])).
% 2.44/2.67 tff(12089,plain,
% 2.44/2.67 (~b(elem!1, s(s(s(z))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[12088, 246, 1051, 2003, 12082, 12080])).
% 2.44/2.67 tff(12090,plain,
% 2.44/2.67 (r(elem!1, s(s(s(z))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[470, 12089, 2602])).
% 2.44/2.67 tff(12091,plain,
% 2.44/2.67 (~r(s(s(s(s(z)))), elem!1)),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[2618, 183, 12090, 2593])).
% 2.44/2.67 tff(12092,plain,
% 2.44/2.67 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(z)))) = elem!1)),
% 2.44/2.67 inference(monotonicity,[status(thm)],[12057])).
% 2.44/2.67 tff(12093,plain,
% 2.44/2.67 ((~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[12092])).
% 2.44/2.67 tff(12094,plain,
% 2.44/2.67 (~(s(s(s(s(z)))) = elem!1)),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[1501, 12093])).
% 2.44/2.67 tff(12095,plain,
% 2.44/2.67 (b(s(s(s(s(z)))), elem!1)),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[2442, 47, 12094, 12091])).
% 2.44/2.67 tff(12096,plain,
% 2.44/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(12097,plain,
% 2.44/2.67 (((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(12098,plain,
% 2.44/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1))))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[12097])).
% 2.44/2.67 tff(12099,plain,
% 2.44/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.44/2.67 inference(transitivity,[status(thm)],[12098, 12096])).
% 2.44/2.67 tff(12100,plain,
% 2.44/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.44/2.67 inference(quant_inst,[status(thm)],[])).
% 2.44/2.67 tff(12101,plain,
% 2.44/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[12100, 12099])).
% 2.44/2.67 tff(12102,plain,
% 2.44/2.67 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[12101, 246, 11962, 1051, 2362, 12095])).
% 2.44/2.67 tff(12103,plain,
% 2.44/2.67 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[3488, 246, 201, 12064, 2003])).
% 2.44/2.67 tff(12104,plain,
% 2.44/2.67 (r(s(s(elem!1)), s(s(s(z))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[454, 12103, 4234])).
% 2.44/2.67 tff(12105,plain,
% 2.44/2.67 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[6550, 183, 12104, 2593])).
% 2.44/2.67 tff(12106,plain,
% 2.44/2.67 ((s(s(s(s(z)))) = s(s(elem!1))) | b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[6521, 47, 12105])).
% 2.44/2.67 tff(12107,plain,
% 2.44/2.67 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[12106, 12102])).
% 2.44/2.67 tff(12108,plain,
% 2.44/2.67 (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(z))))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[12107, 12062])).
% 2.44/2.67 tff(12109,plain,
% 2.44/2.67 (~(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(z)))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[7214, 12057])).
% 2.44/2.67 tff(12110,plain,
% 2.44/2.67 ($false),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[12109, 12108])).
% 2.44/2.67 tff(12111,plain,((~b(s(s(s(z))), s(z))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (s(s(s(z))) = s(s(elem!1))) | (~b(s(s(elem!1)), s(z))) | b(s(s(s(s(s(elem!1))))), elem!1) | (~r(s(z), elem!1)) | b(s(s(s(z))), elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.67 tff(12112,plain,
% 2.44/2.67 (~b(s(s(s(z))), s(z))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[12111, 82, 2362, 2593, 171, 266, 119, 201, 1051, 217, 1, 210])).
% 2.44/2.67 tff(12113,plain,
% 2.44/2.67 (r(s(s(s(z))), s(z))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[52, 12112])).
% 2.44/2.67 tff(12114,plain,
% 2.44/2.67 (~r(s(s(s(z))), elem!1)),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[2282, 12113, 2232, 210])).
% 2.44/2.67 tff(12115,plain,
% 2.44/2.67 (s(s(s(z))) = elem!1),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[647, 12114, 1])).
% 2.44/2.67 tff(12116,plain,
% 2.44/2.67 (r(s(elem!1), elem!1)),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[5548, 12115, 2593])).
% 2.44/2.67 tff(12117,plain,
% 2.44/2.67 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[7041, 12115])).
% 2.44/2.67 tff(12118,plain,
% 2.44/2.67 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[86, 12117, 82])).
% 2.44/2.67 tff(12119,plain,
% 2.44/2.67 (b(s(elem!1), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[5379])).
% 2.44/2.67 tff(12120,plain,
% 2.44/2.67 (b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))) <=> b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 2.44/2.67 inference(symmetry,[status(thm)],[12119])).
% 2.44/2.67 tff(12121,plain,
% 2.44/2.67 (r(s(elem!1), s(s(s(s(s(elem!1)))))) <=> r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[5379])).
% 2.44/2.67 tff(12122,plain,
% 2.44/2.67 ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) <=> (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[12121])).
% 2.44/2.67 tff(12123,plain,
% 2.44/2.67 (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[392, 12122])).
% 2.44/2.67 tff(12124,plain,
% 2.44/2.67 (b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[1506, 12123])).
% 2.44/2.67 tff(12125,plain,
% 2.44/2.67 (b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[12124, 12120])).
% 2.44/2.67 tff(12126,plain,
% 2.44/2.67 (b(s(z), s(elem!1))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[6070, 11130])).
% 2.44/2.67 tff(12127,plain,
% 2.44/2.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(12128,plain,
% 2.44/2.67 (((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(z), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(12129,plain,
% 2.44/2.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(z), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1))))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[12128])).
% 2.44/2.67 tff(12130,plain,
% 2.44/2.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(z), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.44/2.67 inference(transitivity,[status(thm)],[12129, 12127])).
% 2.44/2.67 tff(12131,plain,
% 2.44/2.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 2.44/2.67 inference(quant_inst,[status(thm)],[])).
% 2.44/2.67 tff(12132,plain,
% 2.44/2.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[12131, 12130])).
% 2.44/2.67 tff(12133,plain,
% 2.44/2.67 (~r(s(z), s(s(s(s(s(elem!1))))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[12132, 183, 217, 333])).
% 2.44/2.67 tff(12134,plain,
% 2.44/2.67 ((s(z) = s(s(s(s(s(elem!1)))))) | b(s(z), s(s(s(s(s(elem!1))))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[6253, 47, 12133])).
% 2.44/2.67 tff(12135,plain,
% 2.44/2.67 (b(s(z), s(s(s(s(s(elem!1))))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[12134, 6243])).
% 2.44/2.67 tff(12136,plain,
% 2.44/2.67 ((s(s(s(s(s(elem!1))))) = s(elem!1)) <=> (s(s(s(s(s(elem!1))))) = s(s(s(s(z)))))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[5379])).
% 2.44/2.67 tff(12137,plain,
% 2.44/2.67 ((s(s(s(s(s(elem!1))))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))),
% 2.44/2.67 inference(transitivity,[status(thm)],[12136, 1483])).
% 2.44/2.67 tff(12138,plain,
% 2.44/2.67 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(elem!1))),
% 2.44/2.67 inference(symmetry,[status(thm)],[12137])).
% 2.44/2.67 tff(12139,plain,
% 2.44/2.67 ((~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(s(elem!1))))) = s(elem!1)))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[12138])).
% 2.44/2.67 tff(12140,plain,
% 2.44/2.67 (~(s(s(s(s(s(elem!1))))) = s(elem!1))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[1501, 12139])).
% 2.44/2.67 tff(12141,plain,
% 2.44/2.67 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[1795, 2749, 12140])).
% 2.44/2.67 tff(12142,plain,
% 2.44/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(12143,plain,
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% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(12144,plain,
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% 2.44/2.67 inference(monotonicity,[status(thm)],[12143])).
% 2.44/2.67 tff(12145,plain,
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% 2.44/2.67 inference(transitivity,[status(thm)],[12144, 12142])).
% 2.44/2.67 tff(12146,plain,
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% 2.44/2.67 inference(quant_inst,[status(thm)],[])).
% 2.44/2.67 tff(12147,plain,
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% 2.44/2.67 inference(modus_ponens,[status(thm)],[12146, 12145])).
% 2.44/2.67 tff(12148,plain,
% 2.44/2.67 ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(elem!1)))))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[12147, 246, 12141, 12135])).
% 2.44/2.67 tff(12149,plain,
% 2.44/2.67 (~b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[12148, 12126])).
% 2.44/2.67 tff(12150,plain,
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% 2.44/2.67 inference(unit_resolution,[status(thm)],[12149, 12125])).
% 2.44/2.67 tff(12151,plain,((~r(s(elem!1), elem!1)) | (~(s(s(s(z))) = elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.67 tff(12152,plain,
% 2.44/2.67 ($false),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[12151, 12118, 12116, 217, 12115])).
% 2.44/2.67 tff(12153,plain,(b(s(s(s(s(s(elem!1))))), elem!1) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | b(s(s(s(z))), elem!1) | r(s(s(elem!1)), elem!1) | b(elem!1, s(z)) | (~b(s(s(elem!1)), elem!1)) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (s(s(s(z))) = s(s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.67 tff(12154,plain,
% 2.44/2.67 ($false),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[12153, 12055, 12053, 12051, 217, 2232, 210, 2362, 171, 266, 119, 201, 1051])).
% 2.44/2.67 tff(12155,plain,((~(s(s(s(z))) = elem!1)) | (~r(s(z), elem!1)) | r(s(s(elem!1)), elem!1) | b(elem!1, s(z)) | (~b(s(s(elem!1)), elem!1)) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (s(s(s(z))) = s(s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.67 tff(12156,plain,
% 2.44/2.67 (~(s(s(s(z))) = elem!1)),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[12155, 12050, 2232, 210, 2362, 171, 266, 7736, 12049, 12009, 12047])).
% 2.44/2.67 tff(12157,plain,
% 2.44/2.67 (r(s(s(s(z))), elem!1)),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[647, 12156, 12028])).
% 2.44/2.67 tff(12158,plain,
% 2.44/2.67 (~r(s(s(s(z))), s(z))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[2713, 12157, 2232, 12006])).
% 2.44/2.67 tff(12159,plain,
% 2.44/2.67 (b(s(s(s(z))), s(z))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[52, 12158])).
% 2.44/2.67 tff(12160,plain,
% 2.44/2.67 (~r(s(s(s(z))), s(z))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[2713, 634, 2232, 1445])).
% 2.44/2.67 tff(12161,plain,
% 2.44/2.67 (b(s(s(s(z))), s(z))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[52, 12160])).
% 2.44/2.67 tff(12162,plain,
% 2.44/2.67 (~b(z, s(s(s(z))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[7450, 2328, 171, 1833, 12161])).
% 2.44/2.67 tff(12163,plain,
% 2.44/2.67 (r(z, s(s(s(z))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[6165, 12162])).
% 2.44/2.67 tff(12164,plain,
% 2.44/2.67 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[12070, 246, 201, 12064, 12161])).
% 2.44/2.67 tff(12165,plain,
% 2.44/2.67 (r(s(s(s(z))), s(s(elem!1)))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[689, 12164, 119])).
% 2.44/2.67 tff(12166,plain,
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% 2.44/2.67 inference(unit_resolution,[status(thm)],[10424, 183, 266, 12165, 12163])).
% 2.44/2.67 tff(12167,plain,((~r(s(s(s(z))), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (s(s(s(z))) = s(s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | r(s(s(elem!1)), elem!1) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.67 tff(12168,plain,
% 2.44/2.67 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[12167, 12157, 171, 266, 7736, 12049, 12050, 2232, 12006])).
% 2.44/2.67 tff(12169,plain,
% 2.44/2.67 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[1702, 12168])).
% 2.44/2.67 tff(12170,plain,
% 2.44/2.67 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[12153, 1, 2593, 217, 2232, 210, 2362, 171, 266, 119, 12049, 1051])).
% 2.44/2.67 tff(12171,plain,
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% 2.44/2.67 inference(unit_resolution,[status(thm)],[12052, 12170, 2362, 1051])).
% 2.44/2.67 tff(12172,plain,
% 2.44/2.67 (~(s(s(s(z))) = elem!1)),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[5623, 12171])).
% 2.44/2.67 tff(12173,plain,
% 2.44/2.67 (r(s(s(s(z))), elem!1)),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[647, 12172, 1])).
% 2.44/2.67 tff(12174,plain,
% 2.44/2.67 (~r(s(s(s(z))), s(z))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[2713, 12173, 2232, 1445])).
% 2.44/2.67 tff(12175,plain,
% 2.44/2.67 (b(s(s(s(z))), s(z))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[52, 12174])).
% 2.44/2.67 tff(12176,plain,
% 2.44/2.67 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[3488, 246, 12049, 12064, 12175])).
% 2.44/2.67 tff(12177,plain,
% 2.44/2.67 (r(s(s(elem!1)), s(s(s(z))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[454, 12176, 4234])).
% 2.44/2.67 tff(12178,plain,
% 2.44/2.67 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[6550, 183, 12177, 2593])).
% 2.44/2.67 tff(12179,plain,
% 2.44/2.67 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[12171])).
% 2.44/2.67 tff(12180,plain,
% 2.44/2.67 ((~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(z)))) = s(s(elem!1))))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[12179])).
% 2.44/2.67 tff(12181,plain,
% 2.44/2.67 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[1501, 12180])).
% 2.44/2.67 tff(12182,plain,
% 2.44/2.67 (b(s(s(s(s(z)))), s(s(elem!1)))),
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% 2.44/2.67 tff(12183,plain,
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% 2.44/2.67 tff(12185,plain,
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% 2.44/2.67 inference(unit_resolution,[status(thm)],[647, 12184, 1])).
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% 2.44/2.67 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[3545, 12185, 217])).
% 2.44/2.67 tff(12187,plain,
% 2.44/2.67 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[3488, 246, 12049, 12064, 10310])).
% 2.44/2.67 tff(12188,plain,
% 2.44/2.67 (r(s(s(elem!1)), s(s(s(z))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[454, 12187, 4234])).
% 2.44/2.67 tff(12189,plain,
% 2.44/2.67 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[12070, 246, 12049, 12064, 10310])).
% 2.44/2.67 tff(12190,plain,
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% 2.44/2.67 inference(unit_resolution,[status(thm)],[689, 12189, 119])).
% 2.44/2.67 tff(12191,plain,
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% 2.44/2.67 tff(12192,plain,
% 2.44/2.67 (b(s(s(s(z))), z)),
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% 2.44/2.67 tff(12193,plain,
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% 2.44/2.67 tff(12194,plain,
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% 2.44/2.67 tff(12195,plain,
% 2.44/2.67 (~b(elem!1, s(s(s(z))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[12088, 246, 1051, 10310, 12194, 12192])).
% 2.44/2.67 tff(12196,plain,
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% 2.44/2.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(12198,plain,
% 2.44/2.67 (((~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
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% 2.44/2.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[12198])).
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% 2.44/2.67 inference(transitivity,[status(thm)],[12199, 12197])).
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% 2.44/2.67 inference(quant_inst,[status(thm)],[])).
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% 2.44/2.67 inference(modus_ponens,[status(thm)],[12201, 12200])).
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% 2.44/2.67 (~r(elem!1, s(s(elem!1)))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[12202, 183, 172, 12196, 12188])).
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% 2.44/2.68 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[344])).
% 2.44/2.68 tff(12208,plain,
% 2.44/2.68 ((~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(z)))) = s(s(elem!1))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[12207])).
% 2.44/2.68 tff(12209,plain,
% 2.44/2.68 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[1501, 12208])).
% 2.44/2.68 tff(12210,assumption,(~r(s(s(s(s(z)))), s(s(elem!1)))), introduced(assumption)).
% 2.44/2.68 tff(12211,plain,
% 2.44/2.68 ((s(s(s(s(z)))) = s(s(elem!1))) | b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[6521, 47, 12210])).
% 2.44/2.68 tff(12212,plain,
% 2.44/2.68 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[12211, 12209])).
% 2.44/2.68 tff(12213,plain,
% 2.44/2.68 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[6283])).
% 2.44/2.68 tff(12214,plain,
% 2.44/2.68 ((s(s(s(s(z)))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 2.44/2.68 inference(commutativity,[status(thm)],[])).
% 2.44/2.68 tff(12215,plain,
% 2.44/2.68 ((s(s(s(s(z)))) = elem!1) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[6283])).
% 2.44/2.68 tff(12216,plain,
% 2.44/2.68 ((s(s(s(s(z)))) = elem!1) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 2.44/2.68 inference(transitivity,[status(thm)],[12215, 12214])).
% 2.44/2.68 tff(12217,plain,
% 2.44/2.68 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 2.44/2.68 inference(symmetry,[status(thm)],[12216])).
% 2.44/2.68 tff(12218,plain,
% 2.44/2.68 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[12217])).
% 2.44/2.68 tff(12219,plain,
% 2.44/2.68 (~(s(s(s(s(z)))) = elem!1)),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[6330, 12218])).
% 2.44/2.68 tff(12220,assumption,(~r(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 2.44/2.68 tff(12221,plain,
% 2.44/2.68 ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[2442, 47, 12220])).
% 2.44/2.68 tff(12222,plain,
% 2.44/2.68 (b(s(s(s(s(z)))), elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[12221, 12219])).
% 2.44/2.68 tff(12223,plain,
% 2.44/2.68 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[12222, 12213])).
% 2.44/2.68 tff(12224,plain,
% 2.44/2.68 (b(elem!1, s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[6283])).
% 2.44/2.68 tff(12225,plain,
% 2.44/2.68 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[947, 12224])).
% 2.44/2.68 tff(12226,plain,
% 2.44/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.44/2.68 inference(rewrite,[status(thm)],[])).
% 2.44/2.68 tff(12227,plain,
% 2.44/2.68 (((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.44/2.68 inference(rewrite,[status(thm)],[])).
% 2.44/2.68 tff(12228,plain,
% 2.44/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[12227])).
% 2.44/2.68 tff(12229,plain,
% 2.44/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.44/2.68 inference(transitivity,[status(thm)],[12228, 12226])).
% 2.44/2.68 tff(12230,plain,
% 2.44/2.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.44/2.68 inference(quant_inst,[status(thm)],[])).
% 2.44/2.68 tff(12231,plain,
% 2.44/2.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[12230, 12229])).
% 2.44/2.68 tff(12232,plain,
% 2.44/2.68 ($false),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[12231, 246, 201, 235, 12225, 12223, 12212])).
% 2.44/2.68 tff(12233,plain,((~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | r(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), s(s(elem!1))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~b(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.68 tff(12234,plain,
% 2.44/2.68 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[12233, 12206, 12064, 12049, 12205, 6705, 12204])).
% 2.44/2.68 tff(12235,plain,
% 2.44/2.68 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[12052, 12234, 2362, 1051])).
% 2.44/2.68 tff(12236,plain,
% 2.44/2.68 (s(s(s(s(s(elem!1))))) = elem!1),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[86, 12235, 12186])).
% 2.44/2.68 tff(12237,plain,
% 2.44/2.68 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(z)))) = elem!1)),
% 2.44/2.68 inference(monotonicity,[status(thm)],[12236])).
% 2.44/2.68 tff(12238,plain,
% 2.44/2.68 ((~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[12237])).
% 2.44/2.68 tff(12239,plain,
% 2.44/2.68 (~(s(s(s(s(z)))) = elem!1)),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[1501, 12238])).
% 2.44/2.68 tff(12240,plain,
% 2.44/2.68 ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[2442, 47, 12206])).
% 2.44/2.68 tff(12241,plain,
% 2.44/2.68 (b(s(s(s(s(z)))), elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[12240, 12239])).
% 2.44/2.68 tff(12242,plain,
% 2.44/2.68 (~r(s(s(s(s(z)))), z)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[9423, 6095, 1114])).
% 2.44/2.68 tff(12243,plain,
% 2.44/2.68 (b(s(s(s(s(z)))), z)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[6040, 12242])).
% 2.44/2.68 tff(12244,plain,
% 2.44/2.68 ($false),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[2466, 246, 11962, 1051, 12243, 12241])).
% 2.44/2.68 tff(12245,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (elem!1 = s(s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(z), elem!1)) | b(s(s(s(z))), elem!1) | b(elem!1, s(z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.68 tff(12246,plain,
% 2.44/2.68 (~r(s(s(s(s(z)))), s(z))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[12245, 1, 2362, 1204, 172, 2593, 171, 266, 119, 217, 1051, 210, 1114])).
% 2.44/2.68 tff(12247,plain,
% 2.44/2.68 (b(s(s(s(s(z)))), s(z))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[6103, 12246])).
% 2.44/2.68 tff(12248,plain,
% 2.44/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.44/2.68 inference(rewrite,[status(thm)],[])).
% 2.44/2.68 tff(12249,plain,
% 2.44/2.68 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.44/2.68 inference(rewrite,[status(thm)],[])).
% 2.44/2.68 tff(12250,plain,
% 2.44/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[12249])).
% 2.44/2.68 tff(12251,plain,
% 2.44/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.44/2.68 inference(transitivity,[status(thm)],[12250, 12248])).
% 2.44/2.68 tff(12252,plain,
% 2.44/2.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.44/2.68 inference(quant_inst,[status(thm)],[])).
% 2.44/2.68 tff(12253,plain,
% 2.44/2.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[12252, 12251])).
% 2.44/2.68 tff(12254,plain,
% 2.44/2.68 ($false),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[12253, 246, 12049, 12064, 12247, 12182])).
% 2.44/2.68 tff(12255,plain,(b(s(s(s(z))), elem!1) | (~r(s(s(s(s(z)))), s(s(s(z))))) | r(s(s(elem!1)), elem!1) | b(s(z), elem!1) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~r(s(z), elem!1)) | b(elem!1, s(z)) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (s(s(s(z))) = s(s(elem!1))) | (elem!1 = s(s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.68 tff(12256,plain,
% 2.44/2.68 (~r(s(z), z)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[12255, 12169, 2232, 12006, 2362, 12009, 12050, 210, 171, 266, 7736, 1204, 172, 12028])).
% 2.44/2.68 tff(12257,plain,
% 2.44/2.68 (b(s(z), z)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[1069, 12256])).
% 2.44/2.68 tff(12258,plain,
% 2.44/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))))),
% 2.44/2.68 inference(rewrite,[status(thm)],[])).
% 2.44/2.68 tff(12259,plain,
% 2.44/2.68 (((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))))),
% 2.44/2.68 inference(rewrite,[status(thm)],[])).
% 2.44/2.68 tff(12260,plain,
% 2.44/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z)))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[12259])).
% 2.44/2.68 tff(12261,plain,
% 2.44/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))))),
% 2.44/2.68 inference(transitivity,[status(thm)],[12260, 12258])).
% 2.44/2.68 tff(12262,plain,
% 2.44/2.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.44/2.68 inference(quant_inst,[status(thm)],[])).
% 2.44/2.68 tff(12263,plain,
% 2.44/2.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z)))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[12262, 12261])).
% 2.44/2.68 tff(12264,plain,
% 2.44/2.68 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[12263, 246, 11962, 12049, 12257, 2362, 12159])).
% 2.44/2.68 tff(12265,plain,
% 2.44/2.68 (r(s(s(s(z))), s(s(elem!1)))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[689, 12264, 7736])).
% 2.44/2.68 tff(12266,plain,
% 2.44/2.68 (~r(s(s(s(z))), z)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[12078, 183, 171, 266, 12265])).
% 2.44/2.68 tff(12267,plain,
% 2.44/2.68 (b(s(s(s(z))), z)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[995, 12266])).
% 2.44/2.68 tff(12268,plain,
% 2.44/2.68 (~r(z, s(s(s(z))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[10424, 183, 266, 12265])).
% 2.44/2.68 tff(12269,plain,
% 2.44/2.68 (b(z, s(s(s(z))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[6165, 12268])).
% 2.44/2.68 tff(12270,plain,
% 2.44/2.68 (~r(s(z), s(s(s(z))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[2326, 183, 12050, 12157])).
% 2.44/2.68 tff(12271,plain,
% 2.44/2.68 (b(s(z), s(s(s(z))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[1291, 12270])).
% 2.44/2.68 tff(12272,plain,
% 2.44/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.44/2.68 inference(rewrite,[status(thm)],[])).
% 2.44/2.68 tff(12273,plain,
% 2.44/2.68 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.44/2.68 inference(rewrite,[status(thm)],[])).
% 2.44/2.68 tff(12274,plain,
% 2.44/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[12273])).
% 2.44/2.68 tff(12275,plain,
% 2.44/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.44/2.68 inference(transitivity,[status(thm)],[12274, 12272])).
% 2.44/2.68 tff(12276,plain,
% 2.44/2.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 2.44/2.68 inference(quant_inst,[status(thm)],[])).
% 2.44/2.68 tff(12277,plain,
% 2.44/2.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[12276, 12275])).
% 2.44/2.68 tff(12278,plain,
% 2.44/2.68 ($false),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[12277, 246, 12257, 12271, 12159, 12269, 12267])).
% 2.44/2.68 tff(12279,plain,(b(elem!1, s(z)) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | r(s(s(elem!1)), elem!1) | (elem!1 = s(s(elem!1))) | (~r(s(s(elem!1)), z)) | (s(s(elem!1)) = s(elem!1)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.68 tff(12280,plain,
% 2.44/2.68 (b(elem!1, s(z))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[12279, 11972, 171, 11984, 2232, 11983, 172, 11982, 3])).
% 2.44/2.68 tff(12281,plain,
% 2.44/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 2.44/2.68 inference(rewrite,[status(thm)],[])).
% 2.44/2.68 tff(12282,plain,
% 2.44/2.68 (((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 2.44/2.68 inference(rewrite,[status(thm)],[])).
% 2.44/2.68 tff(12283,plain,
% 2.44/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z)))))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[12282])).
% 2.44/2.69 tff(12284,plain,
% 2.44/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 2.44/2.69 inference(transitivity,[status(thm)],[12283, 12281])).
% 2.44/2.69 tff(12285,plain,
% 2.44/2.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))),
% 2.44/2.69 inference(quant_inst,[status(thm)],[])).
% 2.44/2.69 tff(12286,plain,
% 2.44/2.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z)))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[12285, 12284])).
% 2.44/2.69 tff(12287,plain,
% 2.44/2.69 ($false),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[12286, 246, 12049, 11984, 12280, 11974])).
% 2.44/2.69 tff(12288,plain,(b(z, s(s(elem!1))) | (~r(z, s(z))) | r(s(s(elem!1)), elem!1) | (~r(s(s(elem!1)), z)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.69 tff(12289,plain,
% 2.44/2.69 (b(z, s(s(elem!1)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[12288, 172, 2232, 171, 3])).
% 2.44/2.69 tff(12290,plain,
% 2.44/2.69 (~(s(s(elem!1)) = elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[7022, 7016, 172])).
% 2.44/2.69 tff(12291,plain,
% 2.44/2.69 (b(s(s(elem!1)), elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[156, 12290, 2232])).
% 2.44/2.69 tff(12292,plain,
% 2.44/2.69 (b(elem!1, z)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[12008, 7016])).
% 2.44/2.69 tff(12293,plain,
% 2.44/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(12294,plain,
% 2.44/2.69 (((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(12295,plain,
% 2.44/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1))))))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[12294])).
% 2.44/2.69 tff(12296,plain,
% 2.44/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))),
% 2.44/2.69 inference(transitivity,[status(thm)],[12295, 12293])).
% 2.44/2.69 tff(12297,plain,
% 2.44/2.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))),
% 2.44/2.69 inference(quant_inst,[status(thm)],[])).
% 2.44/2.69 tff(12298,plain,
% 2.44/2.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1))))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[12297, 12296])).
% 2.44/2.69 tff(12299,plain,
% 2.44/2.69 ($false),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[12298, 246, 11962, 12292, 12291, 1099])).
% 2.44/2.69 tff(12300,plain,(r(elem!1, z) | (~b(z, s(s(elem!1)))) | r(s(s(elem!1)), elem!1) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.69 tff(12301,plain,
% 2.44/2.69 (r(elem!1, z)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[12300, 12289, 2232, 172])).
% 2.44/2.69 tff(12302,plain,
% 2.44/2.69 (~r(elem!1, s(s(elem!1)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[7107, 183, 12301, 172])).
% 2.44/2.69 tff(12303,plain,
% 2.44/2.69 (~r(elem!1, s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[2351, 2246, 171])).
% 2.44/2.69 tff(12304,plain,
% 2.44/2.69 (b(elem!1, s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[214, 12303, 3])).
% 2.44/2.69 tff(12305,plain,
% 2.44/2.69 (~(s(s(elem!1)) = s(s(s(z))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[421, 7736])).
% 2.44/2.69 tff(12306,plain,
% 2.44/2.69 (~(elem!1 = s(s(s(z))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[8772, 2125, 12305])).
% 2.44/2.69 tff(12307,plain,
% 2.44/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(12308,plain,
% 2.44/2.69 (((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))) <=> ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(12309,plain,
% 2.44/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z)))))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[12308])).
% 2.44/2.69 tff(12310,plain,
% 2.44/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))))),
% 2.44/2.69 inference(transitivity,[status(thm)],[12309, 12307])).
% 2.44/2.69 tff(12311,plain,
% 2.44/2.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 2.44/2.69 inference(quant_inst,[status(thm)],[])).
% 2.44/2.69 tff(12312,plain,
% 2.44/2.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z)))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[12311, 12310])).
% 2.44/2.69 tff(12313,plain,
% 2.44/2.69 (~b(s(z), z)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[12312, 246, 11962, 1044, 2001])).
% 2.44/2.69 tff(12314,plain,
% 2.44/2.69 (r(s(z), z)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[1069, 12313])).
% 2.44/2.69 tff(12315,plain,
% 2.44/2.69 (~r(s(s(s(s(z)))), s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[9423, 7218, 12314])).
% 2.44/2.69 tff(12316,plain,
% 2.44/2.69 (b(s(s(s(s(z)))), s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[6103, 12315])).
% 2.44/2.69 tff(12317,plain,
% 2.44/2.69 (~b(s(s(s(s(z)))), elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[9050, 12316, 2001, 1044])).
% 2.44/2.69 tff(12318,plain,
% 2.44/2.69 ($false),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[2442, 47, 3074, 12317, 7237])).
% 2.44/2.69 tff(12319,plain,((~r(s(s(s(s(z)))), z)) | (s(s(s(s(z)))) = elem!1) | (~r(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.69 tff(12320,plain,
% 2.44/2.69 (~r(s(s(s(s(z)))), z)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[12319, 1044, 2246, 12304, 3074])).
% 2.44/2.69 tff(12321,plain,
% 2.44/2.69 (b(s(s(s(s(z)))), z)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[6040, 12320])).
% 2.44/2.69 tff(12322,plain,
% 2.44/2.69 (~b(s(z), z)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[12312, 246, 11962, 1044, 12304])).
% 2.44/2.69 tff(12323,plain,
% 2.44/2.69 (r(s(z), z)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[1069, 12322])).
% 2.44/2.69 tff(12324,plain,
% 2.44/2.69 (~r(elem!1, s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[1163, 2246, 1114])).
% 2.44/2.69 tff(12325,plain,
% 2.44/2.69 (b(elem!1, s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[214, 12324, 3])).
% 2.44/2.69 tff(12326,plain,
% 2.44/2.69 (~r(elem!1, s(s(s(z))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[2254, 2246, 429])).
% 2.44/2.69 tff(12327,plain,
% 2.44/2.69 (b(elem!1, s(s(s(z))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[470, 12326, 1675])).
% 2.44/2.69 tff(12328,plain,
% 2.44/2.69 ($false),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[2011, 12327, 12325, 1044, 2003])).
% 2.44/2.69 tff(12329,plain,((~r(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (elem!1 = s(s(s(z)))) | (elem!1 = s(z)) | (~r(z, s(s(s(z))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.69 tff(12330,plain,
% 2.44/2.69 (~r(z, s(s(s(z))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[12329, 2003, 1044, 1114, 3, 1675, 2246])).
% 2.44/2.69 tff(12331,plain,
% 2.44/2.69 (b(z, s(s(s(z))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[6165, 12330])).
% 2.44/2.69 tff(12332,plain,
% 2.44/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(12333,plain,
% 2.44/2.69 (((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(12334,plain,
% 2.44/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[12333])).
% 2.44/2.69 tff(12335,plain,
% 2.44/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.44/2.69 inference(transitivity,[status(thm)],[12334, 12332])).
% 2.44/2.69 tff(12336,plain,
% 2.44/2.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.44/2.69 inference(quant_inst,[status(thm)],[])).
% 2.44/2.69 tff(12337,plain,
% 2.44/2.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[12336, 12335])).
% 2.44/2.69 tff(12338,plain,
% 2.44/2.69 ($false),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[12337, 246, 11962, 1044, 2003, 12331, 1833, 8266])).
% 2.44/2.69 tff(12339,plain,((~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (elem!1 = s(z)) | (elem!1 = s(s(s(z)))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.69 tff(12340,plain,
% 2.44/2.69 (~b(s(s(s(z))), s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[12339, 1833, 1044, 8266, 12323, 3, 1675, 2246])).
% 2.44/2.69 tff(12341,plain,
% 2.44/2.69 (r(s(s(s(z))), s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[52, 12340])).
% 2.44/2.69 tff(12342,plain,
% 2.44/2.69 (~r(z, s(s(s(z))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[438, 12341, 171])).
% 2.44/2.69 tff(12343,plain,
% 2.44/2.69 (b(z, s(s(s(z))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[6165, 12342])).
% 2.44/2.69 tff(12344,plain,
% 2.44/2.69 (~b(s(s(s(z))), z)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[9844, 12343, 8266, 1833])).
% 2.44/2.69 tff(12345,plain,
% 2.44/2.69 (r(s(s(s(z))), z)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[995, 12344])).
% 2.44/2.69 tff(12346,plain,
% 2.44/2.69 ($false),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[11271, 183, 171, 12341, 12345])).
% 2.44/2.69 tff(12347,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), elem!1)) | (elem!1 = s(z)) | (elem!1 = s(s(s(z)))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.69 tff(12348,plain,
% 2.44/2.69 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[12347, 12321, 171, 1044, 3, 1675, 2246])).
% 2.44/2.69 tff(12349,plain,
% 2.44/2.69 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[1702, 12348])).
% 2.44/2.69 tff(12350,plain,
% 2.44/2.69 (~r(s(s(s(z))), s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[9060, 12349, 12304, 3074, 634, 1044])).
% 2.44/2.69 tff(12351,plain,
% 2.44/2.69 (b(s(s(s(z))), s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[52, 12350])).
% 2.44/2.69 tff(12352,plain,
% 2.44/2.69 (~b(elem!1, s(s(s(z))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[2011, 12351, 12304, 1044])).
% 2.44/2.69 tff(12353,plain,
% 2.44/2.69 (r(elem!1, s(s(s(z))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[470, 12352, 1675])).
% 2.44/2.69 tff(12354,plain,
% 2.44/2.69 (~r(s(s(s(s(z)))), elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[7886, 183, 2246, 12353, 12349])).
% 2.44/2.69 tff(12355,plain,
% 2.44/2.69 (b(s(s(s(s(z)))), elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[2442, 47, 3074, 12354])).
% 2.44/2.69 tff(12356,plain,
% 2.44/2.69 (~r(elem!1, s(s(s(s(z)))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[7165, 183, 12353, 12349])).
% 2.44/2.69 tff(12357,plain,
% 2.44/2.69 (b(elem!1, s(s(s(s(z)))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[5969, 47, 12356, 9815])).
% 2.44/2.69 tff(12358,plain,
% 2.44/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(12359,plain,
% 2.44/2.69 (((~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(12360,plain,
% 2.44/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z))))))))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[12359])).
% 2.44/2.69 tff(12361,plain,
% 2.44/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.44/2.69 inference(transitivity,[status(thm)],[12360, 12358])).
% 2.44/2.69 tff(12362,plain,
% 2.44/2.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 2.44/2.69 inference(quant_inst,[status(thm)],[])).
% 2.44/2.69 tff(12363,plain,
% 2.44/2.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z))))))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[12362, 12361])).
% 2.44/2.69 tff(12364,plain,
% 2.44/2.69 ($false),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[12363, 246, 11962, 12357, 12321, 12355])).
% 2.44/2.69 tff(12365,plain,((~b(s(z), elem!1)) | (s(s(s(s(z)))) = elem!1) | (~r(elem!1, z)) | (elem!1 = s(s(s(z)))) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(z))) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.69 tff(12366,plain,
% 2.44/2.69 (~b(s(z), elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[12365, 634, 2246, 1675, 3074, 171, 3])).
% 2.44/2.69 tff(12367,plain,
% 2.44/2.69 (r(s(z), elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[1034, 12366, 10])).
% 2.44/2.69 tff(12368,plain,
% 2.44/2.69 (~r(s(z), s(s(s(z))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[2326, 183, 12367, 634])).
% 2.44/2.69 tff(12369,plain,
% 2.44/2.69 (b(s(z), s(s(s(z))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[1291, 12368])).
% 2.44/2.69 tff(12370,plain,
% 2.44/2.69 (~r(s(s(s(z))), s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[2713, 12366, 2232, 634])).
% 2.44/2.69 tff(12371,plain,
% 2.44/2.69 (b(s(s(s(z))), s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[52, 12370])).
% 2.44/2.69 tff(12372,plain,
% 2.44/2.69 (~r(s(z), z)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[2725, 12367, 2246])).
% 2.44/2.69 tff(12373,plain,
% 2.44/2.69 (b(s(z), z)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[1069, 12372])).
% 2.44/2.69 tff(12374,plain,
% 2.44/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(12375,plain,
% 2.44/2.69 (((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(12376,plain,
% 2.44/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[12375])).
% 2.44/2.69 tff(12377,plain,
% 2.44/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.44/2.69 inference(transitivity,[status(thm)],[12376, 12374])).
% 2.44/2.69 tff(12378,plain,
% 2.44/2.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 2.44/2.69 inference(quant_inst,[status(thm)],[])).
% 2.44/2.69 tff(12379,plain,
% 2.44/2.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[12378, 12377])).
% 2.44/2.69 tff(12380,plain,
% 2.44/2.69 ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[12379, 246, 11962, 12373, 12304, 12371])).
% 2.44/2.69 tff(12381,plain,
% 2.44/2.69 (~b(s(s(s(z))), z)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[12380, 12369])).
% 2.44/2.69 tff(12382,plain,
% 2.44/2.69 (r(s(s(s(z))), z)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[995, 12381])).
% 2.44/2.69 tff(12383,plain,
% 2.44/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(12384,plain,
% 2.44/2.69 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(12385,plain,
% 2.44/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 2.44/2.70 inference(monotonicity,[status(thm)],[12384])).
% 2.44/2.70 tff(12386,plain,
% 2.44/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.44/2.70 inference(transitivity,[status(thm)],[12385, 12383])).
% 2.44/2.70 tff(12387,plain,
% 2.44/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))),
% 2.44/2.70 inference(quant_inst,[status(thm)],[])).
% 2.44/2.70 tff(12388,plain,
% 2.44/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 2.44/2.70 inference(modus_ponens,[status(thm)],[12387, 12386])).
% 2.44/2.70 tff(12389,plain,
% 2.44/2.70 (~b(elem!1, s(s(s(z))))),
% 2.44/2.70 inference(unit_resolution,[status(thm)],[12388, 246, 12304, 12369, 12371])).
% 2.44/2.70 tff(12390,plain,
% 2.44/2.70 (r(elem!1, s(s(s(z))))),
% 2.44/2.70 inference(unit_resolution,[status(thm)],[470, 12389, 1675])).
% 2.44/2.70 tff(12391,plain,
% 2.44/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 2.44/2.70 inference(rewrite,[status(thm)],[])).
% 2.44/2.70 tff(12392,plain,
% 2.44/2.70 (((~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), 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))))))),
% 2.44/2.70 inference(rewrite,[status(thm)],[])).
% 2.44/2.70 tff(12393,plain,
% 2.44/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z)))))))),
% 2.44/2.70 inference(monotonicity,[status(thm)],[12392])).
% 2.44/2.70 tff(12394,plain,
% 2.44/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 2.44/2.70 inference(transitivity,[status(thm)],[12393, 12391])).
% 2.44/2.70 tff(12395,plain,
% 2.44/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 2.44/2.70 inference(quant_inst,[status(thm)],[])).
% 2.44/2.70 tff(12396,plain,
% 2.44/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z)))))),
% 2.44/2.70 inference(modus_ponens,[status(thm)],[12395, 12394])).
% 2.44/2.70 tff(12397,plain,
% 2.44/2.70 ($false),
% 2.44/2.70 inference(unit_resolution,[status(thm)],[12396, 183, 2246, 12390, 12382])).
% 2.44/2.70 tff(12398,plain,((~r(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (elem!1 = s(s(s(z)))) | r(s(s(elem!1)), elem!1) | (s(s(s(s(z)))) = elem!1) | (~r(z, s(z))) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.70 tff(12399,plain,
% 2.54/2.70 (~r(s(s(s(z))), elem!1)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[12398, 12306, 2246, 2232, 7592, 171, 3])).
% 2.54/2.70 tff(12400,plain,
% 2.54/2.70 (b(s(s(s(z))), elem!1)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[647, 12399, 5386])).
% 2.54/2.70 tff(12401,plain,
% 2.54/2.70 (~r(s(z), z)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[2725, 217, 2246])).
% 2.54/2.70 tff(12402,plain,
% 2.54/2.70 (b(s(z), z)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[1069, 12401])).
% 2.54/2.70 tff(12403,plain,
% 2.54/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 2.54/2.70 inference(rewrite,[status(thm)],[])).
% 2.54/2.70 tff(12404,plain,
% 2.54/2.70 (((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z)))))) <=> ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 2.54/2.70 inference(rewrite,[status(thm)],[])).
% 2.54/2.70 tff(12405,plain,
% 2.54/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z))))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[12404])).
% 2.54/2.70 tff(12406,plain,
% 2.54/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 2.54/2.70 inference(transitivity,[status(thm)],[12405, 12403])).
% 2.54/2.70 tff(12407,plain,
% 2.54/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))),
% 2.54/2.70 inference(quant_inst,[status(thm)],[])).
% 2.54/2.70 tff(12408,plain,
% 2.54/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[12407, 12406])).
% 2.54/2.70 tff(12409,plain,
% 2.54/2.70 ($false),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[12408, 246, 11962, 1056, 2001, 3697, 6456, 11273])).
% 2.54/2.70 tff(12410,plain,((~r(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.70 tff(12411,plain,
% 2.54/2.70 (~r(s(s(s(z))), s(z))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[12410, 12402, 2001, 3697, 171])).
% 2.54/2.70 tff(12412,plain,
% 2.54/2.70 (b(s(s(s(z))), s(z))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[52, 12411])).
% 2.54/2.70 tff(12413,plain,
% 2.54/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.54/2.70 inference(rewrite,[status(thm)],[])).
% 2.54/2.70 tff(12414,plain,
% 2.54/2.70 (((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.54/2.70 inference(rewrite,[status(thm)],[])).
% 2.54/2.70 tff(12415,plain,
% 2.54/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[12414])).
% 2.54/2.70 tff(12416,plain,
% 2.54/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.54/2.70 inference(transitivity,[status(thm)],[12415, 12413])).
% 2.54/2.70 tff(12417,plain,
% 2.54/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))),
% 2.54/2.70 inference(quant_inst,[status(thm)],[])).
% 2.54/2.70 tff(12418,plain,
% 2.54/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[12417, 12416])).
% 2.54/2.70 tff(12419,plain,
% 2.54/2.70 ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[12418, 246, 11962, 12402, 2001, 3697])).
% 2.54/2.70 tff(12420,plain,
% 2.54/2.70 (~b(elem!1, s(s(s(z))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[12419, 12412])).
% 2.54/2.70 tff(12421,plain,
% 2.54/2.70 (r(elem!1, s(s(s(z))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[470, 12420, 1675])).
% 2.54/2.70 tff(12422,plain,
% 2.54/2.70 (~r(z, s(s(s(z))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[2254, 12421, 2246])).
% 2.54/2.70 tff(12423,plain,
% 2.54/2.70 (b(z, s(s(s(z))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[6165, 12422])).
% 2.54/2.70 tff(12424,plain,
% 2.54/2.70 (~r(s(s(s(s(z)))), elem!1)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[7886, 183, 2246, 413, 2593])).
% 2.54/2.70 tff(12425,plain,
% 2.54/2.70 (b(s(s(s(s(z)))), elem!1)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[2442, 47, 3074, 12424])).
% 2.54/2.70 tff(12426,plain,
% 2.54/2.70 (b(elem!1, s(s(s(s(z)))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[5969, 47, 7166, 9815])).
% 2.54/2.70 tff(12427,plain,
% 2.54/2.70 (~r(z, s(s(s(z))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[2254, 413, 2246])).
% 2.54/2.70 tff(12428,plain,
% 2.54/2.70 (b(z, s(s(s(z))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[6165, 12427])).
% 2.54/2.70 tff(12429,plain,
% 2.54/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.54/2.70 inference(rewrite,[status(thm)],[])).
% 2.54/2.70 tff(12430,plain,
% 2.54/2.70 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z)))))) <=> ((~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.54/2.70 inference(rewrite,[status(thm)],[])).
% 2.54/2.70 tff(12431,plain,
% 2.54/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z))))))))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[12430])).
% 2.54/2.70 tff(12432,plain,
% 2.54/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.54/2.70 inference(transitivity,[status(thm)],[12431, 12429])).
% 2.54/2.70 tff(12433,plain,
% 2.54/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))),
% 2.54/2.70 inference(quant_inst,[status(thm)],[])).
% 2.54/2.70 tff(12434,plain,
% 2.54/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z))))))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[12433, 12432])).
% 2.54/2.70 tff(12435,plain,
% 2.54/2.70 ($false),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[12434, 246, 11962, 3697, 12428, 12426, 12425])).
% 2.54/2.70 tff(12436,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (s(s(s(s(z)))) = elem!1) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.70 tff(12437,plain,
% 2.54/2.70 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[12436, 12421, 3074, 2246, 3697])).
% 2.54/2.70 tff(12438,plain,
% 2.54/2.70 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[1702, 12437])).
% 2.54/2.70 tff(12439,plain,
% 2.54/2.70 (~b(s(z), s(s(s(z))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[7450, 12438, 171, 12412, 12423])).
% 2.54/2.70 tff(12440,plain,
% 2.54/2.70 (r(s(z), s(s(s(z))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[1291, 12439])).
% 2.54/2.70 tff(12441,plain,
% 2.54/2.70 ($false),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[10299, 183, 2246, 217, 12421, 12440])).
% 2.54/2.70 tff(12442,plain,((~r(s(z), elem!1)) | (~r(elem!1, z)) | (~r(z, s(z))) | (s(s(s(s(z)))) = elem!1) | (~b(s(s(s(z))), elem!1)) | (elem!1 = s(s(s(z)))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.70 tff(12443,plain,
% 2.54/2.70 (~r(s(z), elem!1)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[12442, 7592, 171, 2246, 12400, 12306, 12304])).
% 2.54/2.70 tff(12444,plain,
% 2.54/2.70 (b(s(z), elem!1)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[1034, 12443, 10])).
% 2.54/2.70 tff(12445,plain,
% 2.54/2.70 (~r(s(s(s(s(z)))), z)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[12319, 12444, 2246, 12304, 7592])).
% 2.54/2.70 tff(12446,plain,
% 2.54/2.70 (b(s(s(s(s(z)))), z)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[6040, 12445])).
% 2.54/2.70 tff(12447,plain,
% 2.54/2.70 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[12347, 12446, 171, 12444, 3, 12306, 2246])).
% 2.54/2.70 tff(12448,plain,
% 2.54/2.70 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[1702, 12447])).
% 2.54/2.70 tff(12449,plain,
% 2.54/2.70 (~r(elem!1, s(s(s(z))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[12436, 12448, 7592, 2246, 12400])).
% 2.54/2.70 tff(12450,plain,
% 2.54/2.70 (b(elem!1, s(s(s(z))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[470, 12449, 12306])).
% 2.54/2.70 tff(12451,plain,
% 2.54/2.70 (~b(s(s(s(z))), s(z))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[2011, 12450, 12304, 12444])).
% 2.54/2.70 tff(12452,plain,
% 2.54/2.70 (r(s(s(s(z))), s(z))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[52, 12451])).
% 2.54/2.70 tff(12453,plain,
% 2.54/2.70 (~r(z, s(s(s(z))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[438, 12452, 171])).
% 2.54/2.70 tff(12454,plain,
% 2.54/2.70 (b(z, s(s(s(z))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[6165, 12453])).
% 2.54/2.70 tff(12455,plain,
% 2.54/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.54/2.70 inference(rewrite,[status(thm)],[])).
% 2.54/2.70 tff(12456,plain,
% 2.54/2.70 (((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z)))))) <=> ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.54/2.70 inference(rewrite,[status(thm)],[])).
% 2.54/2.70 tff(12457,plain,
% 2.54/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[12456])).
% 2.54/2.70 tff(12458,plain,
% 2.54/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.54/2.70 inference(transitivity,[status(thm)],[12457, 12455])).
% 2.54/2.70 tff(12459,plain,
% 2.54/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))),
% 2.54/2.70 inference(quant_inst,[status(thm)],[])).
% 2.54/2.70 tff(12460,plain,
% 2.54/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[12459, 12458])).
% 2.54/2.70 tff(12461,plain,
% 2.54/2.70 ($false),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[12460, 246, 11962, 12444, 12304, 12400, 12454])).
% 2.54/2.70 tff(12462,plain,((~(s(s(elem!1)) = elem!1)) | (~r(z, s(z))) | (~r(elem!1, z)) | (elem!1 = s(z)) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.54/2.70 tff(12463,plain,
% 2.54/2.70 (~(s(s(elem!1)) = elem!1)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[12462, 12301, 171, 3, 2232])).
% 2.54/2.70 tff(12464,plain,
% 2.54/2.70 (~(elem!1 = s(s(elem!1)))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[5450, 12463])).
% 2.54/2.70 tff(12465,plain,
% 2.54/2.70 (b(elem!1, s(s(elem!1)))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[1268, 12464, 12302])).
% 2.54/2.70 tff(12466,plain,
% 2.54/2.70 (~r(elem!1, s(z))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[2351, 12301, 171])).
% 2.54/2.70 tff(12467,plain,
% 2.54/2.70 (b(elem!1, s(z))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[214, 12466, 3])).
% 2.54/2.70 tff(12468,plain,
% 2.54/2.70 (b(s(s(elem!1)), elem!1)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[156, 12463, 2232])).
% 2.54/2.70 tff(12469,plain,
% 2.54/2.70 (~b(s(z), elem!1)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[3799, 12468, 12049, 12467])).
% 2.54/2.70 tff(12470,plain,
% 2.54/2.70 (r(s(z), elem!1)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[1034, 12469, 10])).
% 2.54/2.70 tff(12471,plain,
% 2.54/2.70 (~r(s(z), z)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[2725, 12470, 12301])).
% 2.54/2.70 tff(12472,plain,
% 2.54/2.70 (b(s(z), z)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[1069, 12471])).
% 2.54/2.70 tff(12473,plain,
% 2.54/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))),
% 2.54/2.70 inference(rewrite,[status(thm)],[])).
% 2.54/2.70 tff(12474,plain,
% 2.54/2.70 (((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))),
% 2.54/2.70 inference(rewrite,[status(thm)],[])).
% 2.54/2.70 tff(12475,plain,
% 2.54/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z)))))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[12474])).
% 2.54/2.70 tff(12476,plain,
% 2.54/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))),
% 2.54/2.70 inference(transitivity,[status(thm)],[12475, 12473])).
% 2.54/2.70 tff(12477,plain,
% 2.54/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))))),
% 2.54/2.70 inference(quant_inst,[status(thm)],[])).
% 2.54/2.70 tff(12478,plain,
% 2.54/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z)))),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[12477, 12476])).
% 2.54/2.71 tff(12479,plain,
% 2.54/2.71 ($false),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[12478, 246, 11962, 12049, 12472, 12468, 12467, 12465])).
% 2.54/2.71 tff(12480,plain,((~r(s(s(elem!1)), z)) | r(s(s(elem!1)), elem!1) | (~r(z, s(z))) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.71 tff(12481,plain,
% 2.54/2.71 (~r(s(s(elem!1)), z)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[12480, 171, 2232, 3])).
% 2.54/2.71 tff(12482,plain,
% 2.54/2.71 (b(s(s(elem!1)), z)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[523, 12481])).
% 2.54/2.71 tff(12483,plain,
% 2.54/2.71 ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[2370, 11962])).
% 2.54/2.71 tff(12484,plain,
% 2.54/2.71 (~b(s(s(elem!1)), elem!1)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[12483, 12009, 12482])).
% 2.54/2.71 tff(12485,plain,
% 2.54/2.71 (s(s(elem!1)) = elem!1),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[156, 12484, 2232])).
% 2.54/2.71 tff(12486,plain,
% 2.54/2.71 (~(s(s(s(z))) = elem!1)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[5385, 12485])).
% 2.54/2.71 tff(12487,plain,
% 2.54/2.71 (elem!1 = s(s(elem!1))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[6867, 12485])).
% 2.54/2.71 tff(12488,plain,
% 2.54/2.71 (s(s(s(elem!1))) = s(elem!1)),
% 2.54/2.71 inference(monotonicity,[status(thm)],[12485])).
% 2.54/2.71 tff(12489,plain,
% 2.54/2.71 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[12488])).
% 2.54/2.71 tff(12490,plain,
% 2.54/2.71 (s(s(s(s(elem!1)))) = elem!1),
% 2.54/2.71 inference(transitivity,[status(thm)],[12489, 12485])).
% 2.54/2.71 tff(12491,plain,
% 2.54/2.71 (s(s(s(s(s(elem!1))))) = s(elem!1)),
% 2.54/2.71 inference(monotonicity,[status(thm)],[12490])).
% 2.54/2.71 tff(12492,plain,
% 2.54/2.71 ((s(s(s(s(s(elem!1))))) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[12491])).
% 2.54/2.71 tff(12493,plain,
% 2.54/2.71 ((~(s(s(s(s(s(elem!1))))) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[12492])).
% 2.54/2.71 tff(12494,plain,
% 2.54/2.71 (~(s(elem!1) = s(s(s(z))))),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[1622, 12493])).
% 2.54/2.71 tff(12495,plain,
% 2.54/2.71 (~(s(s(s(s(z)))) = elem!1)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[2399, 12494, 12487])).
% 2.54/2.71 tff(12496,plain,
% 2.54/2.71 (~(elem!1 = s(s(s(z))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[8772, 12485, 12305])).
% 2.54/2.71 tff(12497,plain,
% 2.54/2.71 (~(s(s(z)) = elem!1)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[9813, 12485])).
% 2.54/2.71 tff(12498,plain,
% 2.54/2.71 (~r(s(s(s(z))), elem!1)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[2282, 430, 2232, 210])).
% 2.54/2.71 tff(12499,plain,
% 2.54/2.71 (b(s(s(s(z))), elem!1)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[647, 12498, 3011])).
% 2.54/2.71 tff(12500,plain,
% 2.54/2.71 ($false),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[12015, 246, 11962, 1051, 12499, 6456])).
% 2.54/2.71 tff(12501,plain,((~r(s(s(s(z))), s(z))) | (~b(elem!1, z)) | (s(s(s(z))) = elem!1) | (~r(z, s(z))) | r(s(s(elem!1)), elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.71 tff(12502,plain,
% 2.54/2.71 (~r(s(s(s(z))), s(z))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[12501, 12009, 12486, 171, 2232, 210])).
% 2.54/2.71 tff(12503,plain,
% 2.54/2.71 (b(s(s(s(z))), s(z))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[52, 12502])).
% 2.54/2.71 tff(12504,plain,
% 2.54/2.71 (~r(elem!1, z)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[2351, 474, 171])).
% 2.54/2.71 tff(12505,plain,
% 2.54/2.71 (b(elem!1, z)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[12008, 12504])).
% 2.54/2.71 tff(12506,assumption,(r(s(s(z)), elem!1)), introduced(assumption)).
% 2.54/2.71 tff(12507,plain,
% 2.54/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), s(s(z)))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(12508,plain,
% 2.54/2.71 (((~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), s(s(z)))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(12509,plain,
% 2.54/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), s(s(z))))))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[12508])).
% 2.54/2.71 tff(12510,plain,
% 2.54/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), s(s(z)))))),
% 2.54/2.71 inference(transitivity,[status(thm)],[12509, 12507])).
% 2.54/2.71 tff(12511,plain,
% 2.54/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), s(s(z)))))),
% 2.54/2.71 inference(quant_inst,[status(thm)],[])).
% 2.54/2.71 tff(12512,plain,
% 2.54/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), s(s(z))))),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[12511, 12510])).
% 2.54/2.71 tff(12513,plain,
% 2.54/2.71 (~r(s(s(s(z))), s(s(z)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[12512, 183, 634, 12506])).
% 2.54/2.71 tff(12514,plain,
% 2.54/2.71 (b(s(s(s(z))), s(s(z)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[8991, 47, 8374, 12513])).
% 2.54/2.71 tff(12515,plain,
% 2.54/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(12516,plain,
% 2.54/2.71 (((~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(12517,plain,
% 2.54/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z))))))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[12516])).
% 2.54/2.71 tff(12518,plain,
% 2.54/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))))),
% 2.54/2.71 inference(transitivity,[status(thm)],[12517, 12515])).
% 2.54/2.71 tff(12519,plain,
% 2.54/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))))),
% 2.54/2.71 inference(quant_inst,[status(thm)],[])).
% 2.54/2.71 tff(12520,plain,
% 2.54/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z))))),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[12519, 12518])).
% 2.54/2.71 tff(12521,plain,
% 2.54/2.71 (~r(s(z), s(s(z)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[12520, 183, 217, 12506])).
% 2.54/2.71 tff(12522,plain,
% 2.54/2.71 (b(s(z), s(s(z)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[8343, 47, 8340, 12521])).
% 2.54/2.71 tff(12523,plain,
% 2.54/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(12524,plain,
% 2.54/2.71 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(12525,plain,
% 2.54/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z)))))))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[12524])).
% 2.54/2.71 tff(12526,plain,
% 2.54/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))))),
% 2.54/2.71 inference(transitivity,[status(thm)],[12525, 12523])).
% 2.54/2.71 tff(12527,plain,
% 2.54/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))))),
% 2.54/2.71 inference(quant_inst,[status(thm)],[])).
% 2.54/2.71 tff(12528,plain,
% 2.54/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z)))))),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[12527, 12526])).
% 2.54/2.71 tff(12529,plain,
% 2.54/2.71 (~r(s(s(z)), s(s(s(z))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[12528, 183, 634, 12506])).
% 2.54/2.71 tff(12530,plain,
% 2.54/2.71 (b(s(s(z)), s(s(s(z))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[8382, 12529])).
% 2.54/2.71 tff(12531,plain,
% 2.54/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(12532,plain,
% 2.54/2.71 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(12533,plain,
% 2.54/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z))))))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[12532])).
% 2.54/2.71 tff(12534,plain,
% 2.54/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))))),
% 2.54/2.71 inference(transitivity,[status(thm)],[12533, 12531])).
% 2.54/2.71 tff(12535,plain,
% 2.54/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 2.54/2.71 inference(quant_inst,[status(thm)],[])).
% 2.54/2.71 tff(12536,plain,
% 2.54/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z))))),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[12535, 12534])).
% 2.54/2.71 tff(12537,plain,
% 2.54/2.71 ($false),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[12536, 246, 2328, 2003, 12530, 12522, 12514])).
% 2.54/2.71 tff(12538,plain,((~r(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.71 tff(12539,plain,
% 2.54/2.71 (~r(s(s(z)), elem!1)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[12538, 634, 2003, 217])).
% 2.54/2.71 tff(12540,plain,
% 2.54/2.71 (b(s(s(z)), elem!1)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[9920, 47, 9917, 12539])).
% 2.54/2.71 tff(12541,assumption,(b(s(s(z)), elem!1)), introduced(assumption)).
% 2.54/2.71 tff(12542,plain,
% 2.54/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(12543,plain,
% 2.54/2.71 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(12544,plain,
% 2.54/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1))))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[12543])).
% 2.54/2.71 tff(12545,plain,
% 2.54/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 2.54/2.71 inference(transitivity,[status(thm)],[12544, 12542])).
% 2.54/2.71 tff(12546,plain,
% 2.54/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 2.54/2.71 inference(quant_inst,[status(thm)],[])).
% 2.54/2.71 tff(12547,plain,
% 2.54/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1))),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[12546, 12545])).
% 2.54/2.71 tff(12548,plain,
% 2.54/2.71 (~b(s(s(z)), z)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[12547, 246, 11962, 1051, 12541])).
% 2.54/2.71 tff(12549,assumption,(~b(s(s(z)), z)), introduced(assumption)).
% 2.54/2.71 tff(12550,assumption,(~r(s(s(z)), z)), introduced(assumption)).
% 2.54/2.71 tff(12551,plain,
% 2.54/2.71 ($false),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[3215, 47, 35, 12550, 12549])).
% 2.54/2.71 tff(12552,plain,(b(s(s(z)), z) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 2.54/2.71 tff(12553,plain,
% 2.54/2.71 (r(s(s(z)), z)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[12552, 12548])).
% 2.54/2.71 tff(12554,plain,
% 2.54/2.71 (~b(s(s(s(s(z)))), z)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[2466, 246, 11962, 1051, 5913])).
% 2.54/2.71 tff(12555,plain,
% 2.54/2.71 (r(s(s(s(s(z)))), z)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[6040, 12554])).
% 2.54/2.71 tff(12556,plain,
% 2.54/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(12557,plain,
% 2.54/2.71 (((~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(12558,plain,
% 2.54/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1))))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[12557])).
% 2.54/2.71 tff(12559,plain,
% 2.54/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 2.54/2.71 inference(transitivity,[status(thm)],[12558, 12556])).
% 2.54/2.71 tff(12560,plain,
% 2.54/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.54/2.71 inference(quant_inst,[status(thm)],[])).
% 2.54/2.71 tff(12561,plain,
% 2.54/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1))),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[12560, 12559])).
% 2.54/2.71 tff(12562,plain,
% 2.54/2.71 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[12561, 246, 11962, 1051, 5913, 12541])).
% 2.54/2.71 tff(12563,plain,
% 2.54/2.71 (r(s(s(z)), s(s(s(s(z)))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[1531, 12562])).
% 2.54/2.71 tff(12564,plain,
% 2.54/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(12565,plain,
% 2.54/2.71 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(12566,plain,
% 2.54/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z))))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[12565])).
% 2.54/2.71 tff(12567,plain,
% 2.54/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)))),
% 2.54/2.71 inference(transitivity,[status(thm)],[12566, 12564])).
% 2.54/2.71 tff(12568,plain,
% 2.54/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.54/2.71 inference(quant_inst,[status(thm)],[])).
% 2.54/2.71 tff(12569,plain,
% 2.54/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z))),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[12568, 12567])).
% 2.54/2.71 tff(12570,plain,
% 2.54/2.71 ($false),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[12569, 183, 12563, 12555, 12553])).
% 2.54/2.71 tff(12571,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.71 tff(12572,plain,
% 2.54/2.71 (~b(s(s(s(s(z)))), elem!1)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[12571, 12540, 1051])).
% 2.54/2.71 tff(12573,plain,
% 2.54/2.71 (r(s(s(s(s(z)))), elem!1)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[2442, 47, 3074, 12572])).
% 2.54/2.71 tff(12574,plain,
% 2.54/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(12575,plain,
% 2.54/2.71 (((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(12576,plain,
% 2.54/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1))))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[12575])).
% 2.54/2.71 tff(12577,plain,
% 2.54/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.54/2.72 inference(transitivity,[status(thm)],[12576, 12574])).
% 2.54/2.72 tff(12578,plain,
% 2.54/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 2.54/2.72 inference(quant_inst,[status(thm)],[])).
% 2.54/2.72 tff(12579,plain,
% 2.54/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1))),
% 2.54/2.72 inference(modus_ponens,[status(thm)],[12578, 12577])).
% 2.54/2.72 tff(12580,plain,
% 2.54/2.72 (~r(s(s(s(s(z)))), s(z))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[12579, 183, 217, 12573])).
% 2.54/2.72 tff(12581,plain,
% 2.54/2.72 (b(s(s(s(s(z)))), s(z))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[6103, 12580])).
% 2.54/2.72 tff(12582,plain,
% 2.54/2.72 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[9058, 183, 634, 12573])).
% 2.54/2.72 tff(12583,plain,
% 2.54/2.72 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[1702, 12582])).
% 2.54/2.72 tff(12584,plain,
% 2.54/2.72 ($false),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[3591, 246, 2328, 2003, 12583, 12581])).
% 2.54/2.72 tff(12585,plain,((~r(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))) | (~r(s(z), elem!1)) | (s(s(s(s(z)))) = elem!1) | (~b(elem!1, z)) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.54/2.72 tff(12586,plain,
% 2.54/2.72 (~r(s(s(s(z))), elem!1)),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[12585, 2003, 217, 3074, 12505, 9917])).
% 2.54/2.72 tff(12587,plain,
% 2.54/2.72 (b(s(s(s(z))), elem!1)),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[647, 12586, 3011])).
% 2.54/2.72 tff(12588,plain,
% 2.54/2.72 (~b(z, s(s(s(z))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[12015, 246, 11962, 12505, 12587])).
% 2.54/2.72 tff(12589,plain,
% 2.54/2.72 (r(z, s(s(s(z))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[6165, 12588])).
% 2.54/2.72 tff(12590,plain,
% 2.54/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(12591,plain,
% 2.54/2.72 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(12592,plain,
% 2.54/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z))))),
% 2.54/2.72 inference(monotonicity,[status(thm)],[12591])).
% 2.54/2.72 tff(12593,plain,
% 2.54/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 2.54/2.72 inference(transitivity,[status(thm)],[12592, 12590])).
% 2.54/2.72 tff(12594,plain,
% 2.54/2.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 2.54/2.72 inference(quant_inst,[status(thm)],[])).
% 2.54/2.72 tff(12595,plain,
% 2.54/2.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z))),
% 2.54/2.72 inference(modus_ponens,[status(thm)],[12594, 12593])).
% 2.54/2.72 tff(12596,plain,
% 2.54/2.72 (~b(s(s(s(z))), z)),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[12595, 246, 11962, 12505, 12587])).
% 2.54/2.72 tff(12597,plain,
% 2.54/2.72 (r(s(s(s(z))), z)),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[995, 12596])).
% 2.54/2.72 tff(12598,plain,
% 2.54/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(12599,plain,
% 2.54/2.72 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(12600,plain,
% 2.54/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))))),
% 2.54/2.72 inference(monotonicity,[status(thm)],[12599])).
% 2.54/2.72 tff(12601,plain,
% 2.54/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 2.54/2.72 inference(transitivity,[status(thm)],[12600, 12598])).
% 2.54/2.72 tff(12602,plain,
% 2.54/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))),
% 2.54/2.72 inference(quant_inst,[status(thm)],[])).
% 2.54/2.72 tff(12603,plain,
% 2.54/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))),
% 2.54/2.72 inference(modus_ponens,[status(thm)],[12602, 12601])).
% 2.54/2.72 tff(12604,plain,
% 2.54/2.72 (~r(s(s(s(s(z)))), z)),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[12603, 183, 171, 429, 2593])).
% 2.54/2.72 tff(12605,plain,
% 2.54/2.72 (b(s(s(s(s(z)))), z)),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[6040, 12604])).
% 2.54/2.72 tff(12606,plain,
% 2.54/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(12607,plain,
% 2.54/2.72 (((~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(12608,plain,
% 2.54/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z))))))))),
% 2.54/2.72 inference(monotonicity,[status(thm)],[12607])).
% 2.54/2.72 tff(12609,plain,
% 2.54/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.54/2.72 inference(transitivity,[status(thm)],[12608, 12606])).
% 2.54/2.72 tff(12610,plain,
% 2.54/2.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.54/2.72 inference(quant_inst,[status(thm)],[])).
% 2.54/2.72 tff(12611,plain,
% 2.54/2.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z))))))),
% 2.54/2.72 inference(modus_ponens,[status(thm)],[12610, 12609])).
% 2.54/2.72 tff(12612,plain,
% 2.54/2.72 (~b(elem!1, s(s(s(s(z)))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[12611, 246, 11962, 12505, 12605])).
% 2.54/2.72 tff(12613,plain,
% 2.54/2.72 (r(elem!1, s(s(s(s(z)))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[5969, 47, 12612, 9815])).
% 2.54/2.72 tff(12614,plain,
% 2.54/2.72 (~r(s(s(s(s(z)))), s(z))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[7665, 12613, 474])).
% 2.54/2.72 tff(12615,plain,
% 2.54/2.72 (b(s(s(s(s(z)))), s(z))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[6103, 12614])).
% 2.54/2.72 tff(12616,plain,
% 2.54/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(12617,plain,
% 2.54/2.72 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(12618,plain,
% 2.54/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.54/2.72 inference(monotonicity,[status(thm)],[12617])).
% 2.54/2.72 tff(12619,plain,
% 2.54/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.54/2.72 inference(transitivity,[status(thm)],[12618, 12616])).
% 2.54/2.72 tff(12620,plain,
% 2.54/2.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.54/2.72 inference(quant_inst,[status(thm)],[])).
% 2.54/2.72 tff(12621,plain,
% 2.54/2.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.54/2.72 inference(modus_ponens,[status(thm)],[12620, 12619])).
% 2.54/2.72 tff(12622,plain,
% 2.54/2.72 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[12621, 246, 9091, 2003, 12615])).
% 2.54/2.72 tff(12623,plain,
% 2.54/2.72 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[8213, 47, 8210, 12622])).
% 2.54/2.72 tff(12624,plain,
% 2.54/2.72 (~b(s(s(s(s(z)))), elem!1)),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[2431, 246, 11962, 12505, 12605])).
% 2.54/2.72 tff(12625,plain,
% 2.54/2.72 (r(s(s(s(s(z)))), elem!1)),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[2442, 47, 3074, 12624])).
% 2.54/2.72 tff(12626,plain,
% 2.54/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(12627,plain,
% 2.54/2.72 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(12628,plain,
% 2.54/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))))),
% 2.54/2.72 inference(monotonicity,[status(thm)],[12627])).
% 2.54/2.72 tff(12629,plain,
% 2.54/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.54/2.72 inference(transitivity,[status(thm)],[12628, 12626])).
% 2.54/2.72 tff(12630,plain,
% 2.54/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))))),
% 2.54/2.72 inference(quant_inst,[status(thm)],[])).
% 2.54/2.72 tff(12631,plain,
% 2.54/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))),
% 2.54/2.72 inference(modus_ponens,[status(thm)],[12630, 12629])).
% 2.54/2.72 tff(12632,plain,
% 2.54/2.72 (~r(s(z), s(s(s(s(z)))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[12631, 183, 217, 12625])).
% 2.54/2.72 tff(12633,plain,
% 2.54/2.72 ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z)))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[6092, 47, 12632])).
% 2.54/2.72 tff(12634,plain,
% 2.54/2.72 (b(s(z), s(s(s(s(z)))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[12633, 5790])).
% 2.54/2.72 tff(12635,plain,
% 2.54/2.72 (~r(z, s(s(s(s(z)))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[2641, 183, 429, 2593])).
% 2.54/2.72 tff(12636,plain,
% 2.54/2.72 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z)))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[2645, 47, 12635])).
% 2.54/2.72 tff(12637,plain,
% 2.54/2.72 (b(z, s(s(s(s(z)))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[12636, 2635])).
% 2.54/2.72 tff(12638,plain,
% 2.54/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(12639,plain,
% 2.54/2.72 (((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(12640,plain,
% 2.54/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 2.54/2.72 inference(monotonicity,[status(thm)],[12639])).
% 2.54/2.72 tff(12641,plain,
% 2.54/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.54/2.72 inference(transitivity,[status(thm)],[12640, 12638])).
% 2.54/2.72 tff(12642,plain,
% 2.54/2.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))),
% 2.54/2.72 inference(quant_inst,[status(thm)],[])).
% 2.54/2.72 tff(12643,plain,
% 2.54/2.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 2.54/2.72 inference(modus_ponens,[status(thm)],[12642, 12641])).
% 2.54/2.72 tff(12644,plain,
% 2.54/2.72 (~b(s(z), z)),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[12643, 246, 8267, 8550, 9862])).
% 2.54/2.72 tff(12645,plain,
% 2.54/2.72 (r(s(z), z)),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[1069, 12644])).
% 2.54/2.72 tff(12646,plain,
% 2.54/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(12647,plain,
% 2.54/2.72 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(12648,plain,
% 2.54/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z))))))),
% 2.54/2.73 inference(monotonicity,[status(thm)],[12647])).
% 2.54/2.73 tff(12649,plain,
% 2.54/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 2.54/2.73 inference(transitivity,[status(thm)],[12648, 12646])).
% 2.54/2.73 tff(12650,plain,
% 2.54/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 2.54/2.73 inference(quant_inst,[status(thm)],[])).
% 2.54/2.73 tff(12651,plain,
% 2.54/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z))))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[12650, 12649])).
% 2.54/2.73 tff(12652,plain,
% 2.54/2.73 (~b(s(z), s(s(z)))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[12651, 246, 3457, 8550, 8266, 9862])).
% 2.54/2.73 tff(12653,plain,
% 2.54/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(12654,plain,
% 2.54/2.73 (((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(12655,plain,
% 2.54/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z))))),
% 2.54/2.73 inference(monotonicity,[status(thm)],[12654])).
% 2.54/2.73 tff(12656,plain,
% 2.54/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 2.54/2.73 inference(transitivity,[status(thm)],[12655, 12653])).
% 2.54/2.73 tff(12657,plain,
% 2.54/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 2.54/2.73 inference(quant_inst,[status(thm)],[])).
% 2.54/2.73 tff(12658,plain,
% 2.54/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[12657, 12656])).
% 2.54/2.73 tff(12659,plain,
% 2.54/2.73 (~b(s(s(z)), z)),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[12658, 246, 3457, 8267, 8550, 9862])).
% 2.54/2.73 tff(12660,plain,
% 2.54/2.73 (r(s(s(z)), z)),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[12552, 12659])).
% 2.54/2.73 tff(12661,plain,
% 2.54/2.73 ($false),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[9028, 12660, 12652, 12645])).
% 2.54/2.73 tff(12662,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.73 tff(12663,plain,
% 2.54/2.73 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[12662, 12637, 12605, 12634, 12615])).
% 2.54/2.73 tff(12664,plain,
% 2.54/2.73 (r(s(s(z)), s(s(s(s(z)))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[1531, 12663])).
% 2.54/2.73 tff(12665,plain,
% 2.54/2.73 (~r(s(s(s(z))), s(s(z)))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[8987, 183, 12664, 12623])).
% 2.54/2.73 tff(12666,plain,
% 2.54/2.73 (b(s(s(s(z))), s(s(z)))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[8991, 47, 8374, 12665])).
% 2.54/2.73 tff(12667,plain,
% 2.54/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(12668,plain,
% 2.54/2.73 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1))) <=> ((~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(12669,plain,
% 2.54/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 2.54/2.73 inference(monotonicity,[status(thm)],[12668])).
% 2.54/2.73 tff(12670,plain,
% 2.54/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.54/2.73 inference(transitivity,[status(thm)],[12669, 12667])).
% 2.54/2.73 tff(12671,plain,
% 2.54/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)))),
% 2.54/2.73 inference(quant_inst,[status(thm)],[])).
% 2.54/2.73 tff(12672,plain,
% 2.54/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[12671, 12670])).
% 2.54/2.73 tff(12673,plain,
% 2.54/2.73 (~r(s(s(z)), elem!1)),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[12672, 183, 474, 12664, 12613])).
% 2.54/2.73 tff(12674,plain,
% 2.54/2.73 (b(s(s(z)), elem!1)),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[9920, 47, 9917, 12673])).
% 2.54/2.73 tff(12675,plain,
% 2.54/2.73 (~r(s(s(z)), s(s(s(z))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[8558, 12664, 12623, 997])).
% 2.54/2.73 tff(12676,plain,
% 2.54/2.73 (b(s(s(z)), s(s(s(z))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[8382, 12675])).
% 2.54/2.73 tff(12677,plain,
% 2.54/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(12678,plain,
% 2.54/2.73 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(12679,plain,
% 2.54/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))))),
% 2.54/2.73 inference(monotonicity,[status(thm)],[12678])).
% 2.54/2.73 tff(12680,plain,
% 2.54/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.54/2.73 inference(transitivity,[status(thm)],[12679, 12677])).
% 2.54/2.73 tff(12681,plain,
% 2.54/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(z))))))),
% 2.54/2.73 inference(quant_inst,[status(thm)],[])).
% 2.54/2.73 tff(12682,plain,
% 2.54/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[12681, 12680])).
% 2.54/2.73 tff(12683,plain,
% 2.54/2.73 (~r(elem!1, s(s(s(z))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[12682, 183, 12623, 12613])).
% 2.54/2.73 tff(12684,plain,
% 2.54/2.73 (b(elem!1, s(s(s(z))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[470, 12683, 1675])).
% 2.54/2.73 tff(12685,plain,
% 2.54/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(12686,plain,
% 2.54/2.73 (((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(12687,plain,
% 2.54/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), elem!1))))),
% 2.54/2.73 inference(monotonicity,[status(thm)],[12686])).
% 2.54/2.73 tff(12688,plain,
% 2.54/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 2.54/2.73 inference(transitivity,[status(thm)],[12687, 12685])).
% 2.54/2.73 tff(12689,plain,
% 2.54/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 2.54/2.73 inference(quant_inst,[status(thm)],[])).
% 2.54/2.73 tff(12690,plain,
% 2.54/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), elem!1))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[12689, 12688])).
% 2.54/2.73 tff(12691,plain,
% 2.54/2.73 ($false),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[12690, 246, 12684, 12676, 12674, 12666])).
% 2.54/2.73 tff(12692,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (s(s(z)) = elem!1) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), z)) | (elem!1 = s(s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), elem!1)) | (s(s(s(s(z)))) = elem!1) | (~r(z, s(z))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.73 tff(12693,plain,
% 2.54/2.73 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[12692, 12597, 474, 9917, 1675, 2003, 217, 3074, 171, 12589])).
% 2.54/2.73 tff(12694,plain,
% 2.54/2.73 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[1702, 12693])).
% 2.54/2.73 tff(12695,plain,
% 2.54/2.73 (~r(s(z), s(s(s(z))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[6607, 12589, 171])).
% 2.54/2.73 tff(12696,plain,
% 2.54/2.73 (b(s(z), s(s(s(z))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[1291, 12695])).
% 2.54/2.73 tff(12697,plain,
% 2.54/2.73 (~b(s(s(s(s(z)))), s(z))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[3591, 246, 12696, 2003, 12694])).
% 2.54/2.73 tff(12698,plain,
% 2.54/2.73 (r(s(s(s(s(z)))), s(z))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[6103, 12697])).
% 2.54/2.73 tff(12699,plain,
% 2.54/2.73 (~r(s(s(s(s(z)))), elem!1)),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[2438, 183, 474, 12698])).
% 2.54/2.73 tff(12700,plain,
% 2.54/2.73 (b(s(s(s(s(z)))), elem!1)),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[2442, 47, 3074, 12699])).
% 2.54/2.73 tff(12701,plain,
% 2.54/2.73 (r(s(s(s(s(z)))), s(z))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[6103, 2408])).
% 2.54/2.73 tff(12702,plain,
% 2.54/2.73 (~r(elem!1, s(s(s(s(z)))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[7665, 12701, 474])).
% 2.54/2.73 tff(12703,plain,
% 2.54/2.73 ((~b(s(s(s(s(z)))), s(s(s(z))))) | b(elem!1, s(s(s(z)))) | (~b(elem!1, z)) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[2450, 11962])).
% 2.54/2.73 tff(12704,plain,
% 2.54/2.73 (b(elem!1, s(s(s(z))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[12703, 1833, 12505, 2401, 1056, 474, 171, 2003])).
% 2.54/2.73 tff(12705,plain,
% 2.54/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(12706,plain,
% 2.54/2.73 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(12707,plain,
% 2.54/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z))))))))),
% 2.54/2.73 inference(monotonicity,[status(thm)],[12706])).
% 2.54/2.73 tff(12708,plain,
% 2.54/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.54/2.73 inference(transitivity,[status(thm)],[12707, 12705])).
% 2.54/2.73 tff(12709,plain,
% 2.54/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.54/2.73 inference(quant_inst,[status(thm)],[])).
% 2.54/2.73 tff(12710,plain,
% 2.54/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z))))))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[12709, 12708])).
% 2.54/2.73 tff(12711,plain,
% 2.54/2.73 (~b(elem!1, s(s(s(s(z)))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[12710, 246, 12704, 2401, 2003, 1833])).
% 2.54/2.73 tff(12712,plain,
% 2.54/2.73 ($false),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[5969, 47, 12711, 12702, 8714])).
% 2.54/2.73 tff(12713,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (elem!1 = s(s(s(s(z))))) | (~r(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.73 tff(12714,plain,
% 2.54/2.73 (~b(s(z), z)),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[12713, 12694, 474, 12696, 2003, 9815, 171])).
% 2.54/2.73 tff(12715,plain,
% 2.54/2.73 (r(s(z), z)),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[1069, 12714])).
% 2.54/2.73 tff(12716,plain,
% 2.54/2.73 (~r(s(s(s(s(z)))), z)),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[9423, 12698, 12715])).
% 2.54/2.73 tff(12717,plain,
% 2.54/2.73 (b(s(s(s(s(z)))), z)),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[6040, 12716])).
% 2.54/2.73 tff(12718,plain,
% 2.54/2.73 (~r(elem!1, s(s(s(s(z)))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[7665, 12698, 474])).
% 2.54/2.73 tff(12719,plain,
% 2.54/2.73 (b(elem!1, s(s(s(s(z)))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[5969, 47, 12718, 9815])).
% 2.54/2.73 tff(12720,plain,
% 2.54/2.73 ($false),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[12363, 246, 11962, 12719, 12717, 12700])).
% 2.54/2.73 tff(12721,plain,((~b(s(s(s(z))), s(z))) | (s(s(s(s(z)))) = elem!1) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (s(s(z)) = elem!1) | (elem!1 = s(s(s(z)))) | (~r(s(z), elem!1)) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.54/2.73 tff(12722,plain,
% 2.54/2.73 (~r(s(z), elem!1)),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[12721, 12503, 11985, 171, 12497, 12496, 12495, 12486])).
% 2.54/2.73 tff(12723,plain,
% 2.54/2.73 (b(s(z), elem!1)),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[1034, 12722, 10])).
% 2.54/2.73 tff(12724,plain,
% 2.54/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(12725,plain,
% 2.54/2.73 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(12726,plain,
% 2.54/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))))),
% 2.54/2.73 inference(monotonicity,[status(thm)],[12725])).
% 2.54/2.73 tff(12727,plain,
% 2.54/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 2.54/2.73 inference(transitivity,[status(thm)],[12726, 12724])).
% 2.54/2.73 tff(12728,plain,
% 2.54/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 2.54/2.73 inference(quant_inst,[status(thm)],[])).
% 2.54/2.73 tff(12729,plain,
% 2.54/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[12728, 12727])).
% 2.54/2.73 tff(12730,plain,
% 2.54/2.73 (~b(s(z), z)),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[12729, 246, 11962, 1051, 1044])).
% 2.54/2.73 tff(12731,plain,
% 2.54/2.73 (r(s(z), z)),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[1069, 12730])).
% 2.54/2.73 tff(12732,plain,
% 2.54/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(12733,plain,
% 2.54/2.73 (((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(12734,plain,
% 2.54/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[12733])).
% 2.54/2.74 tff(12735,plain,
% 2.54/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.54/2.74 inference(transitivity,[status(thm)],[12734, 12732])).
% 2.54/2.74 tff(12736,plain,
% 2.54/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.54/2.74 inference(quant_inst,[status(thm)],[])).
% 2.54/2.74 tff(12737,plain,
% 2.54/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))),
% 2.54/2.74 inference(modus_ponens,[status(thm)],[12736, 12735])).
% 2.54/2.74 tff(12738,plain,
% 2.54/2.74 (~b(s(s(s(s(z)))), s(z))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[12737, 246, 11962, 1051, 1044, 5913])).
% 2.54/2.74 tff(12739,plain,
% 2.54/2.74 (r(s(s(s(s(z)))), s(z))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[6103, 12738])).
% 2.54/2.74 tff(12740,plain,
% 2.54/2.74 ($false),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[9423, 12739, 12555, 12731])).
% 2.54/2.74 tff(12741,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.74 tff(12742,plain,
% 2.54/2.74 (~b(s(s(s(s(z)))), elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[12741, 12009, 12723])).
% 2.54/2.74 tff(12743,plain,
% 2.54/2.74 (r(s(s(s(s(z)))), elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[2442, 47, 12495, 12742])).
% 2.54/2.74 tff(12744,plain,
% 2.54/2.74 (~b(s(z), z)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[12729, 246, 11962, 12505, 1044])).
% 2.54/2.74 tff(12745,plain,
% 2.54/2.74 (r(s(z), z)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[1069, 12744])).
% 2.54/2.74 tff(12746,plain,
% 2.54/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(12747,plain,
% 2.54/2.74 (((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(12748,plain,
% 2.54/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[12747])).
% 2.54/2.74 tff(12749,plain,
% 2.54/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.54/2.74 inference(transitivity,[status(thm)],[12748, 12746])).
% 2.54/2.74 tff(12750,plain,
% 2.54/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 2.54/2.74 inference(quant_inst,[status(thm)],[])).
% 2.54/2.74 tff(12751,plain,
% 2.54/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 2.54/2.74 inference(modus_ponens,[status(thm)],[12750, 12749])).
% 2.54/2.74 tff(12752,plain,
% 2.54/2.74 (~r(s(z), s(s(s(s(z)))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[12751, 183, 1114, 7218])).
% 2.54/2.74 tff(12753,plain,
% 2.54/2.74 ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z)))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[6092, 47, 12752])).
% 2.54/2.74 tff(12754,plain,
% 2.54/2.74 (b(s(z), s(s(s(s(z)))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[12753, 5790])).
% 2.54/2.74 tff(12755,plain,
% 2.54/2.74 (~r(s(s(s(s(z)))), s(z))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[9423, 7218, 1114])).
% 2.54/2.74 tff(12756,plain,
% 2.54/2.74 (b(s(s(s(s(z)))), s(z))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[6103, 12755])).
% 2.54/2.74 tff(12757,plain,
% 2.54/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(12758,plain,
% 2.54/2.74 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(12759,plain,
% 2.54/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[12758])).
% 2.54/2.74 tff(12760,plain,
% 2.54/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.54/2.74 inference(transitivity,[status(thm)],[12759, 12757])).
% 2.54/2.74 tff(12761,plain,
% 2.54/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.54/2.74 inference(quant_inst,[status(thm)],[])).
% 2.54/2.74 tff(12762,plain,
% 2.54/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))),
% 2.54/2.74 inference(modus_ponens,[status(thm)],[12761, 12760])).
% 2.54/2.74 tff(12763,plain,
% 2.54/2.74 ($false),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[12762, 246, 2003, 1833, 12756, 12754])).
% 2.54/2.74 tff(12764,plain,((~r(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.74 tff(12765,plain,
% 2.54/2.74 (~r(s(s(s(s(z)))), z)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[12764, 1833, 2003, 12745])).
% 2.54/2.74 tff(12766,plain,
% 2.54/2.74 (b(s(s(s(s(z)))), z)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[6040, 12765])).
% 2.54/2.74 tff(12767,plain,
% 2.54/2.74 ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[12337, 246, 11962, 1044, 2003, 1833])).
% 2.54/2.74 tff(12768,plain,
% 2.54/2.74 (~b(z, s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[12767, 12766])).
% 2.54/2.74 tff(12769,plain,
% 2.54/2.74 (r(z, s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[6165, 12768])).
% 2.54/2.74 tff(12770,plain,
% 2.54/2.74 (~r(s(z), s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[6607, 12769, 171])).
% 2.54/2.74 tff(12771,plain,
% 2.54/2.74 (b(s(z), s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[1291, 12770])).
% 2.54/2.74 tff(12772,plain,
% 2.54/2.74 ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[6494, 246, 1044, 2003, 1833])).
% 2.54/2.74 tff(12773,plain,
% 2.54/2.74 (~b(s(s(s(s(z)))), s(z))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[12772, 12771])).
% 2.54/2.74 tff(12774,plain,
% 2.54/2.74 (r(s(s(s(s(z)))), s(z))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[6103, 12773])).
% 2.54/2.74 tff(12775,plain,
% 2.54/2.74 (~r(s(s(s(s(z)))), elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[2438, 183, 474, 12774])).
% 2.54/2.74 tff(12776,plain,
% 2.54/2.74 (~b(s(s(s(s(z)))), elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[2431, 246, 11962, 12505, 12766])).
% 2.54/2.74 tff(12777,plain,
% 2.54/2.74 ($false),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[2442, 47, 3074, 12776, 12775])).
% 2.54/2.74 tff(12778,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (s(s(s(s(z)))) = elem!1) | (~r(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.74 tff(12779,plain,
% 2.54/2.74 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[12778, 12495, 11985, 12723, 12503, 171])).
% 2.54/2.74 tff(12780,plain,
% 2.54/2.74 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[1702, 12779])).
% 2.54/2.74 tff(12781,plain,
% 2.54/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(12782,plain,
% 2.54/2.74 (((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(12783,plain,
% 2.54/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[12782])).
% 2.54/2.74 tff(12784,plain,
% 2.54/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 2.54/2.74 inference(transitivity,[status(thm)],[12783, 12781])).
% 2.54/2.74 tff(12785,plain,
% 2.54/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 2.54/2.74 inference(quant_inst,[status(thm)],[])).
% 2.54/2.74 tff(12786,plain,
% 2.54/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))),
% 2.54/2.74 inference(modus_ponens,[status(thm)],[12785, 12784])).
% 2.54/2.74 tff(12787,plain,
% 2.54/2.74 ($false),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[12786, 246, 11962, 1051, 1044, 3697, 2003])).
% 2.54/2.74 tff(12788,plain,((~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.74 tff(12789,plain,
% 2.54/2.74 (~b(s(s(s(z))), elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[12788, 12009, 12723, 12503])).
% 2.54/2.74 tff(12790,plain,
% 2.54/2.74 (r(s(s(s(z))), elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[647, 12789, 12486])).
% 2.54/2.74 tff(12791,plain,
% 2.54/2.74 ($false),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[9058, 183, 12790, 12780, 12743])).
% 2.54/2.74 tff(12792,plain,(b(elem!1, s(z)) | (~r(z, s(z))) | r(s(s(elem!1)), elem!1) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.74 tff(12793,plain,
% 2.54/2.74 (b(elem!1, s(z))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[12792, 171, 2232, 3])).
% 2.54/2.74 tff(12794,plain,
% 2.54/2.74 (~(elem!1 = s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[6830, 2, 12793])).
% 2.54/2.74 tff(12795,plain,
% 2.54/2.74 (~(s(s(s(z))) = elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[1677, 12794])).
% 2.54/2.74 tff(12796,plain,
% 2.54/2.74 (~(s(s(elem!1)) = elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[12462, 2246, 171, 3, 2232])).
% 2.54/2.74 tff(12797,plain,
% 2.54/2.74 (b(s(s(elem!1)), elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[156, 12796, 2232])).
% 2.54/2.74 tff(12798,plain,
% 2.54/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(12799,plain,
% 2.54/2.74 (((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(12800,plain,
% 2.54/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z)))))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[12799])).
% 2.54/2.74 tff(12801,plain,
% 2.54/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))))),
% 2.54/2.74 inference(transitivity,[status(thm)],[12800, 12798])).
% 2.54/2.74 tff(12802,plain,
% 2.54/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))),
% 2.54/2.74 inference(quant_inst,[status(thm)],[])).
% 2.54/2.74 tff(12803,plain,
% 2.54/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z)))),
% 2.54/2.74 inference(modus_ponens,[status(thm)],[12802, 12801])).
% 2.54/2.74 tff(12804,plain,
% 2.54/2.74 ($false),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[12803, 246, 2239, 1044, 2362, 2001, 1100])).
% 2.54/2.74 tff(12805,plain,((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.74 tff(12806,plain,
% 2.54/2.74 ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[12805, 11962])).
% 2.54/2.74 tff(12807,plain,
% 2.54/2.74 (~b(s(z), elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[12806, 12797, 12482, 12793])).
% 2.54/2.74 tff(12808,plain,
% 2.54/2.74 (~r(s(s(s(z))), elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[2713, 12807, 2232, 430])).
% 2.54/2.74 tff(12809,plain,
% 2.54/2.74 (b(s(s(s(z))), elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[647, 12808, 3011])).
% 2.54/2.74 tff(12810,plain,
% 2.54/2.74 (r(s(z), elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[1034, 12807, 10])).
% 2.54/2.74 tff(12811,plain,
% 2.54/2.74 (~r(s(z), z)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[2725, 12810, 2246])).
% 2.54/2.74 tff(12812,plain,
% 2.54/2.74 (b(s(z), z)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[1069, 12811])).
% 2.54/2.74 tff(12813,plain,
% 2.54/2.74 ($false),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[12410, 12812, 12809, 12793, 430, 171])).
% 2.54/2.74 tff(12814,plain,((~r(elem!1, z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (s(s(s(z))) = elem!1) | r(s(s(elem!1)), elem!1) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.74 tff(12815,plain,
% 2.54/2.74 (~r(elem!1, z)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[12814, 53, 171, 12795, 2232, 3])).
% 2.54/2.74 tff(12816,plain,
% 2.54/2.74 (b(elem!1, z)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[12008, 12815])).
% 2.54/2.74 tff(12817,plain,
% 2.54/2.74 (~b(s(s(elem!1)), elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[12483, 12816, 12482])).
% 2.54/2.74 tff(12818,plain,
% 2.54/2.74 (s(s(elem!1)) = elem!1),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[156, 12817, 2232])).
% 2.54/2.74 tff(12819,plain,
% 2.54/2.74 (elem!1 = s(s(elem!1))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[6867, 12818])).
% 2.54/2.74 tff(12820,plain,
% 2.54/2.74 (s(s(s(elem!1))) = s(elem!1)),
% 2.54/2.74 inference(monotonicity,[status(thm)],[12818])).
% 2.54/2.74 tff(12821,plain,
% 2.54/2.74 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[12820])).
% 2.54/2.74 tff(12822,plain,
% 2.54/2.74 (s(s(s(s(elem!1)))) = elem!1),
% 2.54/2.74 inference(transitivity,[status(thm)],[12821, 12818])).
% 2.54/2.74 tff(12823,plain,
% 2.54/2.74 (s(s(s(s(s(elem!1))))) = s(elem!1)),
% 2.54/2.74 inference(monotonicity,[status(thm)],[12822])).
% 2.54/2.74 tff(12824,plain,
% 2.54/2.74 ((s(s(s(s(s(elem!1))))) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[12823])).
% 2.54/2.74 tff(12825,plain,
% 2.54/2.74 ((~(s(s(s(s(s(elem!1))))) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[12824])).
% 2.54/2.74 tff(12826,plain,
% 2.54/2.74 (~(s(elem!1) = s(s(s(z))))),
% 2.54/2.74 inference(modus_ponens,[status(thm)],[1622, 12825])).
% 2.54/2.74 tff(12827,plain,
% 2.54/2.74 (~(s(s(s(s(z)))) = elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[2399, 12826, 12819])).
% 2.54/2.74 tff(12828,plain,
% 2.54/2.74 (~(elem!1 = s(s(s(s(z)))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[8712, 12827])).
% 2.54/2.74 tff(12829,plain,
% 2.54/2.74 (~r(s(s(s(z))), z)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[11271, 183, 171, 53])).
% 2.54/2.74 tff(12830,plain,
% 2.54/2.74 (b(s(s(s(z))), z)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[995, 12829])).
% 2.54/2.74 tff(12831,plain,
% 2.54/2.74 (~r(z, s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[438, 53, 171])).
% 2.54/2.74 tff(12832,plain,
% 2.54/2.74 (b(z, s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[6165, 12831])).
% 2.54/2.74 tff(12833,plain,
% 2.54/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(12834,plain,
% 2.54/2.74 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z)))))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(12835,plain,
% 2.54/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[12834])).
% 2.54/2.74 tff(12836,plain,
% 2.54/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.54/2.74 inference(transitivity,[status(thm)],[12835, 12833])).
% 2.54/2.74 tff(12837,plain,
% 2.54/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.54/2.74 inference(quant_inst,[status(thm)],[])).
% 2.54/2.74 tff(12838,plain,
% 2.54/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 2.54/2.74 inference(modus_ponens,[status(thm)],[12837, 12836])).
% 2.54/2.74 tff(12839,plain,
% 2.54/2.74 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[12838, 246, 12482, 12832, 12830])).
% 2.54/2.74 tff(12840,plain,
% 2.54/2.74 (r(s(s(elem!1)), s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[454, 12839, 12305])).
% 2.54/2.74 tff(12841,plain,
% 2.54/2.74 (~r(s(s(elem!1)), s(z))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[7762, 12840, 53])).
% 2.54/2.74 tff(12842,plain,
% 2.54/2.74 (b(s(s(elem!1)), s(z))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[197, 12841])).
% 2.54/2.74 tff(12843,plain,
% 2.54/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(12844,plain,
% 2.54/2.75 (((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(12845,plain,
% 2.54/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z))))),
% 2.54/2.75 inference(monotonicity,[status(thm)],[12844])).
% 2.54/2.75 tff(12846,plain,
% 2.54/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))),
% 2.54/2.75 inference(transitivity,[status(thm)],[12845, 12843])).
% 2.54/2.75 tff(12847,plain,
% 2.54/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 2.54/2.75 inference(quant_inst,[status(thm)],[])).
% 2.54/2.75 tff(12848,plain,
% 2.54/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z))),
% 2.54/2.75 inference(modus_ponens,[status(thm)],[12847, 12846])).
% 2.54/2.75 tff(12849,plain,
% 2.54/2.75 ($false),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[12848, 246, 2239, 1051, 201, 1056, 1100])).
% 2.54/2.75 tff(12850,plain,((~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.75 tff(12851,plain,
% 2.54/2.75 ((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[12850, 11962])).
% 2.54/2.75 tff(12852,plain,
% 2.54/2.75 (~b(s(z), z)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[12851, 12816, 12482, 12842])).
% 2.54/2.75 tff(12853,plain,
% 2.54/2.75 (r(s(z), z)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[1069, 12852])).
% 2.54/2.75 tff(12854,plain,
% 2.54/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(12855,plain,
% 2.54/2.75 (((~b(elem!1, s(z))) | (~b(elem!1, 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(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(12856,plain,
% 2.54/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z))))),
% 2.54/2.75 inference(monotonicity,[status(thm)],[12855])).
% 2.54/2.75 tff(12857,plain,
% 2.54/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 2.54/2.75 inference(transitivity,[status(thm)],[12856, 12854])).
% 2.54/2.75 tff(12858,plain,
% 2.54/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 2.54/2.75 inference(quant_inst,[status(thm)],[])).
% 2.54/2.75 tff(12859,plain,
% 2.54/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z))),
% 2.54/2.75 inference(modus_ponens,[status(thm)],[12858, 12857])).
% 2.54/2.75 tff(12860,plain,
% 2.54/2.75 ((~b(elem!1, z)) | (~b(s(s(s(z))), elem!1))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[12859, 246, 11962, 12793, 12830])).
% 2.54/2.75 tff(12861,plain,
% 2.54/2.75 (~b(s(s(s(z))), elem!1)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[12860, 12816])).
% 2.54/2.75 tff(12862,plain,
% 2.54/2.75 (r(s(s(s(z))), elem!1)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[647, 12861, 12795])).
% 2.54/2.75 tff(12863,plain,
% 2.54/2.75 (b(s(z), elem!1)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[2713, 12862, 2232, 53])).
% 2.54/2.75 tff(12864,plain,
% 2.54/2.75 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[9060, 12827, 12793, 12862, 53, 12863])).
% 2.54/2.75 tff(12865,plain,
% 2.54/2.75 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[1702, 12864])).
% 2.54/2.75 tff(12866,plain,
% 2.54/2.75 (~b(s(s(s(s(z)))), z)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[9844, 12865, 12832, 12830])).
% 2.54/2.75 tff(12867,plain,
% 2.54/2.75 (r(s(s(s(s(z)))), z)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[6040, 12866])).
% 2.54/2.75 tff(12868,plain,
% 2.54/2.75 (~r(s(s(s(s(z)))), s(z))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[9423, 12867, 12853])).
% 2.54/2.75 tff(12869,plain,
% 2.54/2.75 (b(s(s(s(s(z)))), s(z))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[6103, 12868])).
% 2.54/2.75 tff(12870,plain,
% 2.54/2.75 (~b(elem!1, s(s(s(s(z)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[7175, 246, 12863, 12793, 12869])).
% 2.54/2.75 tff(12871,plain,
% 2.54/2.75 (r(elem!1, s(s(s(s(z)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[5969, 47, 12870, 12828])).
% 2.54/2.75 tff(12872,plain,
% 2.54/2.75 (~r(s(z), s(s(s(s(z)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[12751, 183, 12853, 12867])).
% 2.54/2.75 tff(12873,plain,
% 2.54/2.75 ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[6092, 47, 12872])).
% 2.54/2.75 tff(12874,plain,
% 2.54/2.75 (b(s(z), s(s(s(s(z)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[12873, 5790])).
% 2.54/2.75 tff(12875,plain,
% 2.54/2.75 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[9907, 12874, 171, 53, 12863, 12869])).
% 2.54/2.75 tff(12876,plain,
% 2.54/2.75 (r(s(s(z)), s(s(s(s(z)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[1531, 12875])).
% 2.54/2.75 tff(12877,plain,
% 2.54/2.75 (~r(s(s(z)), elem!1)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[9915, 183, 12876, 12871])).
% 2.54/2.75 tff(12878,plain,
% 2.54/2.75 (~(s(s(z)) = elem!1)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[9813, 12818])).
% 2.54/2.75 tff(12879,plain,
% 2.54/2.75 (b(s(s(z)), elem!1)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[9920, 47, 12878, 12877])).
% 2.54/2.75 tff(12880,plain,
% 2.54/2.75 (~b(z, s(s(s(s(z)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[8791, 246, 12832, 12830, 12865])).
% 2.54/2.75 tff(12881,plain,
% 2.54/2.75 ((z = s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[2645, 47, 12880])).
% 2.54/2.75 tff(12882,plain,
% 2.54/2.75 (r(z, s(s(s(s(z)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[12881, 2635])).
% 2.54/2.75 tff(12883,plain,
% 2.54/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(12884,plain,
% 2.54/2.75 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(z)), z))) <=> ((~r(z, s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(12885,plain,
% 2.54/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z))))),
% 2.54/2.75 inference(monotonicity,[status(thm)],[12884])).
% 2.54/2.75 tff(12886,plain,
% 2.54/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)))),
% 2.54/2.75 inference(transitivity,[status(thm)],[12885, 12883])).
% 2.54/2.75 tff(12887,plain,
% 2.54/2.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(z)), z)))),
% 2.54/2.75 inference(quant_inst,[status(thm)],[])).
% 2.54/2.75 tff(12888,plain,
% 2.54/2.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z))),
% 2.54/2.75 inference(modus_ponens,[status(thm)],[12887, 12886])).
% 2.54/2.75 tff(12889,plain,
% 2.54/2.75 (~r(s(s(z)), z)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[12888, 183, 171, 12876, 12882])).
% 2.54/2.75 tff(12890,plain,
% 2.54/2.75 (b(s(s(z)), z)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[12552, 12889])).
% 2.54/2.75 tff(12891,plain,
% 2.54/2.75 ($false),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[12547, 246, 11962, 12816, 12890, 12879])).
% 2.54/2.75 tff(12892,plain,(b(s(s(s(z))), s(z)) | (~r(z, s(z))) | r(s(s(elem!1)), elem!1) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.75 tff(12893,plain,
% 2.54/2.75 (b(s(s(s(z))), s(z))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[12892, 170, 2232, 11970])).
% 2.54/2.75 tff(12894,plain,
% 2.54/2.75 (~r(s(s(elem!1)), z)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[12480, 170, 2232, 11970])).
% 2.54/2.75 tff(12895,plain,
% 2.54/2.75 (b(s(s(elem!1)), z)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[523, 12894])).
% 2.54/2.75 tff(12896,plain,
% 2.54/2.75 (~(s(s(elem!1)) = s(elem!1))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[5640, 12796])).
% 2.54/2.75 tff(12897,plain,
% 2.54/2.75 (~(s(elem!1) = s(s(elem!1)))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[6946, 12896])).
% 2.54/2.75 tff(12898,plain,
% 2.54/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(12899,plain,
% 2.54/2.75 (((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(12900,plain,
% 2.54/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(z)))))),
% 2.54/2.75 inference(monotonicity,[status(thm)],[12899])).
% 2.54/2.75 tff(12901,plain,
% 2.54/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 2.54/2.75 inference(transitivity,[status(thm)],[12900, 12898])).
% 2.54/2.75 tff(12902,plain,
% 2.54/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))),
% 2.54/2.75 inference(quant_inst,[status(thm)],[])).
% 2.54/2.75 tff(12903,plain,
% 2.54/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(z)))),
% 2.54/2.75 inference(modus_ponens,[status(thm)],[12902, 12901])).
% 2.54/2.75 tff(12904,plain,
% 2.54/2.75 ($false),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[12903, 246, 2239, 1056, 2362, 2001, 1100, 1099])).
% 2.54/2.75 tff(12905,plain,((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.75 tff(12906,plain,
% 2.54/2.75 ((~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[12905, 11962])).
% 2.54/2.75 tff(12907,plain,
% 2.54/2.75 (~b(z, s(s(elem!1)))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[12906, 12812, 12482, 12793, 12797])).
% 2.54/2.75 tff(12908,plain,
% 2.54/2.75 (r(z, s(s(elem!1)))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[264, 12907])).
% 2.54/2.75 tff(12909,plain,
% 2.54/2.75 (~r(s(z), s(s(elem!1)))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[6407, 12908, 171])).
% 2.54/2.75 tff(12910,plain,
% 2.54/2.75 (b(s(z), s(s(elem!1)))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[233, 12909])).
% 2.54/2.75 tff(12911,plain,
% 2.54/2.75 (~b(s(elem!1), s(s(elem!1)))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[7269, 246, 1056, 2362, 2001, 1100, 1200])).
% 2.54/2.75 tff(12912,plain,
% 2.54/2.75 (r(s(elem!1), s(s(elem!1)))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[5561, 47, 12911, 6963])).
% 2.54/2.75 tff(12913,plain,
% 2.54/2.75 (~b(z, s(s(elem!1)))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[12906, 1056, 1100, 2001, 2362])).
% 2.54/2.75 tff(12914,plain,
% 2.54/2.75 (r(z, s(s(elem!1)))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[264, 12913])).
% 2.54/2.75 tff(12915,plain,
% 2.54/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(12916,plain,
% 2.54/2.75 (((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(12917,plain,
% 2.54/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1)))))),
% 2.54/2.75 inference(monotonicity,[status(thm)],[12916])).
% 2.54/2.75 tff(12918,plain,
% 2.54/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))))),
% 2.54/2.75 inference(transitivity,[status(thm)],[12917, 12915])).
% 2.54/2.75 tff(12919,plain,
% 2.54/2.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))))),
% 2.54/2.75 inference(quant_inst,[status(thm)],[])).
% 2.54/2.75 tff(12920,plain,
% 2.54/2.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1)))),
% 2.54/2.75 inference(modus_ponens,[status(thm)],[12919, 12918])).
% 2.54/2.75 tff(12921,plain,
% 2.54/2.75 (~r(z, s(elem!1))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[12920, 183, 12914, 12912])).
% 2.54/2.75 tff(12922,plain,
% 2.54/2.75 (b(z, s(elem!1))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[2561, 12921])).
% 2.54/2.75 tff(12923,plain,
% 2.54/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(12924,plain,
% 2.54/2.75 (((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(12925,plain,
% 2.54/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1)))))),
% 2.54/2.75 inference(monotonicity,[status(thm)],[12924])).
% 2.54/2.75 tff(12926,plain,
% 2.54/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))))),
% 2.54/2.76 inference(transitivity,[status(thm)],[12925, 12923])).
% 2.54/2.76 tff(12927,plain,
% 2.54/2.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))),
% 2.54/2.76 inference(quant_inst,[status(thm)],[])).
% 2.54/2.76 tff(12928,plain,
% 2.54/2.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1)))),
% 2.54/2.76 inference(modus_ponens,[status(thm)],[12927, 12926])).
% 2.54/2.76 tff(12929,plain,
% 2.54/2.76 ($false),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[12928, 246, 1056, 2362, 1100, 235, 1200, 12922])).
% 2.54/2.76 tff(12930,plain,((~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.76 tff(12931,plain,
% 2.54/2.76 (~b(s(elem!1), elem!1)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[12930, 12812, 12797, 12482, 12910, 12897, 12793])).
% 2.54/2.76 tff(12932,plain,
% 2.54/2.76 (b(s(s(s(z))), s(z))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[12892, 171, 2232, 3])).
% 2.54/2.76 tff(12933,plain,
% 2.54/2.76 ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[12379, 246, 11962, 1056, 2001, 2003])).
% 2.54/2.76 tff(12934,plain,
% 2.54/2.76 (~b(s(s(s(z))), z)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[12933, 2401])).
% 2.54/2.76 tff(12935,plain,
% 2.54/2.76 (r(s(s(s(z))), z)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[995, 12934])).
% 2.54/2.76 tff(12936,plain,
% 2.54/2.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(12937,plain,
% 2.54/2.76 (((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(12938,plain,
% 2.54/2.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[12937])).
% 2.54/2.76 tff(12939,plain,
% 2.54/2.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.54/2.76 inference(transitivity,[status(thm)],[12938, 12936])).
% 2.54/2.76 tff(12940,plain,
% 2.54/2.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))))),
% 2.54/2.76 inference(quant_inst,[status(thm)],[])).
% 2.54/2.76 tff(12941,plain,
% 2.54/2.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 2.54/2.76 inference(modus_ponens,[status(thm)],[12940, 12939])).
% 2.54/2.76 tff(12942,plain,
% 2.54/2.76 ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z)))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[12941, 246, 2362, 2001, 12064, 2003])).
% 2.54/2.76 tff(12943,plain,
% 2.54/2.76 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[12942, 2401])).
% 2.54/2.76 tff(12944,plain,
% 2.54/2.76 (r(s(s(s(z))), s(s(elem!1)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[689, 12943, 119])).
% 2.54/2.76 tff(12945,plain,
% 2.54/2.76 ($false),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[12078, 183, 171, 266, 12944, 12935])).
% 2.54/2.76 tff(12946,plain,((~b(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (s(s(s(z))) = s(s(elem!1))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.76 tff(12947,plain,
% 2.54/2.76 (~b(s(z), s(s(s(z))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[12946, 12908, 171, 7736, 12812, 12793, 12932, 12797])).
% 2.54/2.76 tff(12948,plain,
% 2.54/2.76 (r(s(z), s(s(s(z))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[1291, 12947])).
% 2.54/2.76 tff(12949,plain,
% 2.54/2.76 ($false),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[2326, 183, 217, 634, 6096])).
% 2.54/2.76 tff(12950,plain,((~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.76 tff(12951,plain,
% 2.54/2.76 (~r(s(s(s(z))), elem!1)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[12950, 12810, 12948])).
% 2.54/2.76 tff(12952,plain,
% 2.54/2.76 (~(elem!1 = s(s(elem!1)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[5450, 12796])).
% 2.54/2.76 tff(12953,plain,
% 2.54/2.76 (~r(z, s(s(s(z))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[6607, 12948, 171])).
% 2.54/2.76 tff(12954,plain,
% 2.54/2.76 (b(z, s(s(s(z))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[6165, 12953])).
% 2.54/2.76 tff(12955,plain,
% 2.54/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(12956,plain,
% 2.54/2.76 (((~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z))) <=> ((~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(12957,plain,
% 2.54/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z))))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[12956])).
% 2.54/2.76 tff(12958,plain,
% 2.54/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))),
% 2.54/2.76 inference(transitivity,[status(thm)],[12957, 12955])).
% 2.54/2.76 tff(12959,plain,
% 2.54/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)))),
% 2.54/2.76 inference(quant_inst,[status(thm)],[])).
% 2.54/2.76 tff(12960,plain,
% 2.54/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z))),
% 2.54/2.76 inference(modus_ponens,[status(thm)],[12959, 12958])).
% 2.54/2.76 tff(12961,plain,
% 2.54/2.76 (~r(elem!1, z)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[12960, 183, 602, 266])).
% 2.54/2.76 tff(12962,plain,
% 2.54/2.76 (b(elem!1, z)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[1143, 12961, 1438])).
% 2.54/2.76 tff(12963,plain,
% 2.54/2.76 ($false),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[12015, 246, 2239, 12962, 3697, 4651])).
% 2.54/2.76 tff(12964,plain,((~b(z, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (elem!1 = z) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.76 tff(12965,plain,
% 2.54/2.76 ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[12964, 11962, 11994])).
% 2.54/2.76 tff(12966,plain,
% 2.54/2.76 (~r(elem!1, s(s(elem!1)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[12965, 3697, 266, 4651])).
% 2.54/2.76 tff(12967,plain,
% 2.54/2.76 (b(elem!1, s(s(elem!1)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[1268, 12966, 1204])).
% 2.54/2.76 tff(12968,plain,
% 2.54/2.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(12969,plain,
% 2.54/2.76 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z)))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(12970,plain,
% 2.54/2.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[12969])).
% 2.54/2.76 tff(12971,plain,
% 2.54/2.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.54/2.76 inference(transitivity,[status(thm)],[12970, 12968])).
% 2.54/2.76 tff(12972,plain,
% 2.54/2.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))),
% 2.54/2.76 inference(quant_inst,[status(thm)],[])).
% 2.54/2.76 tff(12973,plain,
% 2.54/2.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 2.54/2.76 inference(modus_ponens,[status(thm)],[12972, 12971])).
% 2.54/2.76 tff(12974,plain,
% 2.54/2.76 ($false),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[12973, 246, 11962, 2362, 12967, 3697, 4651])).
% 2.54/2.76 tff(12975,plain,((~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(s(z))))) | (elem!1 = s(s(elem!1))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.76 tff(12976,plain,
% 2.54/2.76 (~b(s(s(s(z))), elem!1)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[12975, 12797, 12954, 12952, 12908])).
% 2.54/2.76 tff(12977,plain,
% 2.54/2.76 (s(s(s(z))) = elem!1),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[647, 12976, 12951])).
% 2.54/2.76 tff(12978,plain,
% 2.54/2.76 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[5677, 12977, 12931])).
% 2.54/2.76 tff(12979,plain,
% 2.54/2.76 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[12151, 11065, 217, 1673])).
% 2.54/2.76 tff(12980,plain,
% 2.54/2.76 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[86, 12979, 7042])).
% 2.54/2.76 tff(12981,plain,
% 2.54/2.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(12982,plain,
% 2.54/2.76 (((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), z))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(12983,plain,
% 2.54/2.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[12982])).
% 2.54/2.76 tff(12984,plain,
% 2.54/2.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.54/2.76 inference(transitivity,[status(thm)],[12983, 12981])).
% 2.54/2.76 tff(12985,plain,
% 2.54/2.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 2.54/2.76 inference(quant_inst,[status(thm)],[])).
% 2.54/2.76 tff(12986,plain,
% 2.54/2.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 2.54/2.76 inference(modus_ponens,[status(thm)],[12985, 12984])).
% 2.54/2.76 tff(12987,plain,
% 2.54/2.76 (~b(s(s(s(s(s(elem!1))))), z)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[12986, 246, 2239, 2362, 947, 714])).
% 2.54/2.76 tff(12988,plain,
% 2.54/2.76 (r(s(s(s(s(s(elem!1))))), z)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[1601, 12987])).
% 2.54/2.76 tff(12989,plain,
% 2.54/2.76 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[361, 47, 1555, 1554])).
% 2.54/2.76 tff(12990,plain,
% 2.54/2.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(12991,plain,
% 2.54/2.76 (((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(12992,plain,
% 2.54/2.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z))))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[12991])).
% 2.54/2.76 tff(12993,plain,
% 2.54/2.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))),
% 2.54/2.76 inference(transitivity,[status(thm)],[12992, 12990])).
% 2.54/2.76 tff(12994,plain,
% 2.54/2.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))),
% 2.54/2.76 inference(quant_inst,[status(thm)],[])).
% 2.54/2.76 tff(12995,plain,
% 2.54/2.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z))),
% 2.54/2.76 inference(modus_ponens,[status(thm)],[12994, 12993])).
% 2.54/2.76 tff(12996,plain,
% 2.54/2.76 (~b(s(s(elem!1)), z)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[12995, 246, 2239, 2362, 947])).
% 2.54/2.76 tff(12997,plain,
% 2.54/2.76 (r(s(s(elem!1)), z)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[523, 12996])).
% 2.54/2.76 tff(12998,plain,
% 2.54/2.76 ($false),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[2378, 183, 12997, 12989, 12988])).
% 2.54/2.76 tff(12999,plain,((~b(elem!1, s(s(elem!1)))) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | b(s(s(s(s(s(elem!1))))), s(s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.76 tff(13000,plain,
% 2.54/2.76 (~b(elem!1, s(s(elem!1)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[12999, 1554, 1555, 2239, 2362, 714])).
% 2.54/2.76 tff(13001,plain,
% 2.54/2.76 (r(elem!1, s(s(elem!1)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[1268, 13000, 1204])).
% 2.54/2.76 tff(13002,plain,
% 2.54/2.76 (~r(elem!1, s(s(s(s(s(elem!1))))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[5163, 183, 13001, 12989])).
% 2.54/2.76 tff(13003,plain,
% 2.54/2.76 ((elem!1 = s(s(s(s(s(elem!1)))))) | b(elem!1, s(s(s(s(s(elem!1))))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[3407, 47, 13002])).
% 2.54/2.76 tff(13004,plain,
% 2.54/2.76 (b(elem!1, s(s(s(s(s(elem!1))))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[13003, 3397])).
% 2.54/2.76 tff(13005,plain,
% 2.54/2.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(13006,plain,
% 2.54/2.76 (((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(13007,plain,
% 2.54/2.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1)))))))))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[13006])).
% 2.54/2.76 tff(13008,plain,
% 2.54/2.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 2.54/2.76 inference(transitivity,[status(thm)],[13007, 13005])).
% 2.54/2.76 tff(13009,plain,
% 2.54/2.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))),
% 2.54/2.76 inference(quant_inst,[status(thm)],[])).
% 2.54/2.76 tff(13010,plain,
% 2.54/2.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(s(s(elem!1)))))))),
% 2.54/2.76 inference(modus_ponens,[status(thm)],[13009, 13008])).
% 2.54/2.76 tff(13011,plain,
% 2.54/2.76 (~b(s(s(elem!1)), z)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[13010, 246, 2239, 2362, 714, 13004])).
% 2.54/2.77 tff(13012,plain,
% 2.54/2.77 (r(s(s(elem!1)), z)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[523, 13011])).
% 2.54/2.77 tff(13013,plain,
% 2.54/2.77 ($false),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[7107, 183, 2246, 13012, 13001])).
% 2.54/2.77 tff(13014,plain,(b(s(s(s(s(s(elem!1))))), s(s(elem!1))) | (~r(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (s(s(s(s(s(elem!1))))) = elem!1) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.77 tff(13015,plain,
% 2.54/2.77 (b(s(s(s(s(s(elem!1))))), s(s(elem!1))) | (~r(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (s(s(s(s(s(elem!1))))) = elem!1) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | (elem!1 = s(s(elem!1)))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[13014, 11962])).
% 2.54/2.77 tff(13016,plain,
% 2.54/2.77 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[13015, 12980, 1204, 2362, 5624, 7042, 2246])).
% 2.54/2.77 tff(13017,plain,
% 2.54/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(13018,plain,
% 2.54/2.77 (((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(13019,plain,
% 2.54/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[13018])).
% 2.54/2.77 tff(13020,plain,
% 2.54/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.54/2.77 inference(transitivity,[status(thm)],[13019, 13017])).
% 2.54/2.77 tff(13021,plain,
% 2.54/2.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.54/2.77 inference(quant_inst,[status(thm)],[])).
% 2.54/2.77 tff(13022,plain,
% 2.54/2.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 2.54/2.77 inference(modus_ponens,[status(thm)],[13021, 13020])).
% 2.54/2.77 tff(13023,plain,
% 2.54/2.77 ($false),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[13022, 246, 12402, 2362, 2001, 1100, 12980, 13016])).
% 2.54/2.77 tff(13024,plain,((~(s(s(s(z))) = elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (elem!1 = s(s(elem!1))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.77 tff(13025,plain,
% 2.54/2.77 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[13024, 12977, 12793, 12482, 12952, 2246, 12810, 12797])).
% 2.54/2.77 tff(13026,plain,
% 2.54/2.77 ($false),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[1702, 13025, 12978])).
% 2.54/2.77 tff(13027,plain,((~r(elem!1, z)) | (~r(z, s(z))) | r(s(s(elem!1)), elem!1) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.77 tff(13028,plain,
% 2.54/2.77 (~r(elem!1, z)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[13027, 170, 2232, 11970])).
% 2.54/2.77 tff(13029,plain,
% 2.54/2.77 (b(elem!1, z)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[12008, 13028])).
% 2.54/2.77 tff(13030,plain,
% 2.54/2.77 (~b(s(s(elem!1)), elem!1)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[12483, 13029, 12895])).
% 2.54/2.77 tff(13031,plain,
% 2.54/2.77 (s(s(elem!1)) = elem!1),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[156, 13030, 2232])).
% 2.54/2.77 tff(13032,plain,
% 2.54/2.77 (~(s(s(s(z))) = elem!1)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[5385, 13031])).
% 2.54/2.77 tff(13033,plain,
% 2.54/2.77 (elem!1 = s(s(elem!1))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[6867, 13031])).
% 2.54/2.77 tff(13034,plain,
% 2.54/2.77 (s(s(s(elem!1))) = s(elem!1)),
% 2.54/2.77 inference(monotonicity,[status(thm)],[13031])).
% 2.54/2.77 tff(13035,plain,
% 2.54/2.77 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[13034])).
% 2.54/2.77 tff(13036,plain,
% 2.54/2.77 (s(s(s(s(elem!1)))) = elem!1),
% 2.54/2.77 inference(transitivity,[status(thm)],[13035, 13031])).
% 2.54/2.77 tff(13037,plain,
% 2.54/2.77 (s(s(s(s(s(elem!1))))) = s(elem!1)),
% 2.54/2.77 inference(monotonicity,[status(thm)],[13036])).
% 2.54/2.77 tff(13038,plain,
% 2.54/2.77 ((s(s(s(s(s(elem!1))))) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[13037])).
% 2.54/2.77 tff(13039,plain,
% 2.54/2.77 ((~(s(s(s(s(s(elem!1))))) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[13038])).
% 2.54/2.77 tff(13040,plain,
% 2.54/2.77 (~(s(elem!1) = s(s(s(z))))),
% 2.54/2.77 inference(modus_ponens,[status(thm)],[1622, 13039])).
% 2.54/2.77 tff(13041,plain,
% 2.54/2.77 (~(s(s(s(s(z)))) = elem!1)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[2399, 13040, 13033])).
% 2.54/2.77 tff(13042,plain,
% 2.54/2.77 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[5804, 11971])).
% 2.54/2.77 tff(13043,plain,
% 2.54/2.77 (~(s(s(elem!1)) = s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[421, 13042])).
% 2.54/2.77 tff(13044,plain,
% 2.54/2.77 (~(elem!1 = s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[8772, 13031, 13043])).
% 2.54/2.77 tff(13045,plain,
% 2.54/2.77 (~(s(s(z)) = elem!1)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[9813, 13031])).
% 2.54/2.77 tff(13046,plain,
% 2.54/2.77 (b(elem!1, s(z))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[12792, 170, 2232, 11970])).
% 2.54/2.77 tff(13047,plain,
% 2.54/2.77 (b(s(s(elem!1)), s(z))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[2130, 13031, 13046])).
% 2.54/2.77 tff(13048,plain,
% 2.54/2.77 (~b(s(z), z)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[12851, 13047, 12895, 13029])).
% 2.54/2.77 tff(13049,plain,
% 2.54/2.77 (r(s(z), z)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[1069, 13048])).
% 2.54/2.77 tff(13050,plain,
% 2.54/2.77 (~b(s(s(s(s(z)))), elem!1)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[12741, 1044, 1051])).
% 2.54/2.77 tff(13051,plain,
% 2.54/2.77 ($false),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[2442, 47, 3074, 9825, 12220])).
% 2.54/2.77 tff(13052,plain,(r(s(s(s(s(z)))), elem!1) | (s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.54/2.77 tff(13053,plain,
% 2.54/2.77 (r(s(s(s(s(z)))), elem!1)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[13052, 13050, 3074])).
% 2.54/2.77 tff(13054,plain,
% 2.54/2.77 (~b(s(s(s(z))), elem!1)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[12788, 1044, 1051, 2003])).
% 2.54/2.77 tff(13055,plain,
% 2.54/2.77 (r(s(s(s(z))), elem!1)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[647, 13054, 3011])).
% 2.54/2.77 tff(13056,plain,
% 2.54/2.77 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[9058, 183, 13055, 13053])).
% 2.54/2.77 tff(13057,plain,
% 2.54/2.77 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[1702, 13056])).
% 2.54/2.77 tff(13058,plain,
% 2.54/2.77 (~r(s(s(s(s(z)))), z)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[12764, 13057, 2003, 1114])).
% 2.54/2.77 tff(13059,plain,
% 2.54/2.77 (b(s(s(s(s(z)))), z)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[6040, 13058])).
% 2.54/2.77 tff(13060,plain,
% 2.54/2.77 (~b(elem!1, s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[2011, 1044, 2001, 2003])).
% 2.54/2.77 tff(13061,plain,
% 2.54/2.77 (r(elem!1, s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[470, 13060, 1675])).
% 2.54/2.77 tff(13062,plain,
% 2.54/2.77 (r(s(s(s(s(z)))), elem!1)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[2442, 47, 3074, 13050])).
% 2.54/2.77 tff(13063,plain,
% 2.54/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(13064,plain,
% 2.54/2.77 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(13065,plain,
% 2.54/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1))))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[13064])).
% 2.54/2.77 tff(13066,plain,
% 2.54/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.54/2.77 inference(transitivity,[status(thm)],[13065, 13063])).
% 2.54/2.77 tff(13067,plain,
% 2.54/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.54/2.77 inference(quant_inst,[status(thm)],[])).
% 2.54/2.77 tff(13068,plain,
% 2.54/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1))),
% 2.54/2.77 inference(modus_ponens,[status(thm)],[13067, 13066])).
% 2.54/2.77 tff(13069,plain,
% 2.54/2.77 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[13068, 183, 634, 6496, 13062])).
% 2.54/2.77 tff(13070,plain,
% 2.54/2.77 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[8213, 47, 8210, 13069])).
% 2.54/2.77 tff(13071,plain,
% 2.54/2.77 (~r(s(s(s(s(z)))), z)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[12764, 1833, 2003, 1114])).
% 2.54/2.77 tff(13072,plain,
% 2.54/2.77 (b(s(s(s(s(z)))), z)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[6040, 13071])).
% 2.54/2.77 tff(13073,plain,
% 2.54/2.77 (~r(z, s(s(s(s(z)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[9071, 6496, 171])).
% 2.54/2.77 tff(13074,plain,
% 2.54/2.77 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[2645, 47, 13073])).
% 2.54/2.77 tff(13075,plain,
% 2.54/2.77 (b(z, s(s(s(s(z)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[13074, 2635])).
% 2.54/2.77 tff(13076,plain,
% 2.54/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(13077,plain,
% 2.54/2.77 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(13078,plain,
% 2.54/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[13077])).
% 2.54/2.77 tff(13079,plain,
% 2.54/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.54/2.77 inference(transitivity,[status(thm)],[13078, 13076])).
% 2.54/2.77 tff(13080,plain,
% 2.54/2.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.54/2.77 inference(quant_inst,[status(thm)],[])).
% 2.54/2.77 tff(13081,plain,
% 2.54/2.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))),
% 2.54/2.77 inference(modus_ponens,[status(thm)],[13080, 13079])).
% 2.54/2.77 tff(13082,plain,
% 2.54/2.77 (~b(s(z), s(s(s(s(z)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[13081, 246, 2401, 2003, 1833])).
% 2.54/2.77 tff(13083,plain,
% 2.54/2.77 ((s(z) = s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[6092, 47, 13082])).
% 2.54/2.77 tff(13084,plain,
% 2.54/2.77 (r(s(z), s(s(s(s(z)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[13083, 5790])).
% 2.54/2.77 tff(13085,plain,
% 2.54/2.77 (~b(elem!1, s(s(s(s(z)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[12611, 246, 11962, 1051, 13072])).
% 2.54/2.77 tff(13086,plain,
% 2.54/2.77 (r(elem!1, s(s(s(s(z)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[5969, 47, 13085, 9815])).
% 2.54/2.77 tff(13087,plain,
% 2.54/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(13088,plain,
% 2.54/2.77 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), elem!1))) <=> ((~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(13089,plain,
% 2.54/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[13088])).
% 2.54/2.77 tff(13090,plain,
% 2.54/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.54/2.77 inference(transitivity,[status(thm)],[13089, 13087])).
% 2.54/2.77 tff(13091,plain,
% 2.54/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), elem!1)))),
% 2.54/2.77 inference(quant_inst,[status(thm)],[])).
% 2.54/2.77 tff(13092,plain,
% 2.54/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 2.54/2.77 inference(modus_ponens,[status(thm)],[13091, 13090])).
% 2.54/2.77 tff(13093,plain,
% 2.54/2.77 (~r(s(s(z)), elem!1)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[13092, 183, 413, 1908, 5972])).
% 2.54/2.77 tff(13094,plain,
% 2.54/2.77 (b(s(s(z)), elem!1)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[9920, 47, 9917, 13093])).
% 2.54/2.77 tff(13095,plain,
% 2.54/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(13096,plain,
% 2.54/2.77 (((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(13097,plain,
% 2.54/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1))))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[13096])).
% 2.54/2.77 tff(13098,plain,
% 2.54/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 2.54/2.77 inference(transitivity,[status(thm)],[13097, 13095])).
% 2.54/2.77 tff(13099,plain,
% 2.54/2.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))))),
% 2.54/2.77 inference(quant_inst,[status(thm)],[])).
% 2.54/2.77 tff(13100,plain,
% 2.54/2.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1))),
% 2.54/2.77 inference(modus_ponens,[status(thm)],[13099, 13098])).
% 2.54/2.77 tff(13101,plain,
% 2.54/2.77 ($false),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[13100, 246, 11962, 1051, 1044, 10150, 13094])).
% 2.54/2.77 tff(13102,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (s(s(z)) = elem!1) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.77 tff(13103,plain,
% 2.54/2.77 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[13102, 13086, 1044, 9917, 413, 1051, 13084])).
% 2.54/2.77 tff(13104,plain,
% 2.54/2.77 (b(s(s(z)), s(s(s(s(z)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[1531, 13103])).
% 2.54/2.77 tff(13105,plain,
% 2.54/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(13106,plain,
% 2.54/2.77 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(13107,plain,
% 2.54/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z))))))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[13106])).
% 2.54/2.77 tff(13108,plain,
% 2.54/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.54/2.77 inference(transitivity,[status(thm)],[13107, 13105])).
% 2.54/2.77 tff(13109,plain,
% 2.54/2.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.54/2.78 inference(quant_inst,[status(thm)],[])).
% 2.54/2.78 tff(13110,plain,
% 2.54/2.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z))))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[13109, 13108])).
% 2.54/2.78 tff(13111,plain,
% 2.54/2.78 (~b(s(s(s(z))), s(s(z)))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[13110, 246, 13104, 13075, 13072, 13070])).
% 2.54/2.78 tff(13112,plain,
% 2.54/2.78 (r(s(s(s(z))), s(s(z)))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[8991, 47, 8374, 13111])).
% 2.54/2.78 tff(13113,plain,
% 2.54/2.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(13114,plain,
% 2.54/2.78 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(13115,plain,
% 2.54/2.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z))))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[13114])).
% 2.54/2.78 tff(13116,plain,
% 2.54/2.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 2.54/2.78 inference(transitivity,[status(thm)],[13115, 13113])).
% 2.54/2.78 tff(13117,plain,
% 2.54/2.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 2.54/2.78 inference(quant_inst,[status(thm)],[])).
% 2.54/2.78 tff(13118,plain,
% 2.54/2.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[13117, 13116])).
% 2.54/2.78 tff(13119,plain,
% 2.54/2.78 (~b(s(s(z)), z)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[13118, 246, 13104, 1833, 13075, 13070])).
% 2.54/2.78 tff(13120,plain,
% 2.54/2.78 (r(s(s(z)), z)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[12552, 13119])).
% 2.54/2.78 tff(13121,plain,
% 2.54/2.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(13122,plain,
% 2.54/2.78 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(13123,plain,
% 2.54/2.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[13122])).
% 2.54/2.78 tff(13124,plain,
% 2.54/2.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.54/2.78 inference(transitivity,[status(thm)],[13123, 13121])).
% 2.54/2.78 tff(13125,plain,
% 2.54/2.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.54/2.78 inference(quant_inst,[status(thm)],[])).
% 2.54/2.78 tff(13126,plain,
% 2.54/2.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[13125, 13124])).
% 2.54/2.78 tff(13127,plain,
% 2.54/2.78 (~b(s(s(z)), s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[13126, 246, 2003, 13104, 1833, 13070])).
% 2.54/2.78 tff(13128,plain,
% 2.54/2.78 (r(s(s(z)), s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[8382, 13127])).
% 2.54/2.78 tff(13129,plain,
% 2.54/2.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(13130,plain,
% 2.54/2.78 (((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(13131,plain,
% 2.54/2.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[13130])).
% 2.54/2.78 tff(13132,plain,
% 2.54/2.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.54/2.78 inference(transitivity,[status(thm)],[13131, 13129])).
% 2.54/2.78 tff(13133,plain,
% 2.54/2.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.54/2.78 inference(quant_inst,[status(thm)],[])).
% 2.54/2.78 tff(13134,plain,
% 2.54/2.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[13133, 13132])).
% 2.54/2.78 tff(13135,plain,
% 2.54/2.78 (~b(s(s(s(z))), z)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[13134, 246, 11962, 2001, 2003, 1833, 13072])).
% 2.54/2.78 tff(13136,plain,
% 2.54/2.78 (r(s(s(s(z))), z)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[995, 13135])).
% 2.54/2.78 tff(13137,plain,
% 2.54/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z)))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(13138,plain,
% 2.54/2.78 (((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z)))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(13139,plain,
% 2.54/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z))))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[13138])).
% 2.54/2.78 tff(13140,plain,
% 2.54/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z)))),
% 2.54/2.78 inference(transitivity,[status(thm)],[13139, 13137])).
% 2.54/2.78 tff(13141,plain,
% 2.54/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.54/2.78 inference(quant_inst,[status(thm)],[])).
% 2.54/2.78 tff(13142,plain,
% 2.54/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[13141, 13140])).
% 2.54/2.78 tff(13143,plain,
% 2.54/2.78 ($false),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[13142, 183, 13136, 13128, 13120, 13112])).
% 2.54/2.78 tff(13144,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (s(s(z)) = elem!1) | (~r(elem!1, s(s(s(z))))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (s(s(s(s(z)))) = elem!1) | (~r(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.78 tff(13145,plain,
% 2.54/2.78 (~b(s(z), s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[13144, 13057, 1044, 9917, 13061, 1051, 2001, 13055, 3074, 171, 2003, 1114])).
% 2.54/2.78 tff(13146,plain,
% 2.54/2.78 (r(s(z), s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[1291, 13145])).
% 2.54/2.78 tff(13147,plain,
% 2.54/2.78 (~r(z, s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[6607, 13146, 171])).
% 2.54/2.78 tff(13148,plain,
% 2.54/2.78 (b(z, s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[6165, 13147])).
% 2.54/2.78 tff(13149,plain,
% 2.54/2.78 ($false),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[12337, 246, 11962, 1044, 2003, 13148, 13057, 13059])).
% 2.54/2.78 tff(13150,plain,((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~r(z, s(z))) | (s(s(z)) = elem!1) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (s(s(s(s(z)))) = elem!1) | (~r(s(z), z)) | (elem!1 = s(s(s(z)))) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.54/2.78 tff(13151,plain,
% 2.54/2.78 (~b(s(z), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[13150, 12893, 170, 13045, 13029, 13046, 13041, 13049, 13044, 13032])).
% 2.54/2.78 tff(13152,plain,
% 2.54/2.78 (r(s(z), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[1034, 13151, 11971])).
% 2.54/2.78 tff(13153,plain,
% 2.54/2.78 (~r(elem!1, s(z))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[12721, 13152, 12893, 170, 13045, 13044, 13041, 13032])).
% 2.54/2.78 tff(13154,plain,
% 2.54/2.78 (~r(s(s(s(z))), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[12585, 13152, 12893, 13029, 13041, 13045])).
% 2.54/2.78 tff(13155,plain,
% 2.54/2.78 (b(s(s(s(z))), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[647, 13154, 13032])).
% 2.54/2.78 tff(13156,plain,
% 2.54/2.78 (r(s(z), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[1034, 1445, 10])).
% 2.54/2.78 tff(13157,plain,
% 2.54/2.78 (~r(elem!1, z)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[2725, 13156, 1114])).
% 2.54/2.78 tff(13158,plain,
% 2.54/2.78 (b(elem!1, z)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[1143, 13157, 1438])).
% 2.54/2.78 tff(13159,plain,
% 2.54/2.78 (b(z, elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[6422, 1445, 54, 6386, 3])).
% 2.54/2.78 tff(13160,plain,
% 2.54/2.78 ($false),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[12015, 246, 13159, 13158, 3697, 4651])).
% 2.54/2.78 tff(13161,plain,(b(s(z), elem!1) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (elem!1 = z) | (~r(s(z), z)) | b(z, s(z)) | r(elem!1, s(z)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.78 tff(13162,plain,
% 2.54/2.78 (b(s(z), elem!1) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~r(s(z), z)) | b(z, s(z)) | r(elem!1, s(z)) | (elem!1 = s(z))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[13161, 11994])).
% 2.54/2.78 tff(13163,plain,
% 2.54/2.78 (~b(z, s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[13162, 13155, 54, 13049, 11970, 13151, 13153])).
% 2.54/2.78 tff(13164,plain,
% 2.54/2.78 (r(z, s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[6165, 13163])).
% 2.54/2.78 tff(13165,plain,
% 2.54/2.78 (~r(s(z), s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[6607, 13164, 170])).
% 2.54/2.78 tff(13166,plain,
% 2.54/2.78 (b(s(z), s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[1291, 13165])).
% 2.54/2.78 tff(13167,plain,
% 2.54/2.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(13168,plain,
% 2.54/2.78 (((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(13169,plain,
% 2.54/2.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[13168])).
% 2.54/2.78 tff(13170,plain,
% 2.54/2.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.54/2.78 inference(transitivity,[status(thm)],[13169, 13167])).
% 2.54/2.78 tff(13171,plain,
% 2.54/2.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 2.54/2.78 inference(quant_inst,[status(thm)],[])).
% 2.54/2.78 tff(13172,plain,
% 2.54/2.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[13171, 13170])).
% 2.54/2.78 tff(13173,plain,
% 2.54/2.78 ($false),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[13172, 246, 13046, 13155, 13166, 12893])).
% 2.54/2.78 tff(13174,plain,(b(z, s(z)) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.54/2.78 tff(13175,plain,
% 2.54/2.78 (b(z, s(z))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[13174, 2232])).
% 2.54/2.78 tff(13176,plain,
% 2.54/2.78 (r(elem!1, s(z))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[214, 210, 2280])).
% 2.54/2.78 tff(13177,plain,
% 2.54/2.78 (~r(s(s(s(z))), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[2282, 210, 2232, 430])).
% 2.54/2.78 tff(13178,plain,
% 2.54/2.78 (~r(s(z), z)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[2725, 2246, 217])).
% 2.54/2.78 tff(13179,plain,
% 2.54/2.78 (b(s(z), z)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[1069, 13178])).
% 2.54/2.78 tff(13180,plain,
% 2.54/2.78 (~r(s(s(s(s(z)))), z)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[9960, 5972, 2246])).
% 2.54/2.78 tff(13181,plain,
% 2.54/2.78 (b(s(s(s(s(z)))), z)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[6040, 13180])).
% 2.54/2.78 tff(13182,plain,
% 2.54/2.78 (~r(s(s(s(s(z)))), s(z))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[7665, 5972, 474])).
% 2.54/2.78 tff(13183,plain,
% 2.54/2.78 (b(s(s(s(s(z)))), s(z))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[6103, 13182])).
% 2.54/2.78 tff(13184,plain,
% 2.54/2.78 ($false),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[8269, 13183, 13181, 236, 1056])).
% 2.54/2.78 tff(13185,plain,((~r(elem!1, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(elem!1, s(z))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.78 tff(13186,plain,
% 2.54/2.78 (~r(elem!1, s(s(s(s(z)))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[13185, 13179, 13175, 474, 2246])).
% 2.54/2.78 tff(13187,plain,
% 2.54/2.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(13188,plain,
% 2.54/2.78 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z))) <=> ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(13189,plain,
% 2.54/2.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z)))))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[13188])).
% 2.54/2.78 tff(13190,plain,
% 2.54/2.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 2.54/2.78 inference(transitivity,[status(thm)],[13189, 13187])).
% 2.54/2.78 tff(13191,plain,
% 2.54/2.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 2.54/2.78 inference(quant_inst,[status(thm)],[])).
% 2.54/2.78 tff(13192,plain,
% 2.54/2.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z)))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[13191, 13190])).
% 2.54/2.78 tff(13193,plain,
% 2.54/2.78 (~b(s(s(s(s(s(elem!1))))), z)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[13192, 246, 2239, 1056, 236, 2312])).
% 2.54/2.78 tff(13194,plain,
% 2.54/2.78 (r(s(s(s(s(s(elem!1))))), z)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[1601, 13193])).
% 2.54/2.78 tff(13195,plain,
% 2.54/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(13196,plain,
% 2.54/2.78 (((~r(elem!1, z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(elem!1))))), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(13197,plain,
% 2.54/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), elem!1))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[13196])).
% 2.54/2.79 tff(13198,plain,
% 2.54/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.54/2.79 inference(transitivity,[status(thm)],[13197, 13195])).
% 2.54/2.79 tff(13199,plain,
% 2.54/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.54/2.79 inference(quant_inst,[status(thm)],[])).
% 2.54/2.79 tff(13200,plain,
% 2.54/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[13199, 13198])).
% 2.54/2.79 tff(13201,plain,
% 2.54/2.79 ($false),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[13200, 183, 2246, 333, 13194])).
% 2.54/2.79 tff(13202,plain,((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.79 tff(13203,plain,
% 2.54/2.79 ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(z), elem!1))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[13202, 11962])).
% 2.54/2.79 tff(13204,plain,
% 2.54/2.79 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[13203, 13179, 13175, 217, 2246])).
% 2.54/2.79 tff(13205,plain,
% 2.54/2.79 (~r(z, s(z))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[2351, 2246, 474])).
% 2.54/2.79 tff(13206,plain,
% 2.54/2.79 (b(z, s(z))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[169, 13205])).
% 2.54/2.79 tff(13207,plain,
% 2.54/2.79 (~r(s(s(elem!1)), s(z))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[4199, 602, 474])).
% 2.54/2.79 tff(13208,plain,
% 2.54/2.79 (b(s(s(elem!1)), s(z))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[197, 13207])).
% 2.54/2.79 tff(13209,plain,
% 2.54/2.79 (~b(z, s(s(elem!1)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[1154, 13208, 2519, 13206])).
% 2.54/2.79 tff(13210,plain,
% 2.54/2.79 (r(z, s(s(elem!1)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[264, 13209])).
% 2.54/2.79 tff(13211,plain,
% 2.54/2.79 ($false),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[12960, 183, 2246, 602, 13210])).
% 2.54/2.79 tff(13212,plain,((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.79 tff(13213,plain,
% 2.54/2.79 (~r(elem!1, s(s(elem!1)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[13212, 2246, 474])).
% 2.54/2.79 tff(13214,plain,
% 2.54/2.79 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[86, 7042, 10487])).
% 2.54/2.79 tff(13215,plain,
% 2.54/2.79 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[13015, 13214, 5460, 5458, 5624, 7042, 2246])).
% 2.54/2.79 tff(13216,plain,
% 2.54/2.79 ($false),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[4983, 5461, 13215, 5458, 13214])).
% 2.54/2.79 tff(13217,plain,((~(s(s(s(z))) = elem!1)) | r(elem!1, s(s(elem!1))) | (~r(elem!1, z)) | r(s(s(elem!1)), elem!1) | r(s(s(s(s(s(elem!1))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.54/2.79 tff(13218,plain,
% 2.54/2.79 (~(s(s(s(z))) = elem!1)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[13217, 13213, 2246, 2232, 13204])).
% 2.54/2.79 tff(13219,plain,
% 2.54/2.79 (b(s(s(s(z))), elem!1)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[647, 13218, 10369])).
% 2.54/2.79 tff(13220,plain,
% 2.54/2.79 (~(elem!1 = s(s(s(z))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[3013, 13218])).
% 2.54/2.79 tff(13221,plain,
% 2.54/2.79 (b(elem!1, s(s(s(z))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[470, 13220, 5797])).
% 2.54/2.79 tff(13222,plain,
% 2.54/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(13223,plain,
% 2.54/2.79 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z)))))) <=> ((~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(13224,plain,
% 2.54/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[13223])).
% 2.54/2.79 tff(13225,plain,
% 2.54/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 2.54/2.79 inference(transitivity,[status(thm)],[13224, 13222])).
% 2.54/2.79 tff(13226,plain,
% 2.54/2.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))),
% 2.54/2.79 inference(quant_inst,[status(thm)],[])).
% 2.54/2.79 tff(13227,plain,
% 2.54/2.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[13226, 13225])).
% 2.54/2.79 tff(13228,plain,
% 2.54/2.79 (~b(z, s(s(s(z))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[13227, 246, 11962, 13221, 13219])).
% 2.54/2.79 tff(13229,plain,
% 2.54/2.79 (r(z, s(s(s(z))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[6165, 13228])).
% 2.54/2.79 tff(13230,plain,
% 2.54/2.79 (~b(s(s(s(s(z)))), z)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[8269, 8493, 236, 1056])).
% 2.54/2.79 tff(13231,plain,
% 2.54/2.79 (r(s(s(s(s(z)))), z)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[6040, 13230])).
% 2.54/2.79 tff(13232,plain,
% 2.54/2.79 ($false),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[2599, 183, 429, 2593, 13231])).
% 2.54/2.79 tff(13233,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.79 tff(13234,plain,
% 2.54/2.79 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[13233, 13229, 13175, 13179, 430])).
% 2.54/2.79 tff(13235,plain,
% 2.54/2.79 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[1702, 13234])).
% 2.54/2.79 tff(13236,plain,
% 2.54/2.79 (~b(elem!1, s(s(s(s(z)))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[5965, 246, 13221, 13219, 13235])).
% 2.54/2.79 tff(13237,plain,
% 2.54/2.79 ((elem!1 = s(s(s(s(z))))) | r(elem!1, s(s(s(s(z)))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[5969, 47, 13236])).
% 2.54/2.79 tff(13238,plain,
% 2.54/2.79 (elem!1 = s(s(s(s(z))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[13237, 13186])).
% 2.54/2.79 tff(13239,plain,
% 2.54/2.79 (s(s(s(s(z)))) = elem!1),
% 2.54/2.79 inference(symmetry,[status(thm)],[13238])).
% 2.54/2.79 tff(13240,plain,
% 2.54/2.79 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(z))), elem!1)),
% 2.54/2.79 inference(monotonicity,[status(thm)],[13239])).
% 2.54/2.79 tff(13241,plain,
% 2.54/2.79 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 2.54/2.79 inference(symmetry,[status(thm)],[13240])).
% 2.54/2.79 tff(13242,plain,
% 2.54/2.79 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[13219, 13241])).
% 2.54/2.79 tff(13243,plain,
% 2.54/2.79 (r(s(s(s(s(s(elem!1))))), elem!1) <=> r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[13238])).
% 2.54/2.79 tff(13244,plain,
% 2.54/2.79 ((~r(s(s(s(s(s(elem!1))))), elem!1)) <=> (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[13243])).
% 2.54/2.79 tff(13245,plain,
% 2.54/2.79 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[13204, 13244])).
% 2.54/2.79 tff(13246,plain,
% 2.54/2.79 (b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[1897, 13245])).
% 2.54/2.79 tff(13247,plain,
% 2.54/2.79 ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[11947, 246, 13246, 13235])).
% 2.54/2.79 tff(13248,plain,
% 2.54/2.79 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[13247, 13242])).
% 2.54/2.79 tff(13249,plain,
% 2.54/2.79 (r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[1626, 13248])).
% 2.54/2.79 tff(13250,plain,
% 2.54/2.79 (b(z, elem!1) <=> b(z, s(s(s(s(z)))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[13238])).
% 2.54/2.79 tff(13251,plain,
% 2.54/2.79 (b(z, s(s(s(s(z)))))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[11962, 13250])).
% 2.54/2.79 tff(13252,plain,
% 2.54/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(13253,plain,
% 2.54/2.79 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), z))) <=> ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(13254,plain,
% 2.54/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[13253])).
% 2.54/2.79 tff(13255,plain,
% 2.54/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.54/2.79 inference(transitivity,[status(thm)],[13254, 13252])).
% 2.54/2.79 tff(13256,plain,
% 2.54/2.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 2.54/2.79 inference(quant_inst,[status(thm)],[])).
% 2.54/2.79 tff(13257,plain,
% 2.54/2.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[13256, 13255])).
% 2.54/2.79 tff(13258,plain,
% 2.54/2.79 ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[13257, 246, 13246, 13235, 13251])).
% 2.54/2.79 tff(13259,plain,
% 2.54/2.79 (~b(s(s(s(s(s(elem!1))))), z)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[13258, 13242])).
% 2.54/2.79 tff(13260,plain,
% 2.54/2.79 (r(s(s(s(s(s(elem!1))))), z)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[1601, 13259])).
% 2.54/2.79 tff(13261,plain,
% 2.54/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(13262,plain,
% 2.54/2.79 (((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z))) <=> ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(13263,plain,
% 2.54/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[13262])).
% 2.54/2.79 tff(13264,plain,
% 2.54/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 2.54/2.79 inference(transitivity,[status(thm)],[13263, 13261])).
% 2.54/2.79 tff(13265,plain,
% 2.54/2.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 2.54/2.79 inference(quant_inst,[status(thm)],[])).
% 2.54/2.79 tff(13266,plain,
% 2.54/2.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[13265, 13264])).
% 2.54/2.79 tff(13267,plain,
% 2.54/2.79 (~b(s(s(s(z))), z)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[13266, 246, 11962, 13221, 13219])).
% 2.54/2.79 tff(13268,plain,
% 2.54/2.79 (r(s(s(s(z))), z)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[995, 13267])).
% 2.54/2.79 tff(13269,plain,
% 2.54/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(z))), s(z))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(13270,plain,
% 2.54/2.79 (((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(z))), s(z))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(13271,plain,
% 2.54/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(z))), s(z)))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[13270])).
% 2.54/2.79 tff(13272,plain,
% 2.54/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(z))), s(z))))),
% 2.54/2.79 inference(transitivity,[status(thm)],[13271, 13269])).
% 2.54/2.79 tff(13273,plain,
% 2.54/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 2.54/2.79 inference(quant_inst,[status(thm)],[])).
% 2.54/2.79 tff(13274,plain,
% 2.54/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(z))), s(z)))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[13273, 13272])).
% 2.54/2.79 tff(13275,plain,
% 2.54/2.79 ($false),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[13274, 183, 430, 13268, 13260, 13249])).
% 2.54/2.79 tff(13276,plain,((~r(elem!1, z)) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | r(s(s(s(z))), elem!1) | r(s(s(elem!1)), elem!1) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.79 tff(13277,plain,
% 2.54/2.79 (~r(elem!1, z)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[13276, 217, 474, 10369, 2232, 430])).
% 2.54/2.79 tff(13278,plain,
% 2.54/2.79 (b(elem!1, z)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[12008, 13277])).
% 2.54/2.79 tff(13279,plain,
% 2.54/2.79 (b(s(elem!1), elem!1) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.79 inference(symmetry,[status(thm)],[5674])).
% 2.54/2.79 tff(13280,plain,
% 2.54/2.79 ((~b(s(elem!1), elem!1)) <=> (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[13279])).
% 2.54/2.79 tff(13281,plain,
% 2.54/2.79 (~b(z, s(elem!1))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[2551, 246, 2239, 1051, 1200])).
% 2.54/2.79 tff(13282,plain,
% 2.54/2.79 (r(z, s(elem!1))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[2561, 13281])).
% 2.54/2.79 tff(13283,plain,
% 2.54/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(13284,plain,
% 2.54/2.79 (((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(13285,plain,
% 2.54/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[13284])).
% 2.54/2.79 tff(13286,plain,
% 2.54/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.54/2.79 inference(transitivity,[status(thm)],[13285, 13283])).
% 2.54/2.79 tff(13287,plain,
% 2.54/2.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.54/2.79 inference(quant_inst,[status(thm)],[])).
% 2.54/2.79 tff(13288,plain,
% 2.54/2.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[13287, 13286])).
% 2.54/2.79 tff(13289,plain,
% 2.54/2.79 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[13288, 246, 2239, 1051, 714, 1200])).
% 2.54/2.79 tff(13290,plain,
% 2.54/2.79 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[1795, 13289, 3410])).
% 2.54/2.79 tff(13291,plain,
% 2.54/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(z, s(elem!1))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(13292,plain,
% 2.54/2.79 (((~r(z, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(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(elem!1))) | (~r(z, s(elem!1))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(13293,plain,
% 2.54/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(z, s(elem!1)))))),
% 2.54/2.80 inference(monotonicity,[status(thm)],[13292])).
% 2.54/2.80 tff(13294,plain,
% 2.54/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(z, s(elem!1))))),
% 2.54/2.80 inference(transitivity,[status(thm)],[13293, 13291])).
% 2.54/2.80 tff(13295,plain,
% 2.54/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 2.54/2.80 inference(quant_inst,[status(thm)],[])).
% 2.54/2.80 tff(13296,plain,
% 2.54/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(z, s(elem!1)))),
% 2.54/2.80 inference(modus_ponens,[status(thm)],[13295, 13294])).
% 2.54/2.80 tff(13297,plain,
% 2.54/2.80 ($false),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[13296, 183, 13290, 13282, 2361])).
% 2.54/2.80 tff(13298,plain,((~b(s(elem!1), elem!1)) | (s(s(s(s(s(elem!1))))) = s(elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(elem!1))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.80 tff(13299,plain,
% 2.54/2.80 (~b(s(elem!1), elem!1)),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[13298, 1051, 2239, 12140, 714])).
% 2.54/2.80 tff(13300,plain,
% 2.54/2.80 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.80 inference(modus_ponens,[status(thm)],[13299, 13280])).
% 2.54/2.80 tff(13301,plain,
% 2.54/2.80 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[1702, 13300])).
% 2.54/2.80 tff(13302,plain,
% 2.54/2.80 (r(s(elem!1), elem!1)),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[5548, 13301, 1673])).
% 2.54/2.80 tff(13303,plain,
% 2.54/2.80 (~r(s(z), s(elem!1))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[6068, 183, 217, 13302])).
% 2.64/2.80 tff(13304,plain,
% 2.64/2.80 ((s(z) = s(elem!1)) | b(s(z), s(elem!1))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[2973, 47, 13303])).
% 2.64/2.80 tff(13305,plain,
% 2.64/2.80 (b(s(z), s(elem!1))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[13304, 11130])).
% 2.64/2.80 tff(13306,plain,
% 2.64/2.80 (~(s(s(elem!1)) = s(elem!1))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[5501, 11115])).
% 2.64/2.80 tff(13307,plain,
% 2.64/2.80 (r(s(s(elem!1)), s(s(s(z)))) <=> r(s(s(elem!1)), elem!1)),
% 2.64/2.80 inference(monotonicity,[status(thm)],[1673])).
% 2.64/2.80 tff(13308,plain,
% 2.64/2.80 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(s(s(z))))),
% 2.64/2.80 inference(symmetry,[status(thm)],[13307])).
% 2.64/2.80 tff(13309,plain,
% 2.64/2.80 (~b(s(s(elem!1)), elem!1)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[2388, 1051, 714, 1555, 2239])).
% 2.64/2.80 tff(13310,plain,
% 2.64/2.80 (r(s(s(elem!1)), elem!1)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[156, 13309, 5457])).
% 2.64/2.80 tff(13311,plain,
% 2.64/2.80 (r(s(s(elem!1)), s(s(s(z))))),
% 2.64/2.80 inference(modus_ponens,[status(thm)],[13310, 13308])).
% 2.64/2.80 tff(13312,plain,
% 2.64/2.80 ((elem!1 = s(elem!1)) <=> (s(s(s(z))) = s(elem!1))),
% 2.64/2.80 inference(monotonicity,[status(thm)],[7029])).
% 2.64/2.80 tff(13313,plain,
% 2.64/2.80 ((elem!1 = s(elem!1)) <=> (s(elem!1) = s(s(s(z))))),
% 2.64/2.80 inference(transitivity,[status(thm)],[13312, 2181])).
% 2.64/2.80 tff(13314,plain,
% 2.64/2.80 ((s(s(s(s(z)))) = elem!1) <=> (s(elem!1) = s(s(s(z))))),
% 2.64/2.80 inference(transitivity,[status(thm)],[5628, 13313])).
% 2.64/2.80 tff(13315,plain,
% 2.64/2.80 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(s(elem!1) = s(s(s(z)))))),
% 2.64/2.80 inference(monotonicity,[status(thm)],[13314])).
% 2.64/2.80 tff(13316,plain,
% 2.64/2.80 (~(s(elem!1) = s(s(s(z))))),
% 2.64/2.80 inference(modus_ponens,[status(thm)],[5633, 13315])).
% 2.64/2.80 tff(13317,plain,
% 2.64/2.80 (b(s(elem!1), s(s(s(z)))) <=> b(s(elem!1), elem!1)),
% 2.64/2.80 inference(monotonicity,[status(thm)],[1673])).
% 2.64/2.80 tff(13318,plain,
% 2.64/2.80 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(z))))),
% 2.64/2.80 inference(symmetry,[status(thm)],[13317])).
% 2.64/2.80 tff(13319,plain,
% 2.64/2.80 ((~b(s(elem!1), elem!1)) <=> (~b(s(elem!1), s(s(s(z)))))),
% 2.64/2.80 inference(monotonicity,[status(thm)],[13318])).
% 2.64/2.80 tff(13320,plain,
% 2.64/2.80 (~b(s(elem!1), s(s(s(z))))),
% 2.64/2.80 inference(modus_ponens,[status(thm)],[13299, 13319])).
% 2.64/2.80 tff(13321,plain,
% 2.64/2.80 (r(s(elem!1), s(s(s(z))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[1754, 13320, 13316])).
% 2.64/2.80 tff(13322,plain,
% 2.64/2.80 (~r(s(s(elem!1)), s(elem!1))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[3894, 13321, 13311])).
% 2.64/2.80 tff(13323,plain,
% 2.64/2.80 (b(s(s(elem!1)), s(elem!1))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[1949, 47, 13322, 13306])).
% 2.64/2.80 tff(13324,plain,
% 2.64/2.80 (~(s(elem!1) = s(s(elem!1)))),
% 2.64/2.80 inference(modus_ponens,[status(thm)],[13306, 5464])).
% 2.64/2.80 tff(13325,plain,
% 2.64/2.80 (~r(s(elem!1), s(s(elem!1)))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[373, 183, 13310, 13302])).
% 2.64/2.80 tff(13326,plain,
% 2.64/2.80 ((s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1)))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[5561, 47, 13325])).
% 2.64/2.80 tff(13327,plain,
% 2.64/2.80 (b(s(elem!1), s(s(elem!1)))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[13326, 13324])).
% 2.64/2.80 tff(13328,plain,
% 2.64/2.80 (~r(s(z), s(s(elem!1)))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[223, 183, 217, 13310])).
% 2.64/2.80 tff(13329,plain,
% 2.64/2.80 (b(s(z), s(s(elem!1)))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[233, 13328])).
% 2.64/2.80 tff(13330,plain,
% 2.64/2.80 (~r(s(s(elem!1)), s(z))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[2139, 183, 217, 13310])).
% 2.64/2.80 tff(13331,plain,
% 2.64/2.80 (b(s(s(elem!1)), s(z))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[197, 13330])).
% 2.64/2.80 tff(13332,plain,
% 2.64/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(13333,plain,
% 2.64/2.80 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(13334,plain,
% 2.64/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1)))))),
% 2.64/2.80 inference(monotonicity,[status(thm)],[13333])).
% 2.64/2.80 tff(13335,plain,
% 2.64/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))))),
% 2.64/2.80 inference(transitivity,[status(thm)],[13334, 13332])).
% 2.64/2.80 tff(13336,plain,
% 2.64/2.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1)))))),
% 2.64/2.80 inference(quant_inst,[status(thm)],[])).
% 2.64/2.80 tff(13337,plain,
% 2.64/2.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1)))),
% 2.64/2.80 inference(modus_ponens,[status(thm)],[13336, 13335])).
% 2.64/2.80 tff(13338,plain,
% 2.64/2.80 ($false),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[13337, 246, 13331, 13329, 13327, 13323, 13305])).
% 2.64/2.80 tff(13339,plain,((~b(elem!1, z)) | (~(s(s(s(z))) = elem!1)) | (~r(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (s(s(s(s(s(elem!1))))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.80 tff(13340,plain,
% 2.64/2.80 ((~b(elem!1, z)) | (~(s(s(s(z))) = elem!1)) | (~r(s(z), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[13339, 11962])).
% 2.64/2.80 tff(13341,plain,
% 2.64/2.80 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[13340, 5624, 1051, 217, 1673])).
% 2.64/2.80 tff(13342,plain,
% 2.64/2.80 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[86, 13341, 7042])).
% 2.64/2.80 tff(13343,plain,
% 2.64/2.80 (~r(s(elem!1), elem!1)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[12151, 13342, 217, 1673])).
% 2.64/2.80 tff(13344,plain,
% 2.64/2.80 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[5548, 13343, 1673])).
% 2.64/2.80 tff(13345,plain,
% 2.64/2.80 (~b(s(s(elem!1)), z)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[12483, 5458, 1051])).
% 2.64/2.80 tff(13346,plain,
% 2.64/2.80 (r(s(s(elem!1)), z)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[523, 13345])).
% 2.64/2.80 tff(13347,plain,
% 2.64/2.80 (~b(s(elem!1), elem!1)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[12046, 13346, 1051, 5641, 5458])).
% 2.64/2.80 tff(13348,plain,
% 2.64/2.80 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[5677, 13347, 1673])).
% 2.64/2.80 tff(13349,plain,
% 2.64/2.80 ($false),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[1702, 13348, 13344])).
% 2.64/2.80 tff(13350,plain,((~(s(s(s(z))) = elem!1)) | (~b(elem!1, z)) | (~r(s(z), elem!1)) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.64/2.80 tff(13351,plain,
% 2.64/2.80 (~(s(s(s(z))) = elem!1)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[13350, 13278, 217, 2232])).
% 2.64/2.80 tff(13352,plain,
% 2.64/2.80 (~(elem!1 = s(s(s(z))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[3013, 13351])).
% 2.64/2.80 tff(13353,plain,
% 2.64/2.80 (b(elem!1, s(s(s(z))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[470, 13352, 5797])).
% 2.64/2.80 tff(13354,plain,
% 2.64/2.80 (b(s(s(s(z))), elem!1)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[647, 13351, 10369])).
% 2.64/2.80 tff(13355,plain,
% 2.64/2.80 (~b(s(s(s(z))), z)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[12595, 246, 11962, 13278, 13354])).
% 2.64/2.80 tff(13356,plain,
% 2.64/2.80 (r(s(s(s(z))), z)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[995, 13355])).
% 2.64/2.80 tff(13357,plain,
% 2.64/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(13358,plain,
% 2.64/2.80 (((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(13359,plain,
% 2.64/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))))),
% 2.64/2.80 inference(monotonicity,[status(thm)],[13358])).
% 2.64/2.80 tff(13360,plain,
% 2.64/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 2.64/2.80 inference(transitivity,[status(thm)],[13359, 13357])).
% 2.64/2.80 tff(13361,plain,
% 2.64/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))),
% 2.64/2.80 inference(quant_inst,[status(thm)],[])).
% 2.64/2.80 tff(13362,plain,
% 2.64/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 2.64/2.80 inference(modus_ponens,[status(thm)],[13361, 13360])).
% 2.64/2.80 tff(13363,plain,
% 2.64/2.80 ($false),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[13362, 183, 1114, 430, 997])).
% 2.64/2.80 tff(13364,plain,((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.80 tff(13365,plain,
% 2.64/2.80 (~r(s(z), z)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[13364, 13356, 430])).
% 2.64/2.80 tff(13366,plain,
% 2.64/2.80 (b(s(z), z)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[1069, 13365])).
% 2.64/2.80 tff(13367,plain,
% 2.64/2.80 (~b(z, s(s(s(z))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[12015, 246, 11962, 13278, 13354])).
% 2.64/2.80 tff(13368,plain,
% 2.64/2.80 (r(z, s(s(s(z))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[6165, 13367])).
% 2.64/2.80 tff(13369,plain,
% 2.64/2.80 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[13233, 13366, 13175, 13368, 430])).
% 2.64/2.80 tff(13370,plain,
% 2.64/2.80 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[1702, 13369])).
% 2.64/2.80 tff(13371,plain,
% 2.64/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(13372,plain,
% 2.64/2.80 (((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), 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(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(13373,plain,
% 2.64/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 2.64/2.80 inference(monotonicity,[status(thm)],[13372])).
% 2.64/2.80 tff(13374,plain,
% 2.64/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.64/2.80 inference(transitivity,[status(thm)],[13373, 13371])).
% 2.64/2.80 tff(13375,plain,
% 2.64/2.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 2.64/2.80 inference(quant_inst,[status(thm)],[])).
% 2.64/2.80 tff(13376,plain,
% 2.64/2.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 2.64/2.80 inference(modus_ponens,[status(thm)],[13375, 13374])).
% 2.64/2.80 tff(13377,plain,
% 2.64/2.80 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[13376, 246, 2239, 1051, 3697, 714])).
% 2.64/2.80 tff(13378,plain,
% 2.64/2.80 (r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[1626, 13377])).
% 2.64/2.80 tff(13379,plain,
% 2.64/2.80 (~b(s(s(s(z))), z)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[12595, 246, 2239, 1051, 3697])).
% 2.64/2.80 tff(13380,plain,
% 2.64/2.80 (r(s(s(s(z))), z)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[995, 13379])).
% 2.64/2.80 tff(13381,plain,
% 2.64/2.80 ($false),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[1610, 183, 13380, 2361, 13378])).
% 2.64/2.80 tff(13382,plain,((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.80 tff(13383,plain,
% 2.64/2.80 ((~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[13382, 11962])).
% 2.64/2.80 tff(13384,plain,
% 2.64/2.80 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[13383, 3697, 1051])).
% 2.64/2.80 tff(13385,plain,
% 2.64/2.80 (~(s(elem!1) = s(s(s(z))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[8646, 2125, 13384, 3697])).
% 2.64/2.80 tff(13386,plain,
% 2.64/2.80 (~(s(s(s(s(z)))) = elem!1)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[2399, 13385, 7591])).
% 2.64/2.80 tff(13387,plain,
% 2.64/2.80 (~(elem!1 = s(s(s(s(z)))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[8712, 13386])).
% 2.64/2.80 tff(13388,plain,
% 2.64/2.80 (r(elem!1, s(s(s(s(z)))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[6008, 13387])).
% 2.64/2.80 tff(13389,plain,
% 2.64/2.80 (~r(s(s(s(s(z)))), s(z))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[7665, 13388, 474])).
% 2.64/2.80 tff(13390,plain,
% 2.64/2.80 (b(s(s(s(s(z)))), s(z))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[6103, 13389])).
% 2.64/2.80 tff(13391,plain,
% 2.64/2.80 (~b(s(s(s(s(z)))), z)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[8269, 13390, 236, 1056])).
% 2.64/2.80 tff(13392,plain,
% 2.64/2.80 (r(s(s(s(s(z)))), z)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[6040, 13391])).
% 2.64/2.80 tff(13393,plain,
% 2.64/2.80 (~b(s(s(s(z))), z)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[12595, 246, 11962, 1051, 3697])).
% 2.64/2.80 tff(13394,plain,
% 2.64/2.80 (r(s(s(s(z))), z)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[995, 13393])).
% 2.64/2.80 tff(13395,plain,
% 2.64/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(13396,plain,
% 2.64/2.80 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(13397,plain,
% 2.64/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))))),
% 2.64/2.80 inference(monotonicity,[status(thm)],[13396])).
% 2.64/2.80 tff(13398,plain,
% 2.64/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.64/2.80 inference(transitivity,[status(thm)],[13397, 13395])).
% 2.64/2.80 tff(13399,plain,
% 2.64/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.64/2.80 inference(quant_inst,[status(thm)],[])).
% 2.64/2.80 tff(13400,plain,
% 2.64/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 2.64/2.80 inference(modus_ponens,[status(thm)],[13399, 13398])).
% 2.64/2.80 tff(13401,plain,
% 2.64/2.80 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[13400, 183, 13394, 13392])).
% 2.64/2.80 tff(13402,plain,
% 2.64/2.80 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[8213, 47, 8210, 13401])).
% 2.64/2.80 tff(13403,plain,
% 2.64/2.80 (~b(s(z), s(s(s(z))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[8725, 13387, 474, 3697, 2002, 1833])).
% 2.64/2.80 tff(13404,plain,
% 2.64/2.80 (r(s(z), s(s(s(z))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[1291, 13403])).
% 2.64/2.80 tff(13405,plain,
% 2.64/2.80 (~r(s(s(z)), s(s(s(z))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[10217, 13404, 236, 12017, 1056])).
% 2.64/2.80 tff(13406,plain,
% 2.64/2.80 (b(s(s(z)), s(s(s(z))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[8382, 13405])).
% 2.64/2.80 tff(13407,assumption,(b(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 2.64/2.80 tff(13408,plain,
% 2.64/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(13409,plain,
% 2.64/2.80 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(13410,plain,
% 2.64/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 2.64/2.80 inference(monotonicity,[status(thm)],[13409])).
% 2.64/2.80 tff(13411,plain,
% 2.64/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.64/2.80 inference(transitivity,[status(thm)],[13410, 13408])).
% 2.64/2.81 tff(13412,plain,
% 2.64/2.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.64/2.81 inference(quant_inst,[status(thm)],[])).
% 2.64/2.81 tff(13413,plain,
% 2.64/2.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[13412, 13411])).
% 2.64/2.81 tff(13414,plain,
% 2.64/2.81 ($false),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[13413, 246, 3697, 3457, 1833, 1854, 13407])).
% 2.64/2.81 tff(13415,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.81 tff(13416,plain,
% 2.64/2.81 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[13415, 13406, 1833, 3697, 13402])).
% 2.64/2.81 tff(13417,plain,
% 2.64/2.81 (r(s(s(z)), s(s(s(s(z)))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[1531, 13416])).
% 2.64/2.81 tff(13418,plain,
% 2.64/2.81 (~r(s(s(z)), elem!1)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[12672, 183, 474, 13417, 13388])).
% 2.64/2.81 tff(13419,plain,
% 2.64/2.81 (b(s(s(z)), elem!1)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[9920, 47, 10091, 13418])).
% 2.64/2.81 tff(13420,plain,
% 2.64/2.81 (~b(z, s(s(s(s(z)))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[7673, 246, 1056, 236, 13390])).
% 2.64/2.81 tff(13421,plain,
% 2.64/2.81 ((z = s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[2645, 47, 13420])).
% 2.64/2.81 tff(13422,plain,
% 2.64/2.81 (r(z, s(s(s(s(z)))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[13421, 2635])).
% 2.64/2.81 tff(13423,plain,
% 2.64/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(13424,plain,
% 2.64/2.81 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(13425,plain,
% 2.64/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z))))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[13424])).
% 2.64/2.81 tff(13426,plain,
% 2.64/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)))),
% 2.64/2.81 inference(transitivity,[status(thm)],[13425, 13423])).
% 2.64/2.81 tff(13427,plain,
% 2.64/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z)))),
% 2.64/2.81 inference(quant_inst,[status(thm)],[])).
% 2.64/2.81 tff(13428,plain,
% 2.64/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[13427, 13426])).
% 2.64/2.81 tff(13429,plain,
% 2.64/2.81 (~r(s(s(z)), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[13428, 183, 12017, 13417, 13422])).
% 2.64/2.81 tff(13430,plain,
% 2.64/2.81 (b(s(s(z)), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[12552, 13429])).
% 2.64/2.81 tff(13431,plain,
% 2.64/2.81 ($false),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[12547, 246, 11962, 1051, 13430, 13419])).
% 2.64/2.81 tff(13432,plain,((~(s(s(elem!1)) = elem!1)) | (~b(elem!1, z)) | (~r(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.81 tff(13433,plain,
% 2.64/2.81 (~(s(s(elem!1)) = elem!1)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[13432, 13278, 474, 13370, 13354, 13366, 13175, 13353])).
% 2.64/2.81 tff(13434,plain,
% 2.64/2.81 (b(s(s(elem!1)), elem!1)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[156, 13433, 2232])).
% 2.64/2.81 tff(13435,plain,
% 2.64/2.81 (~b(s(s(elem!1)), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[12483, 13434, 13278])).
% 2.64/2.81 tff(13436,plain,
% 2.64/2.81 (r(s(s(elem!1)), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[523, 13435])).
% 2.64/2.81 tff(13437,plain,
% 2.64/2.81 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[5804, 2275])).
% 2.64/2.81 tff(13438,plain,
% 2.64/2.81 (~r(z, s(s(elem!1)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[12027, 13434, 13437, 13278, 13354])).
% 2.64/2.81 tff(13439,plain,
% 2.64/2.81 (b(z, s(s(elem!1)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[264, 13438])).
% 2.64/2.81 tff(13440,plain,
% 2.64/2.81 ($false),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[12300, 13439, 13436, 2232, 13277])).
% 2.64/2.81 tff(13441,plain,((~r(s(z), elem!1)) | r(s(s(elem!1)), elem!1) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.64/2.81 tff(13442,plain,
% 2.64/2.81 (~r(s(z), elem!1)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[13441, 13176, 2232, 430, 13177])).
% 2.64/2.81 tff(13443,plain,
% 2.64/2.81 (b(s(z), elem!1)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[1034, 13442, 2275])).
% 2.64/2.81 tff(13444,plain,
% 2.64/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(13445,plain,
% 2.64/2.81 (((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z)))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(13446,plain,
% 2.64/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z)))))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[13445])).
% 2.64/2.81 tff(13447,plain,
% 2.64/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))))),
% 2.64/2.81 inference(transitivity,[status(thm)],[13446, 13444])).
% 2.64/2.81 tff(13448,plain,
% 2.64/2.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 2.64/2.81 inference(quant_inst,[status(thm)],[])).
% 2.64/2.81 tff(13449,plain,
% 2.64/2.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z)))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[13448, 13447])).
% 2.64/2.81 tff(13450,plain,
% 2.64/2.81 ($false),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[13449, 246, 11962, 1051, 1044, 236])).
% 2.64/2.81 tff(13451,plain,((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.81 tff(13452,plain,
% 2.64/2.81 (~b(elem!1, z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[13451, 13443, 13175])).
% 2.64/2.81 tff(13453,plain,
% 2.64/2.81 (r(elem!1, z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[12008, 13452])).
% 2.64/2.81 tff(13454,plain,
% 2.64/2.81 (~r(elem!1, s(s(elem!1)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[13212, 13453, 13176])).
% 2.64/2.81 tff(13455,plain,
% 2.64/2.81 (~r(s(z), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[1163, 13453, 13176])).
% 2.64/2.81 tff(13456,plain,
% 2.64/2.81 (b(s(z), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[1069, 13455])).
% 2.64/2.81 tff(13457,plain,
% 2.64/2.81 (~(elem!1 = s(s(elem!1)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[5450, 199])).
% 2.64/2.81 tff(13458,plain,
% 2.64/2.81 (b(elem!1, s(s(elem!1)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[1268, 13457, 5459])).
% 2.64/2.81 tff(13459,plain,
% 2.64/2.81 (b(s(s(elem!1)), elem!1)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[156, 199, 2232])).
% 2.64/2.81 tff(13460,plain,
% 2.64/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(13461,plain,
% 2.64/2.81 (((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(13462,plain,
% 2.64/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[13461])).
% 2.64/2.81 tff(13463,plain,
% 2.64/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 2.64/2.81 inference(transitivity,[status(thm)],[13462, 13460])).
% 2.64/2.81 tff(13464,plain,
% 2.64/2.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 2.64/2.81 inference(quant_inst,[status(thm)],[])).
% 2.64/2.81 tff(13465,plain,
% 2.64/2.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[13464, 13463])).
% 2.64/2.81 tff(13466,plain,
% 2.64/2.81 ($false),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[13465, 246, 11962, 1056, 1044, 13459, 13458])).
% 2.64/2.81 tff(13467,plain,((s(s(elem!1)) = elem!1) | (~b(s(z), z)) | (~b(s(z), elem!1)) | r(elem!1, s(s(elem!1))) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.64/2.81 tff(13468,plain,
% 2.64/2.81 (s(s(elem!1)) = elem!1),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[13467, 13456, 13443, 13454, 2232])).
% 2.64/2.81 tff(13469,plain,
% 2.64/2.81 (s(s(s(elem!1))) = s(elem!1)),
% 2.64/2.81 inference(monotonicity,[status(thm)],[13468])).
% 2.64/2.81 tff(13470,plain,
% 2.64/2.81 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[13469])).
% 2.64/2.81 tff(13471,plain,
% 2.64/2.81 (s(s(s(s(elem!1)))) = elem!1),
% 2.64/2.81 inference(transitivity,[status(thm)],[13470, 13468])).
% 2.64/2.81 tff(13472,plain,
% 2.64/2.81 (s(s(s(s(s(elem!1))))) = s(elem!1)),
% 2.64/2.81 inference(monotonicity,[status(thm)],[13471])).
% 2.64/2.81 tff(13473,plain,
% 2.64/2.81 ((s(s(s(s(s(elem!1))))) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[13472])).
% 2.64/2.81 tff(13474,plain,
% 2.64/2.81 ((s(elem!1) = s(s(s(z)))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(z))))),
% 2.64/2.81 inference(symmetry,[status(thm)],[13473])).
% 2.64/2.81 tff(13475,plain,
% 2.64/2.81 (elem!1 = s(s(elem!1))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[6867, 13468])).
% 2.64/2.81 tff(13476,plain,
% 2.64/2.81 (~(s(s(s(z))) = elem!1)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[5385, 13468])).
% 2.64/2.81 tff(13477,plain,
% 2.64/2.81 (b(s(s(s(z))), elem!1)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[647, 13476, 13177])).
% 2.64/2.81 tff(13478,plain,
% 2.64/2.81 (~r(z, s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[13233, 2519, 13175, 2593, 430])).
% 2.64/2.81 tff(13479,plain,
% 2.64/2.81 (b(z, s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[6165, 13478])).
% 2.64/2.81 tff(13480,plain,
% 2.64/2.81 (~r(s(z), elem!1)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[13441, 474, 2232, 430, 10369])).
% 2.64/2.81 tff(13481,plain,
% 2.64/2.81 (b(s(z), elem!1)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[1034, 13480, 2275])).
% 2.64/2.81 tff(13482,plain,
% 2.64/2.81 (s(s(elem!1)) = elem!1),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[13467, 2519, 13481, 13213, 2232])).
% 2.64/2.81 tff(13483,plain,
% 2.64/2.81 (~(s(s(s(z))) = elem!1)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[5385, 13482])).
% 2.64/2.81 tff(13484,plain,
% 2.64/2.81 (b(s(s(s(z))), elem!1)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[647, 13483, 10369])).
% 2.64/2.81 tff(13485,plain,
% 2.64/2.81 (~(s(s(elem!1)) = s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[421, 13437])).
% 2.64/2.81 tff(13486,plain,
% 2.64/2.81 (~(elem!1 = s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[8772, 13482, 13485])).
% 2.64/2.81 tff(13487,plain,
% 2.64/2.81 (b(elem!1, s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[470, 13486, 5797])).
% 2.64/2.81 tff(13488,plain,
% 2.64/2.81 ($false),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[13227, 246, 11962, 13487, 13484, 13479])).
% 2.64/2.81 tff(13489,plain,((~r(elem!1, z)) | r(s(s(s(z))), elem!1) | r(s(s(elem!1)), elem!1) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.81 tff(13490,plain,
% 2.64/2.81 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[13489, 13453, 2232, 13177, 430, 13176])).
% 2.64/2.81 tff(13491,plain,
% 2.64/2.81 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[1702, 13490])).
% 2.64/2.81 tff(13492,plain,
% 2.64/2.81 (~r(elem!1, s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[5796, 183, 13176, 430])).
% 2.64/2.81 tff(13493,plain,
% 2.64/2.81 (~(elem!1 = s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[8772, 13468, 13485])).
% 2.64/2.81 tff(13494,plain,
% 2.64/2.81 (b(elem!1, s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[470, 13493, 13492])).
% 2.64/2.81 tff(13495,plain,
% 2.64/2.81 (s(s(s(s(z)))) = elem!1),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[7715, 13494, 13175, 13176, 13443, 13453, 13491, 13477])).
% 2.64/2.81 tff(13496,plain,
% 2.64/2.81 (s(elem!1) = s(s(s(z)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[2399, 13495, 13475])).
% 2.64/2.81 tff(13497,plain,
% 2.64/2.81 (s(s(s(s(s(elem!1))))) = s(s(s(z)))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[13496, 13474])).
% 2.64/2.81 tff(13498,plain,
% 2.64/2.81 ($false),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[1622, 13497])).
% 2.64/2.81 tff(13499,plain,(b(elem!1, s(z)) | r(s(s(elem!1)), elem!1) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.81 tff(13500,plain,
% 2.64/2.81 (b(elem!1, s(z))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[13499, 53, 2232])).
% 2.64/2.81 tff(13501,plain,
% 2.64/2.81 (~(s(z) = elem!1)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[2274, 53, 2232])).
% 2.64/2.81 tff(13502,plain,
% 2.64/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(13503,plain,
% 2.64/2.81 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(13504,plain,
% 2.64/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z)))))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[13503])).
% 2.64/2.81 tff(13505,plain,
% 2.64/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))))),
% 2.64/2.81 inference(transitivity,[status(thm)],[13504, 13502])).
% 2.64/2.81 tff(13506,plain,
% 2.64/2.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))),
% 2.64/2.81 inference(quant_inst,[status(thm)],[])).
% 2.64/2.81 tff(13507,plain,
% 2.64/2.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z)))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[13506, 13505])).
% 2.64/2.81 tff(13508,plain,
% 2.64/2.81 ($false),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[13507, 246, 11962, 1044, 2001, 236])).
% 2.64/2.81 tff(13509,plain,((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.81 tff(13510,plain,
% 2.64/2.81 (~b(s(z), elem!1)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[13509, 13500, 13175])).
% 2.64/2.81 tff(13511,plain,
% 2.64/2.81 (r(s(z), elem!1)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[1034, 13510, 13501])).
% 2.64/2.81 tff(13512,plain,
% 2.64/2.81 (~(elem!1 = s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[6830, 13500, 2])).
% 2.64/2.81 tff(13513,plain,
% 2.64/2.81 (~(s(s(s(z))) = elem!1)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[1677, 13512])).
% 2.64/2.81 tff(13514,plain,
% 2.64/2.81 (~r(s(s(s(z))), elem!1)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[2713, 13510, 2232, 53])).
% 2.64/2.81 tff(13515,plain,
% 2.64/2.81 (b(s(s(s(z))), elem!1)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[647, 13514, 13513])).
% 2.64/2.81 tff(13516,plain,
% 2.64/2.81 (~r(s(s(s(z))), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[13364, 1114, 430])).
% 2.64/2.81 tff(13517,plain,
% 2.64/2.81 (b(s(s(s(z))), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[995, 13516])).
% 2.64/2.81 tff(13518,plain,
% 2.64/2.81 (~r(elem!1, z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[2725, 1114, 217])).
% 2.64/2.81 tff(13519,plain,
% 2.64/2.81 (b(elem!1, z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[12008, 13518])).
% 2.64/2.81 tff(13520,plain,
% 2.64/2.81 ($false),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[12595, 246, 11962, 13519, 3697, 13517])).
% 2.64/2.81 tff(13521,plain,((~r(s(z), z)) | (~b(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.81 tff(13522,plain,
% 2.64/2.81 (~r(s(z), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[13521, 13515, 13511, 53])).
% 2.64/2.81 tff(13523,plain,
% 2.64/2.81 (b(s(z), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[1069, 13522])).
% 2.64/2.81 tff(13524,plain,
% 2.64/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(13525,plain,
% 2.64/2.81 (((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(13526,plain,
% 2.64/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z)))))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[13525])).
% 2.64/2.81 tff(13527,plain,
% 2.64/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))))),
% 2.64/2.81 inference(transitivity,[status(thm)],[13526, 13524])).
% 2.64/2.81 tff(13528,plain,
% 2.64/2.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))),
% 2.64/2.81 inference(quant_inst,[status(thm)],[])).
% 2.64/2.81 tff(13529,plain,
% 2.64/2.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z)))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[13528, 13527])).
% 2.64/2.81 tff(13530,plain,
% 2.64/2.81 ($false),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[13529, 246, 11962, 13523, 13500, 13175])).
% 2.64/2.81 tff(13531,plain,(b(s(s(s(z))), s(z)) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.64/2.81 tff(13532,plain,
% 2.64/2.81 (b(s(s(s(z))), s(z))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[13531, 2232])).
% 2.64/2.81 tff(13533,plain,
% 2.64/2.81 (~b(s(s(s(z))), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[2098, 1056, 13175, 13532])).
% 2.64/2.81 tff(13534,plain,
% 2.64/2.81 (r(s(s(s(z))), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[995, 13533])).
% 2.64/2.81 tff(13535,plain,
% 2.64/2.81 (~b(z, s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[6174, 1056, 13175, 13532])).
% 2.64/2.81 tff(13536,plain,
% 2.64/2.81 ((~(s(s(s(z))) = elem!1)) | b(z, s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[2242, 11962])).
% 2.64/2.81 tff(13537,plain,
% 2.64/2.81 (~(s(s(s(z))) = elem!1)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[13536, 13535])).
% 2.64/2.81 tff(13538,plain,
% 2.64/2.81 (r(s(s(s(z))), elem!1)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[647, 13537, 1])).
% 2.64/2.81 tff(13539,plain,
% 2.64/2.81 ($false),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[2533, 183, 2246, 634, 997])).
% 2.64/2.81 tff(13540,plain,((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.81 tff(13541,plain,
% 2.64/2.81 (~r(elem!1, z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[13540, 13538, 13534])).
% 2.64/2.81 tff(13542,plain,
% 2.64/2.81 (b(elem!1, z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[12008, 13541])).
% 2.64/2.81 tff(13543,plain,
% 2.64/2.81 (~b(elem!1, s(z))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[2262, 246, 11962, 13542, 1056])).
% 2.64/2.81 tff(13544,plain,
% 2.64/2.81 (r(elem!1, s(z))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[214, 13543, 5375])).
% 2.64/2.81 tff(13545,plain,
% 2.64/2.81 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[3545, 13538, 6900])).
% 2.64/2.81 tff(13546,plain,
% 2.64/2.81 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[1702, 11518])).
% 2.64/2.81 tff(13547,plain,
% 2.64/2.81 (r(z, s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[6165, 2214])).
% 2.64/2.81 tff(13548,plain,
% 2.64/2.81 (~r(s(s(s(s(z)))), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[2599, 183, 13547, 13546])).
% 2.64/2.81 tff(13549,plain,
% 2.64/2.81 (b(s(s(s(s(z)))), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[6040, 13548])).
% 2.64/2.81 tff(13550,plain,
% 2.64/2.81 (~b(s(s(s(s(z)))), s(z))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[8269, 13549, 236, 1056])).
% 2.64/2.81 tff(13551,plain,
% 2.64/2.81 (r(s(s(s(s(z)))), s(z))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[6103, 13550])).
% 2.64/2.81 tff(13552,plain,
% 2.64/2.81 (~r(elem!1, s(s(s(s(z)))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[7665, 13551, 474])).
% 2.64/2.81 tff(13553,plain,
% 2.64/2.81 (~b(elem!1, s(s(s(s(z)))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[12611, 246, 11962, 1051, 13549])).
% 2.64/2.81 tff(13554,plain,
% 2.64/2.81 (elem!1 = s(s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[5969, 47, 13553, 13552])).
% 2.64/2.81 tff(13555,plain,
% 2.64/2.81 (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[11936, 13554, 6330])).
% 2.64/2.81 tff(13556,plain,
% 2.64/2.81 (s(s(s(s(z)))) = elem!1),
% 2.64/2.81 inference(symmetry,[status(thm)],[13554])).
% 2.64/2.81 tff(13557,plain,
% 2.64/2.81 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(s(elem!1)), elem!1)),
% 2.64/2.81 inference(monotonicity,[status(thm)],[13556])).
% 2.64/2.81 tff(13558,plain,
% 2.64/2.81 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.64/2.81 inference(symmetry,[status(thm)],[13557])).
% 2.64/2.81 tff(13559,plain,
% 2.64/2.81 ((s(s(s(s(s(elem!1))))) = elem!1) <=> (s(s(s(s(s(elem!1))))) = s(s(s(s(z)))))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[13554])).
% 2.64/2.81 tff(13560,plain,
% 2.64/2.81 ((s(s(s(s(s(elem!1))))) = elem!1) <=> (s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))),
% 2.64/2.81 inference(transitivity,[status(thm)],[13559, 1483])).
% 2.64/2.81 tff(13561,plain,
% 2.64/2.81 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 2.64/2.81 inference(symmetry,[status(thm)],[13560])).
% 2.64/2.81 tff(13562,plain,
% 2.64/2.81 ((~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(s(elem!1))))) = elem!1))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[13561])).
% 2.64/2.81 tff(13563,plain,
% 2.64/2.81 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[1501, 13562])).
% 2.64/2.81 tff(13564,plain,
% 2.64/2.81 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[86, 13563, 10487])).
% 2.64/2.82 tff(13565,plain,
% 2.64/2.82 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[13554])).
% 2.64/2.82 tff(13566,plain,
% 2.64/2.82 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.64/2.82 inference(symmetry,[status(thm)],[13565])).
% 2.64/2.82 tff(13567,plain,
% 2.64/2.82 ((~b(s(s(s(s(z)))), s(s(s(z))))) <=> (~b(elem!1, s(s(s(z)))))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[13566])).
% 2.64/2.82 tff(13568,plain,
% 2.64/2.82 (~b(elem!1, s(s(s(z))))),
% 2.64/2.82 inference(modus_ponens,[status(thm)],[11518, 13567])).
% 2.64/2.82 tff(13569,plain,
% 2.64/2.82 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[3593, 13563, 56, 1, 1445, 2214, 13568])).
% 2.64/2.82 tff(13570,plain,
% 2.64/2.82 (b(s(s(s(s(s(elem!1))))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 2.64/2.82 inference(monotonicity,[status(thm)],[344])).
% 2.64/2.82 tff(13571,plain,
% 2.64/2.82 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.64/2.82 inference(symmetry,[status(thm)],[13570])).
% 2.64/2.82 tff(13572,plain,
% 2.64/2.82 ((~b(s(s(elem!1)), elem!1)) <=> (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[13571])).
% 2.64/2.82 tff(13573,plain,
% 2.64/2.82 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.64/2.82 inference(modus_ponens,[status(thm)],[145, 13572])).
% 2.64/2.82 tff(13574,plain,
% 2.64/2.82 ($false),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[714, 13573])).
% 2.64/2.82 tff(13575,plain,((~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.64/2.82 tff(13576,plain,
% 2.64/2.82 (b(s(s(elem!1)), elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[13575, 13569, 13564])).
% 2.64/2.82 tff(13577,plain,
% 2.64/2.82 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.64/2.82 inference(modus_ponens,[status(thm)],[13576, 13558])).
% 2.64/2.82 tff(13578,plain,
% 2.64/2.82 (~r(z, s(s(s(s(z)))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[2641, 183, 13547, 13546])).
% 2.64/2.82 tff(13579,plain,
% 2.64/2.82 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z)))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[2645, 47, 13578])).
% 2.64/2.82 tff(13580,plain,
% 2.64/2.82 (b(z, s(s(s(s(z)))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[13579, 2635])).
% 2.64/2.82 tff(13581,plain,
% 2.64/2.82 (r(s(s(s(s(s(elem!1))))), elem!1) <=> r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[13554])).
% 2.64/2.82 tff(13582,plain,
% 2.64/2.82 ((~r(s(s(s(s(s(elem!1))))), elem!1)) <=> (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[13581])).
% 2.64/2.82 tff(13583,plain,
% 2.64/2.82 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 2.64/2.82 inference(modus_ponens,[status(thm)],[10487, 13582])).
% 2.64/2.82 tff(13584,plain,
% 2.64/2.82 (b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[1897, 13583])).
% 2.64/2.82 tff(13585,plain,
% 2.64/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(13586,plain,
% 2.64/2.82 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(13587,plain,
% 2.64/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[13586])).
% 2.64/2.82 tff(13588,plain,
% 2.64/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.64/2.82 inference(transitivity,[status(thm)],[13587, 13585])).
% 2.64/2.82 tff(13589,plain,
% 2.64/2.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 2.64/2.82 inference(quant_inst,[status(thm)],[])).
% 2.64/2.82 tff(13590,plain,
% 2.64/2.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))),
% 2.64/2.82 inference(modus_ponens,[status(thm)],[13589, 13588])).
% 2.64/2.82 tff(13591,plain,
% 2.64/2.82 ((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[13590, 246, 13584, 13580, 13549])).
% 2.64/2.82 tff(13592,plain,
% 2.64/2.82 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[13591, 13577])).
% 2.64/2.82 tff(13593,plain,
% 2.64/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(13594,plain,
% 2.64/2.82 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), z))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(13595,plain,
% 2.64/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[13594])).
% 2.64/2.82 tff(13596,plain,
% 2.64/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.64/2.82 inference(transitivity,[status(thm)],[13595, 13593])).
% 2.64/2.82 tff(13597,plain,
% 2.64/2.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 2.64/2.82 inference(quant_inst,[status(thm)],[])).
% 2.64/2.82 tff(13598,plain,
% 2.64/2.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))),
% 2.64/2.82 inference(modus_ponens,[status(thm)],[13597, 13596])).
% 2.64/2.82 tff(13599,plain,
% 2.64/2.82 (~b(s(s(s(s(s(elem!1))))), z)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[13598, 246, 236, 13584, 13580, 13549])).
% 2.64/2.82 tff(13600,plain,
% 2.64/2.82 (r(s(s(s(s(s(elem!1))))), z)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[1601, 13599])).
% 2.64/2.82 tff(13601,plain,
% 2.64/2.82 (~b(s(s(elem!1)), z)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[12483, 13576, 1051])).
% 2.64/2.82 tff(13602,plain,
% 2.64/2.82 (r(s(s(elem!1)), z)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[523, 13601])).
% 2.64/2.82 tff(13603,plain,
% 2.64/2.82 (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[9592, 183, 13602, 13600])).
% 2.64/2.82 tff(13604,plain,
% 2.64/2.82 ($false),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[1547, 47, 13603, 13592, 13555])).
% 2.64/2.82 tff(13605,plain,(b(s(s(s(s(z)))), s(s(s(z)))) | (~b(z, s(z))) | (~b(elem!1, z)) | r(z, elem!1) | b(s(s(s(z))), elem!1) | b(s(z), elem!1) | b(z, s(s(s(z)))) | r(s(s(s(s(s(elem!1))))), elem!1) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~r(elem!1, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.82 tff(13606,plain,
% 2.64/2.82 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[13605, 13542, 13175, 56, 1, 1445, 13535, 13545, 8778, 13544, 1056])).
% 2.64/2.82 tff(13607,plain,
% 2.64/2.82 (s(s(s(s(z)))) = elem!1),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[12585, 10091, 2003, 217, 634, 1051])).
% 2.64/2.82 tff(13608,plain,
% 2.64/2.82 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.64/2.82 inference(transitivity,[status(thm)],[13607, 5380])).
% 2.64/2.82 tff(13609,plain,
% 2.64/2.82 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[13608])).
% 2.64/2.82 tff(13610,plain,
% 2.64/2.82 (s(s(s(z))) = s(elem!1)),
% 2.64/2.82 inference(transitivity,[status(thm)],[1492, 13609, 92])).
% 2.64/2.82 tff(13611,plain,
% 2.64/2.82 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[13610])).
% 2.64/2.82 tff(13612,plain,
% 2.64/2.82 (s(s(z)) = elem!1),
% 2.64/2.82 inference(transitivity,[status(thm)],[25, 13611, 343])).
% 2.64/2.82 tff(13613,plain,
% 2.64/2.82 ($false),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[10091, 13612])).
% 2.64/2.82 tff(13614,plain,((~(s(s(elem!1)) = elem!1)) | (~b(s(s(s(z))), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.82 tff(13615,plain,
% 2.64/2.82 (~(s(s(elem!1)) = elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[13614, 13538, 6900, 13532, 13542])).
% 2.64/2.82 tff(13616,plain,
% 2.64/2.82 (b(s(s(elem!1)), elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[156, 13615, 2232])).
% 2.64/2.82 tff(13617,plain,
% 2.64/2.82 (~b(s(s(elem!1)), z)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[12483, 13616, 13542])).
% 2.64/2.82 tff(13618,plain,
% 2.64/2.82 (r(s(s(elem!1)), z)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[523, 13617])).
% 2.64/2.82 tff(13619,plain,
% 2.64/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(13620,plain,
% 2.64/2.82 (((~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z)))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(13621,plain,
% 2.64/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[13620])).
% 2.64/2.82 tff(13622,plain,
% 2.64/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.64/2.82 inference(transitivity,[status(thm)],[13621, 13619])).
% 2.64/2.82 tff(13623,plain,
% 2.64/2.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.64/2.82 inference(quant_inst,[status(thm)],[])).
% 2.64/2.82 tff(13624,plain,
% 2.64/2.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 2.64/2.82 inference(modus_ponens,[status(thm)],[13623, 13622])).
% 2.64/2.82 tff(13625,plain,
% 2.64/2.82 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[13624, 183, 13618, 13538, 13534])).
% 2.64/2.82 tff(13626,plain,
% 2.64/2.82 (b(s(s(elem!1)), s(s(s(z))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[454, 13625, 8762])).
% 2.64/2.82 tff(13627,plain,
% 2.64/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(13628,plain,
% 2.64/2.82 (((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(13629,plain,
% 2.64/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z))))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[13628])).
% 2.64/2.82 tff(13630,plain,
% 2.64/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 2.64/2.82 inference(transitivity,[status(thm)],[13629, 13627])).
% 2.64/2.82 tff(13631,plain,
% 2.64/2.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.64/2.82 inference(quant_inst,[status(thm)],[])).
% 2.64/2.82 tff(13632,plain,
% 2.64/2.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z))),
% 2.64/2.82 inference(modus_ponens,[status(thm)],[13631, 13630])).
% 2.64/2.82 tff(13633,plain,
% 2.64/2.82 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[13632, 183, 13618, 13534])).
% 2.64/2.82 tff(13634,plain,
% 2.64/2.82 (b(s(s(s(z))), s(s(elem!1)))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[689, 13633, 8761])).
% 2.64/2.82 tff(13635,plain,
% 2.64/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(13636,plain,
% 2.64/2.82 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(13637,plain,
% 2.64/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[13636])).
% 2.64/2.82 tff(13638,plain,
% 2.64/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.64/2.82 inference(transitivity,[status(thm)],[13637, 13635])).
% 2.64/2.82 tff(13639,plain,
% 2.64/2.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.64/2.82 inference(quant_inst,[status(thm)],[])).
% 2.64/2.82 tff(13640,plain,
% 2.64/2.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.64/2.82 inference(modus_ponens,[status(thm)],[13639, 13638])).
% 2.64/2.82 tff(13641,plain,
% 2.64/2.82 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[13640, 246, 13616, 13634, 13626, 13606])).
% 2.64/2.82 tff(13642,plain,
% 2.64/2.82 (~r(s(z), s(s(s(z))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[12950, 13538, 6900])).
% 2.64/2.82 tff(13643,plain,
% 2.64/2.82 (b(s(z), s(s(s(z))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[1291, 13642])).
% 2.64/2.82 tff(13644,plain,
% 2.64/2.82 (~b(s(s(s(s(z)))), s(z))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[2407, 246, 1056, 13643, 13532, 13606])).
% 2.64/2.82 tff(13645,plain,
% 2.64/2.82 (r(s(s(s(s(z)))), s(z))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[6103, 13644])).
% 2.64/2.82 tff(13646,plain,
% 2.64/2.82 ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[12263, 246, 11962, 1056, 13616, 13532])).
% 2.64/2.82 tff(13647,plain,
% 2.64/2.82 (~b(s(s(elem!1)), s(z))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[13646, 13634])).
% 2.64/2.82 tff(13648,plain,
% 2.64/2.82 (r(s(s(elem!1)), s(z))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[197, 13647])).
% 2.64/2.82 tff(13649,plain,
% 2.64/2.82 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[6517, 183, 13648, 13645])).
% 2.64/2.82 tff(13650,plain,
% 2.64/2.82 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[6521, 47, 13649, 13641])).
% 2.64/2.82 tff(13651,plain,
% 2.64/2.82 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[13650])).
% 2.64/2.82 tff(13652,plain,
% 2.64/2.82 (s(s(s(z))) = s(elem!1)),
% 2.64/2.82 inference(transitivity,[status(thm)],[1492, 13651, 92])).
% 2.64/2.82 tff(13653,plain,
% 2.64/2.82 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[13652])).
% 2.64/2.82 tff(13654,plain,
% 2.64/2.82 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 2.64/2.82 inference(symmetry,[status(thm)],[13653])).
% 2.64/2.82 tff(13655,plain,
% 2.64/2.82 (~(elem!1 = s(s(elem!1)))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[5450, 13615])).
% 2.64/2.82 tff(13656,plain,
% 2.64/2.82 (~r(elem!1, s(s(elem!1)))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[4199, 13648, 13544])).
% 2.64/2.82 tff(13657,plain,
% 2.64/2.82 (b(elem!1, s(s(elem!1)))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[1268, 13656, 13655])).
% 2.64/2.82 tff(13658,plain,
% 2.64/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(13659,plain,
% 2.64/2.82 (((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(13660,plain,
% 2.64/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z)))))))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[13659])).
% 2.64/2.82 tff(13661,plain,
% 2.64/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))))),
% 2.64/2.82 inference(transitivity,[status(thm)],[13660, 13658])).
% 2.64/2.82 tff(13662,plain,
% 2.64/2.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))))),
% 2.64/2.82 inference(quant_inst,[status(thm)],[])).
% 2.64/2.82 tff(13663,plain,
% 2.64/2.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z)))))),
% 2.64/2.82 inference(modus_ponens,[status(thm)],[13662, 13661])).
% 2.64/2.82 tff(13664,plain,
% 2.64/2.82 (~b(elem!1, s(s(s(z))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[13663, 246, 13616, 13657, 13634])).
% 2.64/2.83 tff(13665,plain,
% 2.64/2.83 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[13650])).
% 2.64/2.83 tff(13666,plain,
% 2.64/2.83 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.64/2.83 inference(transitivity,[status(thm)],[13665, 1534])).
% 2.64/2.83 tff(13667,plain,
% 2.64/2.83 ((~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(elem!1))))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[13666])).
% 2.64/2.83 tff(13668,plain,
% 2.64/2.83 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.64/2.83 inference(modus_ponens,[status(thm)],[1501, 13667])).
% 2.64/2.83 tff(13669,plain,
% 2.64/2.83 (s(s(s(s(s(elem!1))))) = elem!1),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[3593, 13668, 56, 1, 1445, 13535, 13664])).
% 2.64/2.83 tff(13670,plain,
% 2.64/2.83 (s(s(s(s(s(elem!1))))) = s(s(z))),
% 2.64/2.83 inference(transitivity,[status(thm)],[13669, 3154, 13654, 24])).
% 2.64/2.83 tff(13671,plain,
% 2.64/2.83 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(z)))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[13670])).
% 2.64/2.83 tff(13672,plain,
% 2.64/2.83 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(elem!1))))))),
% 2.64/2.83 inference(symmetry,[status(thm)],[13671])).
% 2.64/2.83 tff(13673,plain,
% 2.64/2.83 (s(z) = s(s(s(s(elem!1))))),
% 2.64/2.83 inference(transitivity,[status(thm)],[1523, 13672, 325])).
% 2.64/2.83 tff(13674,plain,
% 2.64/2.83 (inj_0(s(z)) = inj_0(s(s(s(s(elem!1)))))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[13673])).
% 2.64/2.83 tff(13675,plain,
% 2.64/2.83 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(z))),
% 2.64/2.83 inference(symmetry,[status(thm)],[13674])).
% 2.64/2.83 tff(13676,plain,
% 2.64/2.83 (s(s(s(elem!1))) = z),
% 2.64/2.83 inference(transitivity,[status(thm)],[352, 13675, 20])).
% 2.64/2.83 tff(13677,plain,
% 2.64/2.83 ($false),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[355, 13676])).
% 2.64/2.83 tff(13678,plain,((~b(s(z), z)) | r(z, elem!1) | b(s(s(s(z))), elem!1) | b(s(z), elem!1) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.64/2.83 tff(13679,plain,
% 2.64/2.83 (~b(s(z), z)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[13678, 1445, 1, 56, 2232])).
% 2.64/2.83 tff(13680,plain,
% 2.64/2.83 (r(s(z), z)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[1069, 13679])).
% 2.64/2.83 tff(13681,plain,
% 2.64/2.83 (~r(elem!1, z)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[2725, 13680, 6900])).
% 2.64/2.83 tff(13682,plain,
% 2.64/2.83 (b(elem!1, z)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[12008, 13681])).
% 2.64/2.83 tff(13683,plain,
% 2.64/2.83 (~(s(s(s(z))) = elem!1)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[13350, 13682, 6900, 2232])).
% 2.64/2.83 tff(13684,plain,
% 2.64/2.83 (r(s(s(s(z))), elem!1)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[647, 13683, 1])).
% 2.64/2.83 tff(13685,plain,
% 2.64/2.83 (~r(s(z), s(s(s(z))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[12950, 13684, 6900])).
% 2.64/2.83 tff(13686,plain,
% 2.64/2.83 (b(s(z), s(s(s(z))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[1291, 13685])).
% 2.64/2.83 tff(13687,plain,
% 2.64/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(13688,plain,
% 2.64/2.83 (((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(13689,plain,
% 2.64/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[13688])).
% 2.64/2.83 tff(13690,plain,
% 2.64/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.64/2.83 inference(transitivity,[status(thm)],[13689, 13687])).
% 2.64/2.83 tff(13691,plain,
% 2.64/2.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 2.64/2.83 inference(quant_inst,[status(thm)],[])).
% 2.64/2.83 tff(13692,plain,
% 2.64/2.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 2.64/2.83 inference(modus_ponens,[status(thm)],[13691, 13690])).
% 2.64/2.83 tff(13693,plain,
% 2.64/2.83 (~b(s(s(s(z))), z)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[13692, 246, 13175, 13686, 13532])).
% 2.64/2.83 tff(13694,plain,
% 2.64/2.83 (r(s(s(s(z))), z)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[995, 13693])).
% 2.64/2.83 tff(13695,plain,
% 2.64/2.83 (~(s(s(elem!1)) = elem!1)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[13614, 13684, 6900, 13532, 13682])).
% 2.64/2.83 tff(13696,plain,
% 2.64/2.83 (b(s(s(elem!1)), elem!1)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[156, 13695, 2232])).
% 2.64/2.83 tff(13697,plain,
% 2.64/2.83 (~b(s(s(elem!1)), z)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[12483, 13696, 13682])).
% 2.64/2.83 tff(13698,plain,
% 2.64/2.83 (r(s(s(elem!1)), z)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[523, 13697])).
% 2.64/2.83 tff(13699,plain,
% 2.64/2.83 (~r(s(s(elem!1)), s(z))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[6720, 13698, 13680])).
% 2.64/2.83 tff(13700,plain,
% 2.64/2.83 (b(s(s(elem!1)), s(z))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[197, 13699])).
% 2.64/2.83 tff(13701,plain,
% 2.64/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(13702,plain,
% 2.64/2.83 (((~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(13703,plain,
% 2.64/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[13702])).
% 2.64/2.83 tff(13704,plain,
% 2.64/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.64/2.83 inference(transitivity,[status(thm)],[13703, 13701])).
% 2.64/2.83 tff(13705,plain,
% 2.64/2.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.64/2.83 inference(quant_inst,[status(thm)],[])).
% 2.64/2.83 tff(13706,plain,
% 2.64/2.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 2.64/2.83 inference(modus_ponens,[status(thm)],[13705, 13704])).
% 2.64/2.83 tff(13707,plain,
% 2.64/2.83 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[13706, 246, 13700, 13686, 13532])).
% 2.64/2.83 tff(13708,plain,
% 2.64/2.83 (r(s(s(s(z))), s(s(elem!1)))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[689, 13707, 8761])).
% 2.64/2.83 tff(13709,plain,
% 2.64/2.83 (~b(z, s(s(elem!1)))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[12300, 13698, 2232, 13681])).
% 2.64/2.83 tff(13710,plain,
% 2.64/2.83 (r(z, s(s(elem!1)))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[264, 13709])).
% 2.64/2.83 tff(13711,plain,
% 2.64/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(13712,plain,
% 2.64/2.83 (((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(13713,plain,
% 2.64/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z))))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[13712])).
% 2.64/2.83 tff(13714,plain,
% 2.64/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 2.64/2.83 inference(transitivity,[status(thm)],[13713, 13711])).
% 2.64/2.83 tff(13715,plain,
% 2.64/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 2.64/2.83 inference(quant_inst,[status(thm)],[])).
% 2.64/2.83 tff(13716,plain,
% 2.64/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z))),
% 2.64/2.83 inference(modus_ponens,[status(thm)],[13715, 13714])).
% 2.64/2.83 tff(13717,plain,
% 2.64/2.83 ($false),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[13716, 183, 13710, 13708, 13694])).
% 2.64/2.83 tff(13718,plain,(b(s(z), elem!1) | r(s(s(elem!1)), elem!1) | b(s(s(s(z))), elem!1) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.64/2.83 tff(13719,plain,
% 2.64/2.83 (b(s(z), elem!1)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[13718, 1, 2232, 56])).
% 2.64/2.83 tff(13720,plain,
% 2.64/2.83 (~b(elem!1, z)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[13451, 13719, 13175])).
% 2.64/2.83 tff(13721,plain,
% 2.64/2.83 (r(elem!1, z)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[12008, 13720])).
% 2.64/2.83 tff(13722,plain,
% 2.64/2.83 (~b(elem!1, s(z))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[13509, 13719, 13175])).
% 2.64/2.83 tff(13723,plain,
% 2.64/2.83 (r(elem!1, s(z))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[214, 13722, 5375])).
% 2.64/2.83 tff(13724,plain,
% 2.64/2.83 ((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~r(elem!1, s(z)))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[2535, 11962])).
% 2.64/2.83 tff(13725,plain,
% 2.64/2.83 (~r(s(s(s(z))), elem!1)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[13724, 13723, 13721, 13175])).
% 2.64/2.83 tff(13726,plain,
% 2.64/2.83 (~(elem!1 = s(s(s(z))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[2297, 13722, 13532])).
% 2.64/2.83 tff(13727,plain,
% 2.64/2.83 (~(s(s(s(z))) = elem!1)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[1677, 13726])).
% 2.64/2.83 tff(13728,plain,
% 2.64/2.83 ($false),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[647, 13727, 13725, 1])).
% 2.64/2.83 tff(13729,plain,(b(s(s(s(z))), elem!1) | r(s(s(elem!1)), elem!1) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.64/2.83 tff(13730,plain,
% 2.64/2.83 (b(s(s(s(z))), elem!1)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[13729, 2232, 56])).
% 2.64/2.83 tff(13731,assumption,(~b(elem!1, z)), introduced(assumption)).
% 2.64/2.83 tff(13732,plain,
% 2.64/2.83 (r(elem!1, z)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[12008, 13731])).
% 2.64/2.83 tff(13733,plain,
% 2.64/2.83 (b(elem!1, z) <=> b(s(z), z)),
% 2.64/2.83 inference(monotonicity,[status(thm)],[202])).
% 2.64/2.83 tff(13734,plain,
% 2.64/2.83 (b(s(z), z) <=> b(elem!1, z)),
% 2.64/2.83 inference(symmetry,[status(thm)],[13733])).
% 2.64/2.83 tff(13735,plain,
% 2.64/2.83 (b(elem!1, z)),
% 2.64/2.83 inference(modus_ponens,[status(thm)],[1056, 13734])).
% 2.64/2.83 tff(13736,plain,
% 2.64/2.83 ($false),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[13731, 13735])).
% 2.64/2.83 tff(13737,plain,((~(elem!1 = s(z))) | b(elem!1, z) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.83 tff(13738,plain,
% 2.64/2.83 (~(elem!1 = s(z))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[13737, 1056, 13731])).
% 2.64/2.83 tff(13739,plain,
% 2.64/2.83 (~(s(z) = elem!1)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[9, 13738])).
% 2.64/2.83 tff(13740,plain,
% 2.64/2.83 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[5804, 13739])).
% 2.64/2.83 tff(13741,plain,
% 2.64/2.83 (r(z, s(s(s(z))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[6165, 13535])).
% 2.64/2.83 tff(13742,plain,
% 2.64/2.83 (~r(elem!1, s(s(s(z))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[2254, 13741, 13732])).
% 2.64/2.83 tff(13743,plain,
% 2.64/2.83 (b(elem!1, s(s(s(z))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[470, 13742, 7282])).
% 2.64/2.83 tff(13744,plain,
% 2.64/2.83 ($false),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[5965, 246, 2002, 3697, 1833, 8964])).
% 2.64/2.83 tff(13745,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.83 tff(13746,plain,
% 2.64/2.83 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[13745, 8964, 3697, 2002])).
% 2.64/2.83 tff(13747,plain,
% 2.64/2.83 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[1702, 13746])).
% 2.64/2.83 tff(13748,plain,
% 2.64/2.83 (~r(s(s(s(s(z)))), z)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[2599, 183, 429, 13747])).
% 2.64/2.83 tff(13749,plain,
% 2.64/2.83 (b(s(s(s(s(z)))), z)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[6040, 13748])).
% 2.64/2.83 tff(13750,plain,
% 2.64/2.83 (~r(z, s(s(s(s(z)))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[2641, 183, 429, 13747])).
% 2.64/2.83 tff(13751,plain,
% 2.64/2.83 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z)))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[2645, 47, 13750])).
% 2.64/2.83 tff(13752,plain,
% 2.64/2.83 (b(z, s(s(s(s(z)))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[13751, 2635])).
% 2.64/2.83 tff(13753,plain,
% 2.64/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(13754,plain,
% 2.64/2.83 (((~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(13755,plain,
% 2.64/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[13754])).
% 2.64/2.83 tff(13756,plain,
% 2.64/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.64/2.83 inference(transitivity,[status(thm)],[13755, 13753])).
% 2.64/2.83 tff(13757,plain,
% 2.64/2.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1)))),
% 2.64/2.83 inference(quant_inst,[status(thm)],[])).
% 2.64/2.83 tff(13758,plain,
% 2.64/2.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 2.64/2.83 inference(modus_ponens,[status(thm)],[13757, 13756])).
% 2.64/2.83 tff(13759,plain,
% 2.64/2.83 ($false),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[13758, 246, 11962, 8964, 13752, 13749])).
% 2.64/2.83 tff(13760,plain,((~b(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.83 tff(13761,plain,
% 2.64/2.83 (~b(elem!1, s(s(s(s(z)))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[13760, 13741, 3697, 13743])).
% 2.64/2.83 tff(13762,plain,
% 2.64/2.83 (b(z, s(s(elem!1)))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[11980, 2125])).
% 2.64/2.83 tff(13763,plain,
% 2.64/2.83 (~b(s(s(elem!1)), s(z))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[1154, 13762, 236, 1056])).
% 2.64/2.83 tff(13764,plain,
% 2.64/2.83 (~b(elem!1, s(z))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[2130, 13763, 2125])).
% 2.64/2.83 tff(13765,plain,
% 2.64/2.83 (r(elem!1, s(z))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[214, 13764, 3])).
% 2.64/2.83 tff(13766,plain,
% 2.64/2.83 (~r(elem!1, s(s(s(s(z)))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[13185, 13765, 236, 2246, 1056])).
% 2.64/2.83 tff(13767,assumption,(~r(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 2.64/2.83 tff(13768,plain,
% 2.64/2.83 ($false),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[5969, 47, 8155, 13767, 8714])).
% 2.64/2.83 tff(13769,plain,(b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z))))) | (elem!1 = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.83 tff(13770,plain,
% 2.64/2.83 (elem!1 = s(s(s(s(z))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[13769, 13766, 8155])).
% 2.64/2.83 tff(13771,plain,
% 2.64/2.83 (s(s(s(s(z)))) = elem!1),
% 2.64/2.83 inference(symmetry,[status(thm)],[13770])).
% 2.64/2.83 tff(13772,plain,
% 2.64/2.83 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.64/2.83 inference(transitivity,[status(thm)],[13771, 5380])).
% 2.64/2.83 tff(13773,plain,
% 2.64/2.83 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[13772])).
% 2.64/2.83 tff(13774,plain,
% 2.64/2.83 (s(s(s(z))) = s(elem!1)),
% 2.64/2.83 inference(transitivity,[status(thm)],[1492, 13773, 92])).
% 2.64/2.83 tff(13775,plain,
% 2.64/2.83 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[13774])).
% 2.64/2.83 tff(13776,plain,
% 2.64/2.83 (s(s(z)) = elem!1),
% 2.64/2.83 inference(transitivity,[status(thm)],[25, 13775, 343])).
% 2.64/2.83 tff(13777,plain,
% 2.64/2.83 ($false),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[10091, 13776])).
% 2.64/2.83 tff(13778,plain,((~(s(s(elem!1)) = elem!1)) | b(elem!1, s(s(s(s(z))))) | (~b(z, s(z))) | (~r(elem!1, z)) | (~b(s(z), z)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.83 tff(13779,plain,
% 2.64/2.83 (~(s(s(elem!1)) = elem!1)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[13778, 13761, 13175, 13732, 1056, 13738])).
% 2.64/2.83 tff(13780,plain,
% 2.64/2.83 (b(s(s(elem!1)), elem!1)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[156, 13779, 2232])).
% 2.64/2.83 tff(13781,plain,
% 2.64/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(13782,plain,
% 2.64/2.83 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(13783,plain,
% 2.64/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[13782])).
% 2.64/2.83 tff(13784,plain,
% 2.64/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 2.64/2.83 inference(transitivity,[status(thm)],[13783, 13781])).
% 2.64/2.83 tff(13785,plain,
% 2.64/2.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.64/2.83 inference(quant_inst,[status(thm)],[])).
% 2.64/2.83 tff(13786,plain,
% 2.64/2.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))),
% 2.64/2.83 inference(modus_ponens,[status(thm)],[13785, 13784])).
% 2.64/2.83 tff(13787,plain,
% 2.64/2.83 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[13786, 246, 13780, 13743, 3697])).
% 2.64/2.83 tff(13788,plain,
% 2.64/2.83 (r(s(s(s(z))), s(s(elem!1)))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[689, 13787, 13740])).
% 2.64/2.83 tff(13789,plain,
% 2.64/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(13790,plain,
% 2.64/2.84 (((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(13791,plain,
% 2.64/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[13790])).
% 2.64/2.84 tff(13792,plain,
% 2.64/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 2.64/2.84 inference(transitivity,[status(thm)],[13791, 13789])).
% 2.64/2.84 tff(13793,plain,
% 2.64/2.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))),
% 2.64/2.84 inference(quant_inst,[status(thm)],[])).
% 2.64/2.84 tff(13794,plain,
% 2.64/2.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[13793, 13792])).
% 2.64/2.84 tff(13795,plain,
% 2.64/2.84 (~b(s(s(elem!1)), z)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[13794, 246, 11962, 13780, 13743, 3697])).
% 2.64/2.84 tff(13796,plain,
% 2.64/2.84 (r(s(s(elem!1)), z)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[523, 13795])).
% 2.64/2.84 tff(13797,plain,
% 2.64/2.84 ($false),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[13632, 183, 13796, 13788, 13534])).
% 2.64/2.84 tff(13798,plain,((~b(s(z), z)) | (~b(s(s(s(z))), elem!1)) | r(s(s(elem!1)), elem!1) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 2.64/2.84 tff(13799,plain,
% 2.64/2.84 (~b(s(z), z)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[13798, 13731, 2232, 3697])).
% 2.64/2.84 tff(13800,plain,
% 2.64/2.84 (r(s(z), z)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[1069, 13799])).
% 2.64/2.84 tff(13801,plain,
% 2.64/2.84 (~r(s(z), elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[2725, 13800, 13732])).
% 2.64/2.84 tff(13802,plain,
% 2.64/2.84 (~r(elem!1, s(z))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[1163, 13800, 13732])).
% 2.64/2.84 tff(13803,plain,
% 2.64/2.84 ((s(s(s(s(z)))) = s(z)) <=> (elem!1 = s(z))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[2393])).
% 2.64/2.84 tff(13804,plain,
% 2.64/2.84 ((s(s(s(s(z)))) = s(z)) <=> (s(z) = elem!1)),
% 2.64/2.84 inference(transitivity,[status(thm)],[13803, 4])).
% 2.64/2.84 tff(13805,plain,
% 2.64/2.84 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(z) = elem!1))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[13804])).
% 2.64/2.84 tff(13806,plain,
% 2.64/2.84 (~(s(z) = elem!1)),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[1713, 13805])).
% 2.64/2.84 tff(13807,plain,
% 2.64/2.84 (b(s(z), elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[1034, 13806, 6388])).
% 2.64/2.84 tff(13808,plain,
% 2.64/2.84 ((s(s(s(s(z)))) = s(z)) <=> (elem!1 = s(z))),
% 2.64/2.84 inference(transitivity,[status(thm)],[13804, 5])).
% 2.64/2.84 tff(13809,plain,
% 2.64/2.84 ((~(s(s(s(s(z)))) = s(z))) <=> (~(elem!1 = s(z)))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[13808])).
% 2.64/2.84 tff(13810,plain,
% 2.64/2.84 (~(elem!1 = s(z))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[1713, 13809])).
% 2.64/2.84 tff(13811,plain,
% 2.64/2.84 (b(elem!1, s(z))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[214, 13810, 6386])).
% 2.64/2.84 tff(13812,plain,
% 2.64/2.84 ($false),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[13509, 13811, 13807, 236])).
% 2.64/2.84 tff(13813,plain,((~(s(s(s(s(z)))) = elem!1)) | (~b(z, s(z))) | r(elem!1, s(z)) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.64/2.84 tff(13814,plain,
% 2.64/2.84 (~(s(s(s(s(z)))) = elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[13813, 13802, 13175, 13801])).
% 2.64/2.84 tff(13815,plain,
% 2.64/2.84 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[12436, 413, 2246, 3074, 3697])).
% 2.64/2.84 tff(13816,plain,
% 2.64/2.84 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[1702, 13815])).
% 2.64/2.84 tff(13817,plain,
% 2.64/2.84 (~r(s(s(s(s(z)))), z)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[12764, 13816, 2003, 1114])).
% 2.64/2.84 tff(13818,plain,
% 2.64/2.84 (b(s(s(s(s(z)))), z)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[6040, 13817])).
% 2.64/2.84 tff(13819,plain,
% 2.64/2.84 (~b(s(s(s(z))), z)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[9844, 13818, 12428, 13816])).
% 2.64/2.84 tff(13820,plain,
% 2.64/2.84 (r(s(s(s(z))), z)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[995, 13819])).
% 2.64/2.84 tff(13821,plain,
% 2.64/2.84 (~r(s(s(s(z))), elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[13540, 13820, 2246])).
% 2.64/2.84 tff(13822,plain,
% 2.64/2.84 (~r(s(z), elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[2725, 1114, 2246])).
% 2.64/2.84 tff(13823,plain,
% 2.64/2.84 (s(z) = elem!1),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[1034, 13822, 1445])).
% 2.64/2.84 tff(13824,plain,
% 2.64/2.84 ((s(s(s(s(s(elem!1))))) = s(z)) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 2.64/2.84 inference(monotonicity,[status(thm)],[13823])).
% 2.64/2.84 tff(13825,plain,
% 2.64/2.84 ((~(s(s(s(s(s(elem!1))))) = s(z))) <=> (~(s(s(s(s(s(elem!1))))) = elem!1))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[13824])).
% 2.64/2.84 tff(13826,plain,
% 2.64/2.84 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[331, 13825])).
% 2.64/2.84 tff(13827,plain,
% 2.64/2.84 (s(s(s(z))) = s(s(elem!1))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[121, 13823])).
% 2.64/2.84 tff(13828,plain,
% 2.64/2.84 ((s(s(s(s(s(elem!1))))) = s(s(s(z)))) <=> (s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[13827])).
% 2.64/2.84 tff(13829,plain,
% 2.64/2.84 ((~(s(s(s(s(s(elem!1))))) = s(s(s(z))))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(elem!1))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[13828])).
% 2.64/2.84 tff(13830,plain,
% 2.64/2.84 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[1622, 13829])).
% 2.64/2.84 tff(13831,plain,
% 2.64/2.84 (elem!1 = s(z)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[9, 13823])).
% 2.64/2.84 tff(13832,plain,
% 2.64/2.84 (b(s(s(elem!1)), elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[11660, 13831, 10369])).
% 2.64/2.84 tff(13833,plain,
% 2.64/2.84 (s(s(elem!1)) = s(s(s(z)))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[13827, 3393])).
% 2.64/2.84 tff(13834,plain,
% 2.64/2.84 ((s(s(s(s(z)))) = s(z)) <=> (s(s(s(s(z)))) = elem!1)),
% 2.64/2.84 inference(monotonicity,[status(thm)],[13823])).
% 2.64/2.84 tff(13835,plain,
% 2.64/2.84 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[13834])).
% 2.64/2.84 tff(13836,plain,
% 2.64/2.84 (~(s(s(s(s(z)))) = elem!1)),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[1713, 13835])).
% 2.64/2.84 tff(13837,plain,
% 2.64/2.84 ((s(s(s(s(s(elem!1))))) = s(z)) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 2.64/2.84 inference(transitivity,[status(thm)],[13824, 124])).
% 2.64/2.84 tff(13838,plain,
% 2.64/2.84 ((~(s(s(s(s(s(elem!1))))) = s(z))) <=> (~(elem!1 = s(s(s(s(s(elem!1)))))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[13837])).
% 2.64/2.84 tff(13839,plain,
% 2.64/2.84 (~(elem!1 = s(s(s(s(s(elem!1))))))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[331, 13838])).
% 2.64/2.84 tff(13840,plain,
% 2.64/2.84 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[3069])).
% 2.64/2.84 tff(13841,plain,
% 2.64/2.84 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.64/2.84 inference(symmetry,[status(thm)],[13840])).
% 2.64/2.84 tff(13842,plain,
% 2.64/2.84 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[97])).
% 2.64/2.84 tff(13843,plain,
% 2.64/2.84 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.64/2.84 inference(transitivity,[status(thm)],[13842, 13841])).
% 2.64/2.84 tff(13844,plain,
% 2.64/2.84 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[2593, 13843])).
% 2.64/2.84 tff(13845,plain,
% 2.64/2.84 (s(s(elem!1)) = s(s(s(z)))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[97, 3393])).
% 2.64/2.84 tff(13846,plain,
% 2.64/2.84 (~r(elem!1, s(s(s(z))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[12436, 2593, 2246, 3074, 3697])).
% 2.64/2.84 tff(13847,plain,
% 2.64/2.84 (b(elem!1, s(s(s(z))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[470, 13846, 7282])).
% 2.64/2.84 tff(13848,plain,
% 2.64/2.84 (s(s(s(z))) = s(s(elem!1))),
% 2.64/2.84 inference(symmetry,[status(thm)],[418])).
% 2.64/2.84 tff(13849,plain,
% 2.64/2.84 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[13848])).
% 2.64/2.84 tff(13850,plain,
% 2.64/2.84 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(z))))),
% 2.64/2.84 inference(symmetry,[status(thm)],[13849])).
% 2.64/2.84 tff(13851,plain,
% 2.64/2.84 ((~b(elem!1, s(s(elem!1)))) <=> (~b(elem!1, s(s(s(z)))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[13850])).
% 2.64/2.84 tff(13852,assumption,(~b(elem!1, s(s(elem!1)))), introduced(assumption)).
% 2.64/2.84 tff(13853,plain,
% 2.64/2.84 (~b(elem!1, s(s(s(z))))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[13852, 13851])).
% 2.64/2.84 tff(13854,plain,
% 2.64/2.84 ($false),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[2002, 13853])).
% 2.64/2.84 tff(13855,plain,((~(s(s(elem!1)) = s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | b(elem!1, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.84 tff(13856,plain,
% 2.64/2.84 (b(elem!1, s(s(elem!1)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[13855, 13847, 13845])).
% 2.64/2.84 tff(13857,plain,
% 2.64/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(13858,plain,
% 2.64/2.84 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(13859,plain,
% 2.64/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1))))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[13858])).
% 2.64/2.84 tff(13860,plain,
% 2.64/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))),
% 2.64/2.84 inference(transitivity,[status(thm)],[13859, 13857])).
% 2.64/2.84 tff(13861,plain,
% 2.64/2.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))),
% 2.64/2.84 inference(quant_inst,[status(thm)],[])).
% 2.64/2.84 tff(13862,plain,
% 2.64/2.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1))))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[13861, 13860])).
% 2.64/2.84 tff(13863,plain,
% 2.64/2.84 (~b(z, s(s(elem!1)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[13862, 246, 11962, 2362, 13856])).
% 2.64/2.84 tff(13864,plain,
% 2.64/2.84 (r(z, s(s(elem!1)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[264, 13863])).
% 2.64/2.84 tff(13865,plain,
% 2.64/2.84 (~r(s(s(s(elem!1))), z)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[3082, 183, 13864, 13844])).
% 2.64/2.84 tff(13866,plain,
% 2.64/2.84 (b(s(s(s(elem!1))), z)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[3086, 47, 355, 13865])).
% 2.64/2.84 tff(13867,plain,
% 2.64/2.84 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 2.64/2.84 inference(symmetry,[status(thm)],[10677])).
% 2.64/2.84 tff(13868,plain,
% 2.64/2.84 ((s(s(s(s(z)))) = elem!1) <=> (s(s(s(elem!1))) = elem!1)),
% 2.64/2.84 inference(transitivity,[status(thm)],[3072, 13867])).
% 2.64/2.84 tff(13869,plain,
% 2.64/2.84 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[13868])).
% 2.64/2.84 tff(13870,plain,
% 2.64/2.84 (~(s(s(s(elem!1))) = elem!1)),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[3074, 13869])).
% 2.64/2.84 tff(13871,plain,
% 2.64/2.84 ((s(s(s(s(s(elem!1))))) = s(s(s(z)))) <=> (s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[97])).
% 2.64/2.84 tff(13872,plain,
% 2.64/2.84 ((~(s(s(s(s(s(elem!1))))) = s(s(s(z))))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(elem!1))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[13871])).
% 2.64/2.84 tff(13873,plain,
% 2.64/2.84 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[1622, 13872])).
% 2.64/2.84 tff(13874,plain,
% 2.64/2.84 ((~b(elem!1, s(s(elem!1)))) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | b(s(s(s(s(s(elem!1))))), s(s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[12999, 11962])).
% 2.64/2.84 tff(13875,plain,
% 2.64/2.84 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[13874, 714, 1555, 2362, 947])).
% 2.64/2.84 tff(13876,plain,
% 2.64/2.84 ($false),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[4983, 13875, 714, 947, 2362])).
% 2.64/2.84 tff(13877,plain,((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (s(s(s(s(s(elem!1))))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.84 tff(13878,plain,
% 2.64/2.84 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[13877, 13856, 2362, 13873])).
% 2.64/2.84 tff(13879,plain,
% 2.64/2.84 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[86, 13878, 69])).
% 2.64/2.84 tff(13880,plain,
% 2.64/2.84 ($false),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[13200, 183, 2246, 333, 5669])).
% 2.64/2.84 tff(13881,plain,((~r(s(s(s(s(s(elem!1))))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(elem!1))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.84 tff(13882,plain,
% 2.64/2.84 (~r(s(s(s(s(s(elem!1))))), z)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[13881, 13879, 2246])).
% 2.64/2.84 tff(13883,plain,
% 2.64/2.84 (b(s(s(s(s(s(elem!1))))), z)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[1601, 13882])).
% 2.64/2.84 tff(13884,plain,
% 2.64/2.84 ((s(s(s(s(s(elem!1))))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 2.64/2.84 inference(transitivity,[status(thm)],[13871, 1535])).
% 2.64/2.84 tff(13885,plain,
% 2.64/2.84 ((~(s(s(s(s(s(elem!1))))) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(s(s(elem!1)))))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[13884])).
% 2.64/2.84 tff(13886,plain,
% 2.64/2.84 (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[1622, 13885])).
% 2.64/2.84 tff(13887,plain,
% 2.64/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(13888,plain,
% 2.64/2.84 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(13889,plain,
% 2.64/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1)))))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[13888])).
% 2.64/2.84 tff(13890,plain,
% 2.64/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))),
% 2.64/2.84 inference(transitivity,[status(thm)],[13889, 13887])).
% 2.64/2.84 tff(13891,plain,
% 2.64/2.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))),
% 2.64/2.84 inference(quant_inst,[status(thm)],[])).
% 2.64/2.84 tff(13892,plain,
% 2.64/2.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1)))))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[13891, 13890])).
% 2.64/2.84 tff(13893,plain,
% 2.64/2.84 (~r(z, s(s(s(elem!1))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[13892, 183, 13864, 13844])).
% 2.64/2.84 tff(13894,plain,
% 2.64/2.84 ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[9177, 47, 13893])).
% 2.64/2.84 tff(13895,plain,
% 2.64/2.84 (b(z, s(s(s(elem!1))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[13894, 5369])).
% 2.64/2.84 tff(13896,plain,
% 2.64/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(13897,plain,
% 2.64/2.84 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(13898,plain,
% 2.64/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[13897])).
% 2.64/2.84 tff(13899,plain,
% 2.64/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 2.64/2.84 inference(transitivity,[status(thm)],[13898, 13896])).
% 2.64/2.84 tff(13900,plain,
% 2.64/2.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 2.64/2.84 inference(quant_inst,[status(thm)],[])).
% 2.64/2.84 tff(13901,plain,
% 2.64/2.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[13900, 13899])).
% 2.64/2.84 tff(13902,plain,
% 2.64/2.84 (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[13901, 246, 13883, 13866, 13895])).
% 2.64/2.84 tff(13903,plain,
% 2.64/2.84 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(elem!1))) = s(s(s(s(s(elem!1))))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[3068])).
% 2.64/2.84 tff(13904,plain,
% 2.64/2.84 ((~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[13903])).
% 2.64/2.84 tff(13905,plain,
% 2.64/2.84 (~(s(s(s(elem!1))) = s(s(s(s(s(elem!1))))))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[1501, 13904])).
% 2.64/2.84 tff(13906,plain,
% 2.64/2.84 (r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[913, 47, 13905, 13902])).
% 2.64/2.84 tff(13907,assumption,(r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 2.64/2.84 tff(13908,plain,
% 2.64/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(13909,plain,
% 2.64/2.84 (((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(13910,plain,
% 2.64/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[13909])).
% 2.64/2.84 tff(13911,plain,
% 2.64/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 2.64/2.84 inference(transitivity,[status(thm)],[13910, 13908])).
% 2.64/2.84 tff(13912,plain,
% 2.64/2.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.64/2.84 inference(quant_inst,[status(thm)],[])).
% 2.64/2.84 tff(13913,plain,
% 2.64/2.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[13912, 13911])).
% 2.64/2.84 tff(13914,plain,
% 2.64/2.84 ($false),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[13913, 183, 3076, 3306, 13907])).
% 2.64/2.84 tff(13915,plain,((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.84 tff(13916,plain,
% 2.64/2.84 (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[13915, 13844, 13906])).
% 2.64/2.84 tff(13917,plain,
% 2.64/2.84 (b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[1547, 47, 13916, 13886])).
% 2.64/2.84 tff(13918,plain,
% 2.64/2.84 (~b(s(s(elem!1)), z)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[12995, 246, 11962, 2362, 13856])).
% 2.64/2.84 tff(13919,plain,
% 2.64/2.84 (r(s(s(elem!1)), z)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[523, 13918])).
% 2.64/2.84 tff(13920,plain,
% 2.64/2.84 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 2.64/2.84 inference(transitivity,[status(thm)],[13903, 9120])).
% 2.64/2.84 tff(13921,plain,
% 2.64/2.84 ((~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[13920])).
% 2.64/2.84 tff(13922,plain,
% 2.64/2.84 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[1501, 13921])).
% 2.64/2.84 tff(13923,plain,
% 2.64/2.84 (~r(s(s(s(s(s(elem!1))))), z)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[5671, 959, 172])).
% 2.64/2.84 tff(13924,plain,
% 2.64/2.84 (b(s(s(s(s(s(elem!1))))), z)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[1601, 13923])).
% 2.64/2.84 tff(13925,plain,
% 2.64/2.84 ($false),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[9331, 246, 13924, 9677, 9205, 9204])).
% 2.64/2.84 tff(13926,plain,((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.84 tff(13927,plain,
% 2.64/2.84 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[13926, 13866, 13895, 13922, 13844, 13919])).
% 2.64/2.84 tff(13928,plain,
% 2.64/2.84 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[1557, 13927, 13873])).
% 2.64/2.84 tff(13929,plain,
% 2.64/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(13930,plain,
% 2.64/2.84 (((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(elem!1)))))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 2.64/2.85 inference(rewrite,[status(thm)],[])).
% 2.64/2.85 tff(13931,plain,
% 2.64/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1)))))))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[13930])).
% 2.64/2.85 tff(13932,plain,
% 2.64/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 2.64/2.85 inference(transitivity,[status(thm)],[13931, 13929])).
% 2.64/2.85 tff(13933,plain,
% 2.64/2.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 2.64/2.85 inference(quant_inst,[status(thm)],[])).
% 2.64/2.85 tff(13934,plain,
% 2.64/2.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1)))))))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[13933, 13932])).
% 2.64/2.85 tff(13935,plain,
% 2.64/2.85 (~b(elem!1, s(s(s(s(s(elem!1))))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[13934, 246, 13856, 13928, 13917, 13883])).
% 2.64/2.85 tff(13936,plain,
% 2.64/2.85 (r(elem!1, s(s(s(s(s(elem!1))))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[5125, 13935, 5123])).
% 2.64/2.85 tff(13937,plain,
% 2.64/2.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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))))))))),
% 2.64/2.85 inference(rewrite,[status(thm)],[])).
% 2.64/2.85 tff(13938,plain,
% 2.64/2.85 (((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(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))))))))),
% 2.64/2.85 inference(rewrite,[status(thm)],[])).
% 2.64/2.85 tff(13939,plain,
% 2.64/2.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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)))))))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[13938])).
% 2.64/2.85 tff(13940,plain,
% 2.64/2.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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))))))))),
% 2.64/2.85 inference(transitivity,[status(thm)],[13939, 13937])).
% 2.64/2.85 tff(13941,plain,
% 2.64/2.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.64/2.85 inference(quant_inst,[status(thm)],[])).
% 2.64/2.85 tff(13942,plain,
% 2.64/2.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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)))))))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[13941, 13940])).
% 2.64/2.85 tff(13943,plain,
% 2.64/2.85 (~r(s(s(s(elem!1))), elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[13942, 183, 13906, 13936])).
% 2.64/2.85 tff(13944,plain,
% 2.64/2.85 (b(s(s(s(elem!1))), elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[3356, 47, 13943, 13870])).
% 2.64/2.85 tff(13945,plain,
% 2.64/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 2.64/2.85 inference(rewrite,[status(thm)],[])).
% 2.64/2.85 tff(13946,plain,
% 2.64/2.85 (((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 2.64/2.85 inference(rewrite,[status(thm)],[])).
% 2.64/2.85 tff(13947,plain,
% 2.64/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[13946])).
% 2.64/2.85 tff(13948,plain,
% 2.64/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 2.64/2.85 inference(transitivity,[status(thm)],[13947, 13945])).
% 2.64/2.85 tff(13949,plain,
% 2.64/2.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 2.64/2.85 inference(quant_inst,[status(thm)],[])).
% 2.64/2.85 tff(13950,plain,
% 2.64/2.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[13949, 13948])).
% 2.64/2.85 tff(13951,plain,
% 2.64/2.85 ($false),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[13950, 246, 11962, 2362, 13856, 13944, 13866])).
% 2.64/2.85 tff(13952,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (elem!1 = s(s(s(s(s(elem!1)))))) | (~r(elem!1, z)) | (s(s(s(s(s(elem!1))))) = elem!1) | (~(s(s(s(z))) = s(s(elem!1)))) | (s(s(s(s(z)))) = elem!1) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.85 tff(13953,plain,
% 2.64/2.85 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[13952, 13832, 13839, 2246, 13826, 13827, 13836, 3697])).
% 2.64/2.85 tff(13954,plain,
% 2.64/2.85 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[1702, 13953])).
% 2.64/2.85 tff(13955,plain,
% 2.64/2.85 (~r(s(s(s(s(z)))), z)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[12764, 13954, 2003, 1114])).
% 2.64/2.85 tff(13956,plain,
% 2.64/2.85 (b(s(s(s(s(z)))), z)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[6040, 13955])).
% 2.64/2.85 tff(13957,plain,
% 2.64/2.85 (b(s(s(s(elem!1))), z)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[9431, 13956, 13827])).
% 2.64/2.85 tff(13958,plain,
% 2.64/2.85 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[9446, 13954, 13827])).
% 2.64/2.85 tff(13959,plain,
% 2.64/2.85 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[97])).
% 2.64/2.85 tff(13960,plain,
% 2.64/2.85 (r(elem!1, s(s(elem!1)))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[413, 13959])).
% 2.64/2.85 tff(13961,plain,
% 2.64/2.85 (b(z, s(s(elem!1)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[9374, 12428, 97])).
% 2.64/2.85 tff(13962,plain,
% 2.64/2.85 (~b(s(s(elem!1)), z)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[9440, 13961, 1659, 9205])).
% 2.64/2.85 tff(13963,plain,
% 2.64/2.85 (r(s(s(elem!1)), z)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[523, 13962])).
% 2.64/2.85 tff(13964,plain,
% 2.64/2.85 ($false),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[7107, 183, 2246, 13963, 13960])).
% 2.64/2.85 tff(13965,plain,((~r(elem!1, s(s(s(z))))) | (~r(elem!1, z)) | (~(s(s(s(z))) = s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.85 tff(13966,plain,
% 2.64/2.85 (~r(elem!1, s(s(s(z))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[13965, 13827, 2246, 13958, 13957])).
% 2.64/2.85 tff(13967,plain,
% 2.64/2.85 (b(elem!1, s(s(s(z))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[470, 13966, 7282])).
% 2.64/2.85 tff(13968,plain,
% 2.64/2.85 (b(elem!1, s(s(elem!1)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[13855, 13967, 13833])).
% 2.64/2.85 tff(13969,plain,
% 2.64/2.85 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[13877, 13968, 13832, 13830])).
% 2.64/2.85 tff(13970,plain,
% 2.64/2.85 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[86, 13969, 13826])).
% 2.64/2.85 tff(13971,plain,
% 2.64/2.85 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[13827])).
% 2.64/2.85 tff(13972,plain,
% 2.64/2.85 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.64/2.85 inference(symmetry,[status(thm)],[13971])).
% 2.64/2.85 tff(13973,plain,
% 2.64/2.85 ((elem!1 = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(s(z)))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[13972])).
% 2.64/2.85 tff(13974,plain,
% 2.64/2.85 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = elem!1)),
% 2.64/2.85 inference(transitivity,[status(thm)],[13973, 3067])).
% 2.64/2.85 tff(13975,plain,
% 2.64/2.85 ((s(s(s(s(z)))) = elem!1) <=> (elem!1 = s(s(s(elem!1))))),
% 2.64/2.85 inference(symmetry,[status(thm)],[13974])).
% 2.64/2.85 tff(13976,plain,
% 2.64/2.85 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[13975])).
% 2.64/2.85 tff(13977,plain,
% 2.64/2.85 (~(elem!1 = s(s(s(elem!1))))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[13836, 13976])).
% 2.64/2.85 tff(13978,plain,
% 2.64/2.85 (~b(elem!1, s(s(s(elem!1))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[9201, 246, 13832, 13968, 13958])).
% 2.64/2.85 tff(13979,plain,
% 2.64/2.85 (r(elem!1, s(s(s(elem!1))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[9483, 13978, 13977])).
% 2.64/2.85 tff(13980,plain,
% 2.64/2.85 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(elem!1))) = s(s(s(s(s(elem!1))))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[13971])).
% 2.64/2.85 tff(13981,plain,
% 2.64/2.85 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 2.64/2.85 inference(transitivity,[status(thm)],[13980, 9120])).
% 2.64/2.85 tff(13982,plain,
% 2.64/2.85 ((~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[13981])).
% 2.64/2.85 tff(13983,plain,
% 2.64/2.85 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[1501, 13982])).
% 2.64/2.85 tff(13984,plain,
% 2.64/2.85 (~r(s(s(s(s(s(elem!1))))), z)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[13881, 13970, 2246])).
% 2.64/2.85 tff(13985,plain,
% 2.64/2.85 (b(s(s(s(s(s(elem!1))))), z)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[1601, 13984])).
% 2.64/2.85 tff(13986,plain,
% 2.64/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 2.64/2.85 inference(rewrite,[status(thm)],[])).
% 2.64/2.85 tff(13987,plain,
% 2.64/2.85 (((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(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(elem!1)))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 2.64/2.85 inference(rewrite,[status(thm)],[])).
% 2.64/2.85 tff(13988,plain,
% 2.64/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(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(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[13987])).
% 2.64/2.85 tff(13989,plain,
% 2.64/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(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(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 2.64/2.85 inference(transitivity,[status(thm)],[13988, 13986])).
% 2.64/2.85 tff(13990,plain,
% 2.64/2.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(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(elem!1))))))),
% 2.64/2.85 inference(quant_inst,[status(thm)],[])).
% 2.64/2.85 tff(13991,plain,
% 2.64/2.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[13990, 13989])).
% 2.64/2.85 tff(13992,plain,
% 2.64/2.85 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[13991, 246, 11962, 13968, 13985, 13958, 13957])).
% 2.64/2.85 tff(13993,plain,
% 2.64/2.85 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[3693, 13992, 13983])).
% 2.64/2.85 tff(13994,plain,
% 2.64/2.85 ($false),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[4270, 13993, 13979, 13970])).
% 2.64/2.85 tff(13995,plain,((~r(s(z), z)) | (~r(elem!1, z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | r(s(s(s(z))), elem!1) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.64/2.85 tff(13996,plain,
% 2.64/2.85 (b(s(z), elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[13995, 13821, 2003, 3697, 2246, 1114])).
% 2.64/2.85 tff(13997,plain,
% 2.64/2.85 (elem!1 = s(z)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[12339, 13996, 2003, 1114, 2246, 13818, 7282, 13816])).
% 2.64/2.85 tff(13998,plain,
% 2.64/2.85 (s(z) = elem!1),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[2279, 13997])).
% 2.64/2.85 tff(13999,plain,
% 2.64/2.85 (s(s(s(z))) = s(s(elem!1))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[121, 13998])).
% 2.64/2.85 tff(14000,plain,
% 2.64/2.85 (b(s(s(s(elem!1))), z)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[9431, 13999, 13818])).
% 2.64/2.85 tff(14001,plain,
% 2.64/2.85 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[9446, 13999, 13816])).
% 2.64/2.85 tff(14002,plain,
% 2.64/2.85 ($false),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[13965, 14001, 14000, 2246, 413, 13999])).
% 2.64/2.85 tff(14003,plain,((~r(elem!1, s(s(s(z))))) | (~r(elem!1, z)) | (~b(s(s(s(z))), s(z))) | (~r(s(z), z)) | (~b(s(s(s(z))), elem!1)) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.64/2.85 tff(14004,plain,
% 2.64/2.85 (~r(elem!1, s(s(s(z))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[14003, 13732, 13532, 13800, 3697, 13814])).
% 2.64/2.85 tff(14005,plain,
% 2.64/2.85 (b(elem!1, s(s(s(z))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[470, 14004, 7282])).
% 2.64/2.85 tff(14006,plain,
% 2.64/2.85 (~b(s(z), elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[6206, 14005, 13532, 3697])).
% 2.64/2.85 tff(14007,plain,
% 2.64/2.85 (s(z) = elem!1),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[1034, 14006, 13801])).
% 2.64/2.85 tff(14008,plain,
% 2.64/2.85 (r(s(s(s(z))), s(z)) <=> r(s(s(s(z))), elem!1)),
% 2.64/2.85 inference(monotonicity,[status(thm)],[14007])).
% 2.64/2.85 tff(14009,plain,
% 2.64/2.85 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(z))),
% 2.64/2.85 inference(symmetry,[status(thm)],[14008])).
% 2.64/2.85 tff(14010,plain,
% 2.64/2.85 (r(s(s(s(z))), elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[13995, 14006, 13532, 3697, 13732, 13800])).
% 2.64/2.85 tff(14011,plain,
% 2.64/2.85 (r(s(s(s(z))), s(z))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[14010, 14009])).
% 2.64/2.85 tff(14012,plain,
% 2.64/2.85 (~r(s(s(s(z))), s(z))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[2713, 14010, 2232, 14006])).
% 2.64/2.85 tff(14013,plain,
% 2.64/2.85 ($false),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[14012, 14011])).
% 2.64/2.85 tff(14014,plain,(b(elem!1, z) | r(s(s(elem!1)), elem!1) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.85 tff(14015,plain,
% 2.64/2.85 (b(elem!1, z)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[14014, 2232, 13730])).
% 2.64/2.85 tff(14016,plain,
% 2.64/2.85 (~b(z, s(s(s(z))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[12015, 246, 11962, 14015, 13730])).
% 2.64/2.85 tff(14017,plain,
% 2.64/2.85 (r(z, s(s(s(z))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[6165, 14016])).
% 2.64/2.85 tff(14018,plain,
% 2.64/2.85 (r(s(z), z)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[1069, 2118])).
% 2.64/2.85 tff(14019,plain,
% 2.64/2.85 (~r(s(z), s(s(s(z))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[6130, 183, 14018, 13394])).
% 2.64/2.85 tff(14020,plain,
% 2.64/2.85 (b(s(z), s(s(s(z))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[1291, 14019])).
% 2.64/2.85 tff(14021,plain,
% 2.64/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))))),
% 2.64/2.85 inference(rewrite,[status(thm)],[])).
% 2.64/2.85 tff(14022,plain,
% 2.64/2.85 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(elem!1)))))))) <=> ((~b(z, s(z))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))))),
% 2.64/2.85 inference(rewrite,[status(thm)],[])).
% 2.64/2.85 tff(14023,plain,
% 2.64/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z)))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[14022])).
% 2.64/2.85 tff(14024,plain,
% 2.64/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))))),
% 2.64/2.85 inference(transitivity,[status(thm)],[14023, 14021])).
% 2.64/2.85 tff(14025,plain,
% 2.64/2.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 2.64/2.85 inference(quant_inst,[status(thm)],[])).
% 2.64/2.85 tff(14026,plain,
% 2.64/2.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z)))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[14025, 14024])).
% 2.64/2.85 tff(14027,plain,
% 2.64/2.85 (~b(z, s(s(s(s(s(elem!1))))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[14026, 246, 236, 2401, 2003, 6875])).
% 2.64/2.85 tff(14028,plain,
% 2.64/2.85 (r(z, s(s(s(s(s(elem!1))))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[2487, 47, 5706, 14027])).
% 2.64/2.85 tff(14029,plain,
% 2.64/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))))),
% 2.64/2.85 inference(rewrite,[status(thm)],[])).
% 2.64/2.85 tff(14030,plain,
% 2.64/2.85 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(14031,plain,
% 2.64/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z)))))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[14030])).
% 2.64/2.86 tff(14032,plain,
% 2.64/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))))),
% 2.64/2.86 inference(transitivity,[status(thm)],[14031, 14029])).
% 2.64/2.86 tff(14033,plain,
% 2.64/2.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 2.64/2.86 inference(quant_inst,[status(thm)],[])).
% 2.64/2.86 tff(14034,plain,
% 2.64/2.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z)))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[14033, 14032])).
% 2.64/2.86 tff(14035,plain,
% 2.64/2.86 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[14034, 246, 3697, 2401, 2003, 6875])).
% 2.64/2.86 tff(14036,plain,
% 2.64/2.86 (r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[1626, 14035])).
% 2.64/2.86 tff(14037,plain,
% 2.64/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(14038,plain,
% 2.64/2.86 (((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z))) <=> ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(14039,plain,
% 2.64/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z)))))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[14038])).
% 2.64/2.86 tff(14040,plain,
% 2.64/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 2.64/2.86 inference(transitivity,[status(thm)],[14039, 14037])).
% 2.64/2.86 tff(14041,plain,
% 2.64/2.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 2.64/2.86 inference(quant_inst,[status(thm)],[])).
% 2.64/2.86 tff(14042,plain,
% 2.64/2.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z)))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[14041, 14040])).
% 2.64/2.86 tff(14043,plain,
% 2.64/2.86 (~b(s(s(s(s(s(elem!1))))), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[14042, 246, 11962, 236, 3697, 2401, 6875])).
% 2.64/2.86 tff(14044,plain,
% 2.64/2.86 (r(s(s(s(s(s(elem!1))))), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[1601, 14043])).
% 2.64/2.86 tff(14045,plain,
% 2.64/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(14046,plain,
% 2.64/2.86 (((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(s(s(s(s(elem!1)))))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(14047,plain,
% 2.64/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), z))))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[14046])).
% 2.64/2.86 tff(14048,plain,
% 2.64/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 2.64/2.86 inference(transitivity,[status(thm)],[14047, 14045])).
% 2.64/2.86 tff(14049,plain,
% 2.64/2.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(s(s(s(s(elem!1))))))))),
% 2.64/2.86 inference(quant_inst,[status(thm)],[])).
% 2.64/2.86 tff(14050,plain,
% 2.64/2.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), z))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[14049, 14048])).
% 2.64/2.86 tff(14051,plain,
% 2.64/2.86 ($false),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[14050, 183, 429, 14044, 14036, 14028])).
% 2.64/2.86 tff(14052,plain,((~b(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.86 tff(14053,plain,
% 2.64/2.86 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[14052, 14020, 236, 12017, 2003, 3697])).
% 2.64/2.86 tff(14054,plain,
% 2.64/2.86 (r(s(s(s(s(s(elem!1))))), s(z))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[6447, 14053])).
% 2.64/2.86 tff(14055,plain,
% 2.64/2.86 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[13383, 1051, 3697])).
% 2.64/2.86 tff(14056,plain,
% 2.64/2.86 (~b(s(z), elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[13451, 1051, 236])).
% 2.64/2.86 tff(14057,plain,
% 2.64/2.86 (b(elem!1, z) <=> b(s(z), z)),
% 2.64/2.86 inference(symmetry,[status(thm)],[9549])).
% 2.64/2.86 tff(14058,plain,
% 2.64/2.86 (b(s(z), z)),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[1051, 14057])).
% 2.64/2.86 tff(14059,plain,
% 2.64/2.86 ($false),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[2118, 14058])).
% 2.64/2.86 tff(14060,plain,((~(s(z) = elem!1)) | b(s(z), z) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.86 tff(14061,plain,
% 2.64/2.86 (~(s(z) = elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[14060, 2118, 1051])).
% 2.64/2.86 tff(14062,plain,
% 2.64/2.86 (r(s(z), elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[1034, 14061, 14056])).
% 2.64/2.86 tff(14063,plain,
% 2.64/2.86 ($false),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[2927, 183, 1114, 217, 333, 4064])).
% 2.64/2.86 tff(14064,plain,((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.86 tff(14065,plain,
% 2.64/2.86 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[14064, 14062, 14018, 14054])).
% 2.64/2.86 tff(14066,plain,
% 2.64/2.86 (s(s(s(s(s(elem!1))))) = elem!1),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[86, 14065, 14055])).
% 2.64/2.86 tff(14067,plain,
% 2.64/2.86 (r(s(s(s(s(s(elem!1))))), s(z)) <=> r(elem!1, s(z))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[7030])).
% 2.64/2.86 tff(14068,plain,
% 2.64/2.86 (r(elem!1, s(z))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[4064, 14067])).
% 2.64/2.86 tff(14069,plain,
% 2.64/2.86 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (elem!1 = s(s(s(s(z)))))),
% 2.64/2.86 inference(transitivity,[status(thm)],[8044, 5879])).
% 2.64/2.86 tff(14070,plain,
% 2.64/2.86 ((~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))) <=> (~(elem!1 = s(s(s(s(z))))))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[14069])).
% 2.64/2.86 tff(14071,plain,
% 2.64/2.86 (~(elem!1 = s(s(s(s(z)))))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[1501, 14070])).
% 2.64/2.86 tff(14072,plain,
% 2.64/2.86 (~r(s(s(s(s(z)))), elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[2458, 183, 474, 413, 2593])).
% 2.64/2.86 tff(14073,plain,
% 2.64/2.86 (b(s(s(s(s(z)))), elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[13052, 14072, 3074])).
% 2.64/2.86 tff(14074,plain,
% 2.64/2.86 (b(elem!1, s(s(s(s(z)))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[13769, 7166, 8714])).
% 2.64/2.86 tff(14075,plain,
% 2.64/2.86 ($false),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[12363, 246, 11962, 14074, 6311, 14073])).
% 2.64/2.86 tff(14076,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (s(s(s(s(z)))) = elem!1) | (elem!1 = s(s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.86 tff(14077,plain,
% 2.64/2.86 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[14076, 8046, 14071, 429, 14068, 413])).
% 2.64/2.86 tff(14078,plain,
% 2.64/2.86 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[1702, 14077])).
% 2.64/2.86 tff(14079,plain,
% 2.64/2.86 (~b(s(s(s(s(z)))), s(z))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[3591, 246, 2401, 2003, 14078])).
% 2.64/2.86 tff(14080,plain,
% 2.64/2.86 (r(s(s(s(s(z)))), s(z))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[6103, 14079])).
% 2.64/2.86 tff(14081,plain,
% 2.64/2.86 (~r(s(s(s(s(z)))), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[12764, 14078, 2003, 1114])).
% 2.64/2.86 tff(14082,plain,
% 2.64/2.86 (b(s(s(s(s(z)))), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[6040, 14081])).
% 2.64/2.86 tff(14083,plain,
% 2.64/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(14084,plain,
% 2.64/2.86 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(14085,plain,
% 2.64/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z))))))))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[14084])).
% 2.64/2.86 tff(14086,plain,
% 2.64/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.64/2.86 inference(transitivity,[status(thm)],[14085, 14083])).
% 2.64/2.86 tff(14087,plain,
% 2.64/2.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.64/2.86 inference(quant_inst,[status(thm)],[])).
% 2.64/2.86 tff(14088,plain,
% 2.64/2.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z))))))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[14087, 14086])).
% 2.64/2.86 tff(14089,plain,
% 2.64/2.86 (~b(elem!1, s(s(s(s(z)))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[14088, 246, 1051, 236, 2401, 14078, 14082])).
% 2.64/2.86 tff(14090,plain,
% 2.64/2.86 (r(elem!1, s(s(s(s(z)))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[13769, 14089, 14071])).
% 2.64/2.86 tff(14091,plain,
% 2.64/2.86 ($false),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[7665, 14090, 14080, 14068])).
% 2.64/2.86 tff(14092,plain,((~(s(s(s(s(s(elem!1))))) = elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.86 tff(14093,plain,
% 2.64/2.86 (~r(elem!1, s(s(s(z))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[14092, 14066, 236, 14020, 2003, 14018, 12017, 1051, 14054])).
% 2.64/2.86 tff(14094,plain,
% 2.64/2.86 (b(elem!1, s(s(s(z))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[470, 14093, 7282])).
% 2.64/2.86 tff(14095,plain,
% 2.64/2.86 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(z)))) = elem!1)),
% 2.64/2.86 inference(monotonicity,[status(thm)],[14066])).
% 2.64/2.86 tff(14096,plain,
% 2.64/2.86 ((~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[14095])).
% 2.64/2.86 tff(14097,plain,
% 2.64/2.86 (~(s(s(s(s(z)))) = elem!1)),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[1501, 14096])).
% 2.64/2.86 tff(14098,plain,
% 2.64/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(14099,plain,
% 2.64/2.86 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(14100,plain,
% 2.64/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[14099])).
% 2.64/2.86 tff(14101,plain,
% 2.64/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.64/2.86 inference(transitivity,[status(thm)],[14100, 14098])).
% 2.64/2.86 tff(14102,plain,
% 2.64/2.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.64/2.86 inference(quant_inst,[status(thm)],[])).
% 2.64/2.86 tff(14103,plain,
% 2.64/2.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[14102, 14101])).
% 2.64/2.86 tff(14104,plain,
% 2.64/2.86 (~b(s(s(s(s(z)))), elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[14103, 246, 1051, 2002, 3697, 1833])).
% 2.64/2.86 tff(14105,plain,
% 2.64/2.86 (r(s(s(s(s(z)))), elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[2442, 47, 3074, 14104])).
% 2.64/2.86 tff(14106,plain,
% 2.64/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(14107,plain,
% 2.64/2.87 (((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(14108,plain,
% 2.64/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1))))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[14107])).
% 2.64/2.87 tff(14109,plain,
% 2.64/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.64/2.87 inference(transitivity,[status(thm)],[14108, 14106])).
% 2.64/2.87 tff(14110,plain,
% 2.64/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 2.64/2.87 inference(quant_inst,[status(thm)],[])).
% 2.64/2.87 tff(14111,plain,
% 2.64/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[14110, 14109])).
% 2.64/2.87 tff(14112,plain,
% 2.64/2.87 ($false),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[14111, 183, 1114, 217, 8722, 14105])).
% 2.64/2.87 tff(14113,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (s(s(s(s(z)))) = elem!1) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.87 tff(14114,plain,
% 2.64/2.87 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[14113, 14097, 14018, 14062, 1051, 14094, 3697, 14020])).
% 2.64/2.87 tff(14115,plain,
% 2.64/2.87 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[1702, 14114])).
% 2.64/2.87 tff(14116,plain,
% 2.64/2.87 (~r(s(s(s(s(z)))), z)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[2599, 183, 12017, 14115])).
% 2.64/2.87 tff(14117,plain,
% 2.64/2.87 (b(s(s(s(s(z)))), z)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[6040, 14116])).
% 2.64/2.87 tff(14118,plain,
% 2.64/2.87 (~(elem!1 = s(z))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[2279, 14061])).
% 2.64/2.87 tff(14119,plain,
% 2.64/2.87 (~b(elem!1, s(z))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[9994, 14094, 3697, 14020])).
% 2.64/2.87 tff(14120,plain,
% 2.64/2.87 (r(elem!1, s(z))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[214, 14119, 14118])).
% 2.64/2.87 tff(14121,plain,
% 2.64/2.87 (~b(elem!1, s(s(s(s(z)))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[13760, 14094, 3697, 12017])).
% 2.64/2.87 tff(14122,plain,
% 2.64/2.87 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (elem!1 = s(s(s(s(z)))))),
% 2.64/2.87 inference(transitivity,[status(thm)],[14095, 5879])).
% 2.64/2.87 tff(14123,plain,
% 2.64/2.87 ((~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))) <=> (~(elem!1 = s(s(s(s(z))))))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[14122])).
% 2.64/2.87 tff(14124,plain,
% 2.64/2.87 (~(elem!1 = s(s(s(s(z)))))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[1501, 14123])).
% 2.64/2.87 tff(14125,plain,
% 2.64/2.87 (r(elem!1, s(s(s(s(z)))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[13769, 14124, 14121])).
% 2.64/2.87 tff(14126,plain,
% 2.64/2.87 (~r(s(s(s(s(z)))), s(z))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[7665, 14125, 14120])).
% 2.64/2.87 tff(14127,plain,
% 2.64/2.87 (b(s(s(s(s(z)))), s(z))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[6103, 14126])).
% 2.64/2.87 tff(14128,plain,
% 2.64/2.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(14129,plain,
% 2.64/2.87 (((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(14130,plain,
% 2.64/2.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[14129])).
% 2.64/2.87 tff(14131,plain,
% 2.64/2.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.64/2.87 inference(transitivity,[status(thm)],[14130, 14128])).
% 2.64/2.87 tff(14132,plain,
% 2.64/2.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.64/2.87 inference(quant_inst,[status(thm)],[])).
% 2.64/2.87 tff(14133,plain,
% 2.64/2.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[14132, 14131])).
% 2.64/2.87 tff(14134,plain,
% 2.64/2.87 ($false),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[14133, 246, 11962, 236, 3697, 14020, 14127, 14117])).
% 2.64/2.87 tff(14135,plain,(b(s(z), z) | (~b(z, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.87 tff(14136,plain,
% 2.64/2.87 (b(s(z), z)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[14135, 13175, 13730, 14015, 13532])).
% 2.64/2.87 tff(14137,plain,
% 2.64/2.87 (~b(s(z), elem!1)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[13451, 14015, 13175])).
% 2.64/2.87 tff(14138,plain,
% 2.64/2.87 (b(s(s(elem!1)), s(z))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[5773, 202, 3697])).
% 2.64/2.87 tff(14139,plain,
% 2.64/2.87 (b(s(s(elem!1)), elem!1)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[207, 14138, 202])).
% 2.64/2.87 tff(14140,plain,
% 2.64/2.87 (~b(s(s(elem!1)), z)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[12851, 14138, 1051, 1056])).
% 2.64/2.87 tff(14141,plain,
% 2.64/2.87 (r(s(s(elem!1)), z)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[523, 14140])).
% 2.64/2.87 tff(14142,plain,
% 2.64/2.87 (~b(z, s(s(elem!1)))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[1154, 14138, 236, 1056])).
% 2.64/2.87 tff(14143,plain,
% 2.64/2.87 (~(s(s(elem!1)) = elem!1)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[11980, 14142])).
% 2.64/2.87 tff(14144,plain,
% 2.64/2.87 (~(s(s(elem!1)) = s(elem!1))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[5640, 14143])).
% 2.64/2.87 tff(14145,plain,
% 2.64/2.87 (~b(s(elem!1), elem!1)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[12046, 14144, 1051, 14141, 14139])).
% 2.64/2.87 tff(14146,plain,
% 2.64/2.87 (r(s(elem!1), elem!1)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[5655, 10890, 14145])).
% 2.64/2.87 tff(14147,plain,
% 2.64/2.87 ((~(s(s(s(s(s(elem!1))))) = s(z))) <=> (~(s(s(s(s(s(elem!1))))) = elem!1))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[10605])).
% 2.64/2.87 tff(14148,plain,
% 2.64/2.87 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[331, 14147])).
% 2.64/2.87 tff(14149,plain,
% 2.64/2.87 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[86, 14148, 14055])).
% 2.64/2.87 tff(14150,plain,
% 2.64/2.87 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[3455])).
% 2.64/2.87 tff(14151,plain,
% 2.64/2.87 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(s(z)))),
% 2.64/2.87 inference(symmetry,[status(thm)],[14150])).
% 2.64/2.87 tff(14152,plain,
% 2.64/2.87 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[3453])).
% 2.64/2.87 tff(14153,plain,
% 2.64/2.87 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(z)))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[3454])).
% 2.64/2.87 tff(14154,plain,
% 2.64/2.87 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(z)) = s(s(s(s(z)))))),
% 2.64/2.87 inference(transitivity,[status(thm)],[14153, 2786])).
% 2.64/2.87 tff(14155,plain,
% 2.64/2.87 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 2.64/2.87 inference(symmetry,[status(thm)],[14154])).
% 2.64/2.87 tff(14156,plain,
% 2.64/2.87 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[14155])).
% 2.64/2.87 tff(14157,plain,
% 2.64/2.87 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[1526, 14156])).
% 2.64/2.87 tff(14158,plain,
% 2.64/2.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(14159,plain,
% 2.64/2.87 (((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(14160,plain,
% 2.64/2.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[14159])).
% 2.64/2.87 tff(14161,plain,
% 2.64/2.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 2.64/2.87 inference(transitivity,[status(thm)],[14160, 14158])).
% 2.64/2.87 tff(14162,plain,
% 2.64/2.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 2.64/2.87 inference(quant_inst,[status(thm)],[])).
% 2.64/2.87 tff(14163,plain,
% 2.64/2.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[14162, 14161])).
% 2.64/2.87 tff(14164,plain,
% 2.64/2.87 (~b(s(z), s(s(s(elem!1))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[14163, 246, 1056, 236, 9205])).
% 2.64/2.87 tff(14165,plain,
% 2.64/2.87 (~b(elem!1, s(s(s(elem!1))))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[14164, 11012])).
% 2.64/2.87 tff(14166,plain,
% 2.64/2.87 (r(elem!1, s(s(s(elem!1))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[9483, 14165, 10639])).
% 2.64/2.87 tff(14167,plain,
% 2.64/2.87 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[4270, 14166, 333])).
% 2.64/2.87 tff(14168,plain,
% 2.64/2.87 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[3693, 14167, 10672])).
% 2.64/2.87 tff(14169,plain,
% 2.64/2.87 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[4050, 14168, 10792, 333, 367])).
% 2.64/2.87 tff(14170,plain,
% 2.64/2.87 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[3068])).
% 2.64/2.87 tff(14171,plain,
% 2.64/2.87 (b(s(s(s(elem!1))), s(elem!1))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[5914, 14170])).
% 2.64/2.87 tff(14172,plain,
% 2.64/2.87 ($false),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[3659, 14171])).
% 2.64/2.87 tff(14173,plain,((~b(s(s(s(s(z)))), s(elem!1))) | b(s(s(s(elem!1))), s(elem!1)) | (~(s(s(s(z))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.87 tff(14174,plain,
% 2.64/2.87 (~b(s(s(s(s(z)))), s(elem!1))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[14173, 14169, 3452])).
% 2.64/2.87 tff(14175,plain,
% 2.64/2.87 (r(s(s(s(s(z)))), s(elem!1))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[1728, 14174, 14157])).
% 2.64/2.87 tff(14176,plain,
% 2.64/2.87 (r(s(s(s(elem!1))), s(elem!1))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[14175, 14152])).
% 2.64/2.87 tff(14177,plain,
% 2.64/2.87 (r(s(s(s(elem!1))), s(s(z)))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[14176, 14151])).
% 2.64/2.87 tff(14178,plain,
% 2.64/2.87 (r(s(elem!1), elem!1) <=> r(s(s(z)), elem!1)),
% 2.64/2.87 inference(monotonicity,[status(thm)],[3454])).
% 2.64/2.87 tff(14179,plain,
% 2.64/2.87 (r(s(s(z)), elem!1) <=> r(s(elem!1), elem!1)),
% 2.64/2.87 inference(symmetry,[status(thm)],[14178])).
% 2.64/2.87 tff(14180,plain,
% 2.64/2.87 (r(s(s(z)), s(z)) <=> r(s(s(z)), elem!1)),
% 2.64/2.87 inference(monotonicity,[status(thm)],[10602])).
% 2.64/2.87 tff(14181,plain,
% 2.64/2.87 (r(s(s(z)), s(z)) <=> r(s(elem!1), elem!1)),
% 2.64/2.87 inference(transitivity,[status(thm)],[14180, 14179])).
% 2.64/2.87 tff(14182,plain,
% 2.64/2.87 ((~r(s(s(z)), s(z))) <=> (~r(s(elem!1), elem!1))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[14181])).
% 2.64/2.87 tff(14183,assumption,(~r(s(s(z)), s(z))), introduced(assumption)).
% 2.64/2.87 tff(14184,plain,
% 2.64/2.87 (~r(s(elem!1), elem!1)),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[14183, 14182])).
% 2.64/2.87 tff(14185,plain,
% 2.64/2.87 ($false),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[367, 14184])).
% 2.64/2.87 tff(14186,plain,(r(s(s(z)), s(z)) | (~r(s(elem!1), elem!1)) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.87 tff(14187,plain,
% 2.64/2.87 (r(s(s(z)), s(z))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[14186, 367, 202])).
% 2.64/2.87 tff(14188,plain,
% 2.64/2.87 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(14189,plain,
% 2.64/2.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z))))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[14188])).
% 2.64/2.87 tff(14190,plain,
% 2.64/2.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))),
% 2.64/2.87 inference(transitivity,[status(thm)],[14189, 8098])).
% 2.64/2.87 tff(14191,plain,
% 2.64/2.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 2.64/2.87 inference(quant_inst,[status(thm)],[])).
% 2.64/2.87 tff(14192,plain,
% 2.64/2.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[14191, 14190])).
% 2.64/2.87 tff(14193,plain,
% 2.64/2.87 (~b(s(s(s(elem!1))), s(z))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[14192, 246, 1056, 236, 9205])).
% 2.64/2.87 tff(14194,plain,
% 2.64/2.87 ((s(s(s(elem!1))) = s(z)) | r(s(s(s(elem!1))), s(z))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[10692, 47, 14193])).
% 2.64/2.87 tff(14195,plain,
% 2.64/2.87 (r(s(s(s(elem!1))), s(z))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[14194, 10682])).
% 2.64/2.87 tff(14196,plain,
% 2.64/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(14197,plain,
% 2.64/2.87 (((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(14198,plain,
% 2.64/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z)))))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[14197])).
% 2.64/2.87 tff(14199,plain,
% 2.64/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.64/2.87 inference(transitivity,[status(thm)],[14198, 14196])).
% 2.64/2.87 tff(14200,plain,
% 2.64/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.64/2.87 inference(quant_inst,[status(thm)],[])).
% 2.64/2.87 tff(14201,plain,
% 2.64/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z)))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[14200, 14199])).
% 2.64/2.87 tff(14202,plain,
% 2.64/2.87 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[14201, 183, 14195, 14187])).
% 2.64/2.87 tff(14203,plain,
% 2.64/2.87 ($false),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[14202, 14177])).
% 2.64/2.87 tff(14204,plain,((~b(s(s(s(elem!1))), z)) | (~(elem!1 = s(z))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.87 tff(14205,plain,
% 2.64/2.87 (~b(s(s(s(elem!1))), z)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[14204, 202, 14149, 14146, 1056, 236])).
% 2.64/2.87 tff(14206,plain,
% 2.64/2.87 (r(s(s(s(elem!1))), z)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[3086, 47, 355, 14205])).
% 2.64/2.87 tff(14207,plain,
% 2.64/2.87 (r(s(z), s(s(s(z)))) <=> r(s(z), s(s(elem!1)))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[3452])).
% 2.64/2.87 tff(14208,plain,
% 2.64/2.87 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(z))))),
% 2.64/2.87 inference(symmetry,[status(thm)],[14207])).
% 2.64/2.87 tff(14209,plain,
% 2.64/2.87 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[3452])).
% 2.64/2.87 tff(14210,plain,
% 2.64/2.87 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.87 inference(symmetry,[status(thm)],[14209])).
% 2.64/2.87 tff(14211,plain,
% 2.64/2.87 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[10627])).
% 2.64/2.87 tff(14212,plain,
% 2.64/2.87 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.87 inference(transitivity,[status(thm)],[14211, 14210])).
% 2.64/2.87 tff(14213,plain,
% 2.64/2.87 ((~r(s(s(s(elem!1))), s(s(elem!1)))) <=> (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[14212])).
% 2.64/2.87 tff(14214,plain,
% 2.64/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(14215,plain,
% 2.64/2.87 (((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(14216,plain,
% 2.64/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z))))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[14215])).
% 2.64/2.87 tff(14217,plain,
% 2.64/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))),
% 2.64/2.87 inference(transitivity,[status(thm)],[14216, 14214])).
% 2.64/2.87 tff(14218,plain,
% 2.64/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.64/2.87 inference(quant_inst,[status(thm)],[])).
% 2.64/2.87 tff(14219,plain,
% 2.64/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[14218, 14217])).
% 2.64/2.87 tff(14220,plain,
% 2.64/2.87 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[14219, 183, 14141, 14206])).
% 2.64/2.87 tff(14221,plain,
% 2.64/2.87 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[14220, 14213])).
% 2.64/2.87 tff(14222,plain,
% 2.64/2.87 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[1702, 14221])).
% 2.64/2.87 tff(14223,plain,
% 2.64/2.87 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[9446, 14222, 3452])).
% 2.64/2.87 tff(14224,plain,
% 2.64/2.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(14225,plain,
% 2.64/2.88 (((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(14226,plain,
% 2.64/2.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[14225])).
% 2.64/2.88 tff(14227,plain,
% 2.64/2.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.64/2.88 inference(transitivity,[status(thm)],[14226, 14224])).
% 2.64/2.88 tff(14228,plain,
% 2.64/2.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.64/2.88 inference(quant_inst,[status(thm)],[])).
% 2.64/2.88 tff(14229,plain,
% 2.64/2.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[14228, 14227])).
% 2.64/2.88 tff(14230,plain,
% 2.64/2.88 (~b(s(z), s(s(s(elem!1))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[14229, 246, 201, 235, 1659])).
% 2.64/2.88 tff(14231,plain,
% 2.64/2.88 (~b(elem!1, s(s(s(elem!1))))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[14230, 11012])).
% 2.64/2.88 tff(14232,plain,
% 2.64/2.88 (r(elem!1, s(s(s(elem!1))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[9483, 14231, 10639])).
% 2.64/2.88 tff(14233,plain,
% 2.64/2.88 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[4270, 14232, 333])).
% 2.64/2.88 tff(14234,plain,
% 2.64/2.88 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[3693, 14233, 10672])).
% 2.64/2.88 tff(14235,plain,
% 2.64/2.88 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[4050, 14234, 10792, 333, 367])).
% 2.64/2.88 tff(14236,plain,
% 2.64/2.88 (~b(s(s(s(s(z)))), s(elem!1))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[14173, 14235, 3452])).
% 2.64/2.88 tff(14237,plain,
% 2.64/2.88 (r(s(s(s(s(z)))), s(elem!1))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[1728, 14236, 14157])).
% 2.64/2.88 tff(14238,plain,
% 2.64/2.88 (r(s(s(s(elem!1))), s(elem!1))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[14237, 14152])).
% 2.64/2.88 tff(14239,plain,
% 2.64/2.88 (r(s(s(s(elem!1))), s(s(z)))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[14238, 14151])).
% 2.64/2.88 tff(14240,plain,
% 2.64/2.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(14241,plain,
% 2.64/2.88 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(14242,plain,
% 2.64/2.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z)))))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[14241])).
% 2.64/2.88 tff(14243,plain,
% 2.64/2.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.64/2.88 inference(transitivity,[status(thm)],[14242, 14240])).
% 2.64/2.88 tff(14244,plain,
% 2.64/2.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.64/2.88 inference(quant_inst,[status(thm)],[])).
% 2.64/2.88 tff(14245,plain,
% 2.64/2.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z)))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[14244, 14243])).
% 2.64/2.88 tff(14246,plain,
% 2.64/2.88 (~b(s(s(s(elem!1))), s(z))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[14245, 246, 201, 235, 1659])).
% 2.64/2.88 tff(14247,plain,
% 2.64/2.88 ((s(s(s(elem!1))) = s(z)) | r(s(s(s(elem!1))), s(z))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[10692, 47, 14246])).
% 2.64/2.88 tff(14248,plain,
% 2.64/2.88 (r(s(s(s(elem!1))), s(z))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[14247, 10682])).
% 2.64/2.88 tff(14249,plain,
% 2.64/2.88 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[14201, 183, 14248, 14187])).
% 2.64/2.88 tff(14250,plain,
% 2.64/2.88 ($false),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[14249, 14239])).
% 2.64/2.88 tff(14251,plain,((~b(s(z), s(s(elem!1)))) | (~(elem!1 = s(z))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.88 tff(14252,plain,
% 2.64/2.88 (~b(s(z), s(s(elem!1)))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[14251, 202, 14149, 14146, 14138, 14223])).
% 2.64/2.88 tff(14253,plain,
% 2.64/2.88 (r(s(z), s(s(elem!1)))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[233, 14252])).
% 2.64/2.88 tff(14254,plain,
% 2.64/2.88 (r(s(z), s(s(s(z))))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[14253, 14208])).
% 2.64/2.88 tff(14255,plain,
% 2.64/2.88 (~r(s(s(z)), s(s(s(z))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[10217, 14254, 236, 12017, 1056])).
% 2.64/2.88 tff(14256,plain,
% 2.64/2.88 (b(s(s(z)), s(s(s(z))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[8382, 14255])).
% 2.64/2.88 tff(14257,plain,
% 2.64/2.88 (r(s(s(z)), s(z))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[14186, 14146, 202])).
% 2.64/2.88 tff(14258,plain,
% 2.64/2.88 (b(s(s(s(s(s(elem!1))))), elem!1) <=> b(s(s(s(s(s(elem!1))))), s(z))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[202])).
% 2.64/2.88 tff(14259,plain,
% 2.64/2.88 ((~b(s(s(s(s(s(elem!1))))), elem!1)) <=> (~b(s(s(s(s(s(elem!1))))), s(z)))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[14258])).
% 2.64/2.88 tff(14260,plain,
% 2.64/2.88 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[14055, 14259])).
% 2.64/2.88 tff(14261,plain,
% 2.64/2.88 (r(s(s(s(s(s(elem!1))))), s(z))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[6447, 14260])).
% 2.64/2.88 tff(14262,plain,
% 2.64/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(z))))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(14263,plain,
% 2.64/2.88 (((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(z))))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(14264,plain,
% 2.64/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(z)))))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[14263])).
% 2.64/2.88 tff(14265,plain,
% 2.64/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(z))))),
% 2.64/2.88 inference(transitivity,[status(thm)],[14264, 14262])).
% 2.64/2.88 tff(14266,plain,
% 2.64/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 2.64/2.88 inference(quant_inst,[status(thm)],[])).
% 2.64/2.88 tff(14267,plain,
% 2.64/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(z)))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[14266, 14265])).
% 2.64/2.88 tff(14268,plain,
% 2.64/2.88 (~r(s(s(z)), s(s(s(s(s(elem!1))))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[14267, 183, 14261, 14257])).
% 2.64/2.88 tff(14269,plain,
% 2.64/2.88 ((s(s(z)) = s(s(s(s(s(elem!1)))))) | b(s(s(z)), s(s(s(s(s(elem!1))))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[10803, 47, 14268])).
% 2.64/2.88 tff(14270,plain,
% 2.64/2.88 (b(s(s(z)), s(s(s(s(s(elem!1))))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[14269, 10793])).
% 2.64/2.88 tff(14271,plain,
% 2.64/2.88 (~b(s(z), s(s(s(s(s(elem!1))))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[6249, 246, 1056, 236, 9221])).
% 2.64/2.88 tff(14272,plain,
% 2.64/2.88 (~b(elem!1, s(s(s(s(s(elem!1))))))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[14271, 10610])).
% 2.64/2.88 tff(14273,plain,
% 2.64/2.88 (r(elem!1, s(s(s(s(s(elem!1))))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[5125, 14272, 10608])).
% 2.64/2.88 tff(14274,plain,
% 2.64/2.88 (r(s(z), s(s(s(s(s(elem!1))))))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[14273, 10604])).
% 2.64/2.88 tff(14275,plain,
% 2.64/2.88 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(z)), s(s(s(z))))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[10659])).
% 2.64/2.88 tff(14276,plain,
% 2.64/2.88 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), s(s(elem!1)))),
% 2.64/2.88 inference(symmetry,[status(thm)],[14275])).
% 2.64/2.88 tff(14277,plain,
% 2.64/2.88 (b(s(s(z)), s(s(elem!1)))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[1854, 14276])).
% 2.64/2.88 tff(14278,plain,
% 2.64/2.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(14279,plain,
% 2.64/2.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.64/2.88 inference(quant_inst,[status(thm)],[])).
% 2.64/2.88 tff(14280,plain,
% 2.64/2.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(elem!1))))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[14279, 14278])).
% 2.64/2.88 tff(14281,plain,
% 2.64/2.88 ((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(elem!1))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[14280, 246, 201, 236, 9221, 10945])).
% 2.64/2.88 tff(14282,plain,
% 2.64/2.88 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[14281, 14277])).
% 2.64/2.88 tff(14283,plain,
% 2.64/2.88 (r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[1547, 47, 14282, 10668])).
% 2.64/2.88 tff(14284,plain,
% 2.64/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(14285,plain,
% 2.64/2.88 (((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(14286,plain,
% 2.64/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1)))))))))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[14285])).
% 2.64/2.88 tff(14287,plain,
% 2.64/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 2.64/2.88 inference(transitivity,[status(thm)],[14286, 14284])).
% 2.64/2.88 tff(14288,plain,
% 2.64/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(elem!1)))))),
% 2.64/2.88 inference(quant_inst,[status(thm)],[])).
% 2.64/2.88 tff(14289,plain,
% 2.64/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1)))))))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[14288, 14287])).
% 2.64/2.88 tff(14290,plain,
% 2.64/2.88 ($false),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[14289, 183, 1113, 14283, 14274])).
% 2.64/2.88 tff(14291,plain,((~b(s(s(s(s(s(elem!1))))), z)) | (~r(s(z), s(s(elem!1)))) | (~(elem!1 = s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.88 tff(14292,plain,
% 2.64/2.88 (~b(s(s(s(s(s(elem!1))))), z)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[14291, 14253, 202, 14138, 236, 14270, 14256, 1056])).
% 2.64/2.88 tff(14293,plain,
% 2.64/2.88 (r(s(s(s(s(s(elem!1))))), z)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[1601, 14292])).
% 2.64/2.88 tff(14294,plain,
% 2.64/2.88 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[3452])).
% 2.64/2.88 tff(14295,plain,
% 2.64/2.88 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(s(z)))) = s(s(elem!1))))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[14294])).
% 2.64/2.88 tff(14296,plain,
% 2.64/2.88 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[1697, 14295])).
% 2.64/2.88 tff(14297,plain,
% 2.64/2.88 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[14296, 10658])).
% 2.64/2.88 tff(14298,plain,
% 2.64/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(14299,plain,
% 2.64/2.88 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(14300,plain,
% 2.64/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z))))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[14299])).
% 2.64/2.88 tff(14301,plain,
% 2.64/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 2.64/2.88 inference(transitivity,[status(thm)],[14300, 14298])).
% 2.64/2.88 tff(14302,plain,
% 2.64/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.64/2.88 inference(quant_inst,[status(thm)],[])).
% 2.64/2.88 tff(14303,plain,
% 2.64/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[14302, 14301])).
% 2.64/2.88 tff(14304,plain,
% 2.64/2.88 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[14303, 183, 14141, 14206])).
% 2.64/2.88 tff(14305,plain,
% 2.64/2.88 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[4455, 14304, 14297])).
% 2.64/2.88 tff(14306,plain,
% 2.64/2.88 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[5671, 14293, 14141])).
% 2.64/2.88 tff(14307,plain,
% 2.64/2.88 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[1557, 14306, 10674])).
% 2.64/2.88 tff(14308,plain,
% 2.64/2.88 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[1667, 14307, 14305, 14223])).
% 2.64/2.88 tff(14309,plain,
% 2.64/2.88 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[3693, 14308, 10672])).
% 2.64/2.88 tff(14310,plain,
% 2.64/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(elem!1))), z)))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(14311,plain,
% 2.64/2.88 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(elem!1))), z)))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(14312,plain,
% 2.64/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(elem!1))), z))))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[14311])).
% 2.64/2.88 tff(14313,plain,
% 2.64/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(elem!1))), z)))),
% 2.64/2.88 inference(transitivity,[status(thm)],[14312, 14310])).
% 2.64/2.88 tff(14314,plain,
% 2.64/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.64/2.88 inference(quant_inst,[status(thm)],[])).
% 2.64/2.88 tff(14315,plain,
% 2.64/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(elem!1))), z))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[14314, 14313])).
% 2.64/2.88 tff(14316,plain,
% 2.64/2.88 ($false),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[14315, 183, 14309, 14293, 14206])).
% 2.64/2.88 tff(14317,plain,((~(elem!1 = s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.88 tff(14318,plain,
% 2.64/2.88 (~(elem!1 = s(z))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[14317, 13175, 14136, 14015, 13730])).
% 2.64/2.88 tff(14319,plain,
% 2.64/2.88 (~(s(z) = elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[9, 14318])).
% 2.64/2.88 tff(14320,plain,
% 2.64/2.88 (r(s(z), elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[1034, 14319, 14137])).
% 2.64/2.88 tff(14321,plain,
% 2.64/2.88 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[13383, 14015, 13730])).
% 2.64/2.88 tff(14322,plain,
% 2.64/2.88 (b(elem!1, z)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[14014, 2232, 3697])).
% 2.64/2.88 tff(14323,plain,
% 2.64/2.88 (~b(z, s(s(s(z))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[12015, 246, 11962, 14322, 3697])).
% 2.64/2.88 tff(14324,plain,
% 2.64/2.88 (r(z, s(s(s(z))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[6165, 14323])).
% 2.64/2.88 tff(14325,plain,
% 2.64/2.88 (b(s(z), z)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[14135, 236, 3697, 1051, 2003])).
% 2.64/2.88 tff(14326,plain,
% 2.64/2.88 (~r(s(s(s(s(z)))), z)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[2599, 183, 12017, 2593])).
% 2.64/2.88 tff(14327,plain,
% 2.64/2.88 (b(s(s(s(s(z)))), z)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[6040, 14326])).
% 2.64/2.88 tff(14328,plain,
% 2.64/2.88 (~b(s(s(s(s(z)))), s(z))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[8269, 14327, 236, 14325])).
% 2.64/2.88 tff(14329,plain,
% 2.64/2.88 (r(s(s(s(s(z)))), s(z))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[6103, 14328])).
% 2.64/2.88 tff(14330,plain,
% 2.64/2.88 (~r(s(z), s(s(s(z))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[6098, 14329, 2593])).
% 2.64/2.88 tff(14331,plain,
% 2.64/2.88 (b(s(z), s(s(s(z))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[1291, 14330])).
% 2.64/2.88 tff(14332,plain,
% 2.64/2.88 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[14052, 14331, 236, 12017, 2003, 3697])).
% 2.64/2.88 tff(14333,plain,
% 2.64/2.88 (r(s(s(s(s(s(elem!1))))), s(z))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[6447, 14332])).
% 2.64/2.88 tff(14334,plain,
% 2.64/2.88 (~b(elem!1, s(z))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[2262, 246, 11962, 1051, 14325])).
% 2.64/2.88 tff(14335,plain,
% 2.64/2.88 (~(elem!1 = s(z))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[14317, 236, 14325, 1051, 3697])).
% 2.64/2.88 tff(14336,plain,
% 2.64/2.88 (r(elem!1, s(z))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[214, 14335, 14334])).
% 2.64/2.88 tff(14337,plain,
% 2.64/2.88 (~r(elem!1, s(s(s(s(z)))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[7665, 14329, 14336])).
% 2.64/2.88 tff(14338,plain,
% 2.64/2.88 (~b(elem!1, s(s(s(s(z)))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[12611, 246, 11962, 1051, 14327])).
% 2.64/2.88 tff(14339,plain,
% 2.64/2.88 (elem!1 = s(s(s(s(z))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[13769, 14338, 14337])).
% 2.64/2.88 tff(14340,plain,
% 2.64/2.88 (s(s(s(s(z)))) = elem!1),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[8712, 14339])).
% 2.64/2.88 tff(14341,plain,
% 2.64/2.88 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[14340])).
% 2.64/2.88 tff(14342,plain,
% 2.64/2.88 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 2.64/2.88 inference(transitivity,[status(thm)],[14341, 123])).
% 2.64/2.88 tff(14343,plain,
% 2.64/2.88 ((~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(s(elem!1))))) = elem!1))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[14342])).
% 2.64/2.88 tff(14344,plain,
% 2.64/2.88 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[1501, 14343])).
% 2.64/2.88 tff(14345,plain,
% 2.64/2.88 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[86, 14344, 14055])).
% 2.64/2.88 tff(14346,plain,
% 2.64/2.88 (~(s(z) = elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[9, 14335])).
% 2.64/2.88 tff(14347,plain,
% 2.64/2.88 (r(s(z), elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[1034, 14346, 14056])).
% 2.64/2.88 tff(14348,plain,
% 2.64/2.88 ($false),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[2307, 183, 14347, 14345, 14333])).
% 2.64/2.88 tff(14349,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.88 tff(14350,plain,
% 2.64/2.88 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[14349, 14322, 13175, 13532, 3697])).
% 2.64/2.88 tff(14351,plain,
% 2.64/2.88 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[1702, 14350])).
% 2.64/2.88 tff(14352,plain,
% 2.64/2.88 (b(s(z), z)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[14135, 13175, 3697, 14322, 13532])).
% 2.64/2.88 tff(14353,plain,
% 2.64/2.88 (~b(elem!1, s(z))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[2262, 246, 11962, 14322, 14352])).
% 2.64/2.88 tff(14354,plain,
% 2.64/2.88 (~(elem!1 = s(z))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[14317, 13175, 14352, 14322, 3697])).
% 2.64/2.89 tff(14355,plain,
% 2.64/2.89 (r(elem!1, s(z))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[214, 14354, 14353])).
% 2.64/2.89 tff(14356,plain,
% 2.64/2.89 (~r(elem!1, z)),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[13185, 5972, 13175, 14355, 14352])).
% 2.64/2.89 tff(14357,plain,
% 2.64/2.89 (~b(s(s(elem!1)), z)),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[12483, 2362, 14322])).
% 2.64/2.89 tff(14358,plain,
% 2.64/2.89 (r(s(s(elem!1)), z)),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[523, 14357])).
% 2.64/2.89 tff(14359,plain,
% 2.64/2.89 (~(s(z) = elem!1)),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[9, 14354])).
% 2.64/2.89 tff(14360,plain,
% 2.64/2.89 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[5804, 14359])).
% 2.64/2.89 tff(14361,plain,
% 2.64/2.89 (~r(z, s(s(elem!1)))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[12027, 2362, 3697, 14322, 14360])).
% 2.64/2.89 tff(14362,plain,
% 2.64/2.89 (b(z, s(s(elem!1)))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[264, 14361])).
% 2.64/2.89 tff(14363,plain,
% 2.64/2.89 ($false),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[12300, 14362, 14358, 2232, 7016])).
% 2.64/2.89 tff(14364,plain,((~b(s(s(elem!1)), elem!1)) | r(s(s(elem!1)), elem!1) | r(elem!1, z) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.89 tff(14365,plain,
% 2.64/2.89 (~b(s(s(elem!1)), elem!1)),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[14364, 14356, 2232, 3697])).
% 2.64/2.89 tff(14366,plain,
% 2.64/2.89 (s(s(elem!1)) = elem!1),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[156, 14365, 2232])).
% 2.64/2.89 tff(14367,plain,
% 2.64/2.89 (elem!1 = s(s(elem!1))),
% 2.64/2.89 inference(symmetry,[status(thm)],[14366])).
% 2.64/2.89 tff(14368,plain,
% 2.64/2.89 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 2.64/2.89 inference(transitivity,[status(thm)],[7030, 14367])).
% 2.64/2.89 tff(14369,plain,
% 2.64/2.89 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(elem!1)))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[14368])).
% 2.64/2.89 tff(14370,plain,
% 2.64/2.89 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(elem!1))))))),
% 2.64/2.89 inference(symmetry,[status(thm)],[14369])).
% 2.64/2.89 tff(14371,plain,
% 2.64/2.89 (s(elem!1) = s(s(s(s(elem!1))))),
% 2.64/2.89 inference(transitivity,[status(thm)],[108, 14370, 325])).
% 2.64/2.89 tff(14372,plain,
% 2.64/2.89 (inj_0(s(elem!1)) = inj_0(s(s(s(s(elem!1)))))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[14371])).
% 2.64/2.89 tff(14373,plain,
% 2.64/2.89 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(elem!1))),
% 2.64/2.89 inference(symmetry,[status(thm)],[14372])).
% 2.64/2.89 tff(14374,plain,
% 2.64/2.89 (s(s(s(elem!1))) = s(elem!1)),
% 2.64/2.89 inference(monotonicity,[status(thm)],[14366])).
% 2.64/2.89 tff(14375,plain,
% 2.64/2.89 (s(elem!1) = s(s(s(elem!1)))),
% 2.64/2.89 inference(symmetry,[status(thm)],[14374])).
% 2.64/2.89 tff(14376,plain,
% 2.64/2.89 (s(elem!1) = elem!1),
% 2.64/2.89 inference(transitivity,[status(thm)],[14375, 352, 14373, 343])).
% 2.64/2.89 tff(14377,plain,
% 2.64/2.89 (r(s(z), s(elem!1)) <=> r(s(z), elem!1)),
% 2.64/2.89 inference(monotonicity,[status(thm)],[14376])).
% 2.64/2.89 tff(14378,plain,
% 2.64/2.89 (r(s(z), elem!1) <=> r(s(z), s(elem!1))),
% 2.64/2.89 inference(symmetry,[status(thm)],[14377])).
% 2.64/2.89 tff(14379,plain,
% 2.64/2.89 (~b(s(z), elem!1)),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[13451, 14322, 13175])).
% 2.64/2.89 tff(14380,plain,
% 2.64/2.89 (r(s(z), elem!1)),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[1034, 14359, 14379])).
% 2.64/2.89 tff(14381,plain,
% 2.64/2.89 (r(s(z), s(elem!1))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[14380, 14378])).
% 2.64/2.89 tff(14382,plain,
% 2.64/2.89 (r(s(elem!1), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[14376])).
% 2.64/2.89 tff(14383,plain,
% 2.64/2.89 (r(elem!1, s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 2.64/2.89 inference(symmetry,[status(thm)],[14382])).
% 2.64/2.89 tff(14384,plain,
% 2.64/2.89 (~b(elem!1, s(s(s(z))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[13432, 14366, 3697, 14322, 14352, 14355, 13175, 14351])).
% 2.64/2.89 tff(14385,plain,
% 2.64/2.89 (r(elem!1, s(s(s(z))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[470, 14384, 7282])).
% 2.64/2.89 tff(14386,plain,
% 2.64/2.89 (r(s(elem!1), s(s(s(z))))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[14385, 14383])).
% 2.64/2.89 tff(14387,plain,
% 2.64/2.89 (~r(s(s(s(s(z)))), s(z))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[7665, 5972, 14355])).
% 2.64/2.89 tff(14388,plain,
% 2.64/2.89 (b(s(s(s(s(z)))), s(z))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[6103, 14387])).
% 2.64/2.89 tff(14389,plain,
% 2.64/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(14390,plain,
% 2.64/2.89 (((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(14391,plain,
% 2.64/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[14390])).
% 2.64/2.89 tff(14392,plain,
% 2.64/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.64/2.89 inference(transitivity,[status(thm)],[14391, 14389])).
% 2.64/2.89 tff(14393,plain,
% 2.64/2.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.64/2.89 inference(quant_inst,[status(thm)],[])).
% 2.64/2.89 tff(14394,plain,
% 2.64/2.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[14393, 14392])).
% 2.64/2.89 tff(14395,plain,
% 2.64/2.89 ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[14394, 246, 14322, 14352, 3697, 14351])).
% 2.64/2.89 tff(14396,plain,
% 2.64/2.89 (~b(s(z), s(s(s(z))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[14395, 14388])).
% 2.64/2.89 tff(14397,plain,
% 2.64/2.89 (r(s(z), s(s(s(z))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[1291, 14396])).
% 2.64/2.89 tff(14398,plain,
% 2.64/2.89 ($false),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[8830, 183, 14397, 14386, 14381])).
% 2.64/2.89 tff(14399,plain,((~r(elem!1, s(s(s(s(z)))))) | (~(s(s(s(s(s(elem!1))))) = elem!1)) | (~b(s(s(s(z))), elem!1)) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.64/2.89 tff(14400,plain,
% 2.64/2.89 (~r(elem!1, s(s(s(s(z)))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[14399, 7030, 3697, 2232])).
% 2.64/2.89 tff(14401,plain,
% 2.64/2.89 (b(elem!1, s(s(s(s(z)))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[13769, 14400, 14071])).
% 2.64/2.89 tff(14402,plain,
% 2.64/2.89 (~b(elem!1, s(s(s(z))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[13745, 14401, 3697, 14351])).
% 2.64/2.89 tff(14403,plain,
% 2.64/2.89 (r(elem!1, s(s(s(z))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[470, 14402, 7282])).
% 2.64/2.89 tff(14404,plain,
% 2.64/2.89 (~r(elem!1, z)),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[2254, 14403, 14324])).
% 2.64/2.89 tff(14405,plain,
% 2.64/2.89 (~b(s(s(elem!1)), elem!1)),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[14364, 14404, 2232, 3697])).
% 2.64/2.89 tff(14406,plain,
% 2.64/2.89 (s(s(elem!1)) = elem!1),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[156, 14405, 2232])).
% 2.64/2.89 tff(14407,plain,
% 2.64/2.89 (s(s(s(elem!1))) = s(elem!1)),
% 2.64/2.89 inference(monotonicity,[status(thm)],[14406])).
% 2.64/2.89 tff(14408,plain,
% 2.64/2.89 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[14407])).
% 2.64/2.89 tff(14409,plain,
% 2.64/2.89 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 2.64/2.89 inference(transitivity,[status(thm)],[14408, 2891])).
% 2.64/2.89 tff(14410,plain,
% 2.64/2.89 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[14409])).
% 2.64/2.89 tff(14411,plain,
% 2.64/2.89 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[6281, 14360])).
% 2.64/2.89 tff(14412,plain,
% 2.64/2.89 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[14411, 14410])).
% 2.64/2.89 tff(14413,plain,
% 2.64/2.89 (s(elem!1) = s(s(s(elem!1)))),
% 2.64/2.89 inference(symmetry,[status(thm)],[14407])).
% 2.64/2.89 tff(14414,plain,
% 2.64/2.89 (r(s(elem!1), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[14413])).
% 2.64/2.89 tff(14415,plain,
% 2.64/2.89 (r(s(s(s(elem!1))), s(z)) <=> r(s(elem!1), s(z))),
% 2.64/2.89 inference(symmetry,[status(thm)],[14414])).
% 2.64/2.89 tff(14416,plain,
% 2.64/2.89 (elem!1 = s(s(elem!1))),
% 2.64/2.89 inference(symmetry,[status(thm)],[14406])).
% 2.64/2.89 tff(14417,plain,
% 2.64/2.89 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 2.64/2.89 inference(transitivity,[status(thm)],[7030, 14416])).
% 2.64/2.89 tff(14418,plain,
% 2.64/2.89 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(elem!1)))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[14417])).
% 2.64/2.89 tff(14419,plain,
% 2.64/2.89 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(elem!1))))))),
% 2.64/2.89 inference(symmetry,[status(thm)],[14418])).
% 2.64/2.89 tff(14420,plain,
% 2.64/2.89 (s(elem!1) = s(s(s(s(elem!1))))),
% 2.64/2.89 inference(transitivity,[status(thm)],[108, 14419, 325])).
% 2.64/2.89 tff(14421,plain,
% 2.64/2.89 (inj_0(s(elem!1)) = inj_0(s(s(s(s(elem!1)))))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[14420])).
% 2.64/2.89 tff(14422,plain,
% 2.64/2.89 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(elem!1))),
% 2.64/2.89 inference(symmetry,[status(thm)],[14421])).
% 2.64/2.89 tff(14423,plain,
% 2.64/2.89 (s(s(s(elem!1))) = elem!1),
% 2.64/2.89 inference(transitivity,[status(thm)],[352, 14422, 343])).
% 2.64/2.89 tff(14424,plain,
% 2.64/2.89 (r(s(s(s(elem!1))), s(z)) <=> r(elem!1, s(z))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[14423])).
% 2.64/2.89 tff(14425,plain,
% 2.64/2.89 (r(elem!1, s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 2.64/2.89 inference(symmetry,[status(thm)],[14424])).
% 2.64/2.89 tff(14426,plain,
% 2.64/2.89 (r(s(s(s(elem!1))), s(z))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[14355, 14425])).
% 2.64/2.89 tff(14427,plain,
% 2.64/2.89 (r(s(elem!1), s(z))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[14426, 14415])).
% 2.64/2.89 tff(14428,plain,
% 2.64/2.89 (s(elem!1) = elem!1),
% 2.64/2.89 inference(transitivity,[status(thm)],[14413, 352, 14422, 343])).
% 2.64/2.89 tff(14429,plain,
% 2.64/2.89 (r(s(z), s(elem!1)) <=> r(s(z), elem!1)),
% 2.64/2.89 inference(monotonicity,[status(thm)],[14428])).
% 2.64/2.89 tff(14430,plain,
% 2.64/2.89 (r(s(z), elem!1) <=> r(s(z), s(elem!1))),
% 2.64/2.89 inference(symmetry,[status(thm)],[14429])).
% 2.64/2.89 tff(14431,plain,
% 2.64/2.89 (r(s(z), s(elem!1))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[14380, 14430])).
% 2.64/2.89 tff(14432,plain,
% 2.64/2.89 (r(s(elem!1), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[14428])).
% 2.64/2.89 tff(14433,plain,
% 2.64/2.89 (r(elem!1, s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 2.64/2.89 inference(symmetry,[status(thm)],[14432])).
% 2.64/2.89 tff(14434,plain,
% 2.64/2.89 (r(s(elem!1), s(s(s(z))))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[14403, 14433])).
% 2.64/2.89 tff(14435,plain,
% 2.64/2.89 ($false),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[8830, 183, 6096, 3171, 8257])).
% 2.64/2.89 tff(14436,plain,((~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.89 tff(14437,plain,
% 2.64/2.89 (~r(s(z), s(s(s(z))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[14436, 14434, 14431])).
% 2.64/2.89 tff(14438,plain,
% 2.64/2.89 (b(s(z), s(s(s(z))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[1291, 14437])).
% 2.64/2.89 tff(14439,plain,
% 2.64/2.89 (~b(s(s(s(s(z)))), s(z))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[14395, 14438])).
% 2.64/2.89 tff(14440,plain,
% 2.64/2.89 (r(s(s(s(s(z)))), s(z))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[6103, 14439])).
% 2.64/2.89 tff(14441,plain,
% 2.64/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(14442,plain,
% 2.64/2.89 (((~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(elem!1)))) <=> ((~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(14443,plain,
% 2.64/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(elem!1)))))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[14442])).
% 2.64/2.89 tff(14444,plain,
% 2.64/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 2.64/2.89 inference(transitivity,[status(thm)],[14443, 14441])).
% 2.64/2.89 tff(14445,plain,
% 2.64/2.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 2.64/2.89 inference(quant_inst,[status(thm)],[])).
% 2.64/2.89 tff(14446,plain,
% 2.64/2.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[14445, 14444])).
% 2.64/2.89 tff(14447,plain,
% 2.64/2.89 ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[14446, 183, 14434, 14440])).
% 2.64/2.89 tff(14448,plain,
% 2.64/2.89 (~r(s(s(s(s(z)))), s(elem!1))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[14447, 14427])).
% 2.64/2.89 tff(14449,plain,
% 2.64/2.89 (b(s(s(s(s(z)))), s(elem!1))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[1728, 14448, 14412])).
% 2.64/2.89 tff(14450,plain,
% 2.64/2.89 (b(s(elem!1), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[14428])).
% 2.64/2.89 tff(14451,plain,
% 2.64/2.89 (b(elem!1, s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 2.64/2.89 inference(symmetry,[status(thm)],[14450])).
% 2.64/2.89 tff(14452,plain,
% 2.64/2.89 (b(s(elem!1), s(s(s(s(z)))))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[14401, 14451])).
% 2.64/2.89 tff(14453,plain,
% 2.64/2.89 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), elem!1)),
% 2.64/2.89 inference(monotonicity,[status(thm)],[14428])).
% 2.64/2.89 tff(14454,plain,
% 2.64/2.89 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(elem!1))),
% 2.64/2.89 inference(symmetry,[status(thm)],[14453])).
% 2.64/2.89 tff(14455,plain,
% 2.64/2.89 (b(s(s(s(z))), s(elem!1))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[3697, 14454])).
% 2.64/2.89 tff(14456,plain,
% 2.64/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(14457,plain,
% 2.64/2.89 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(14458,plain,
% 2.64/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[14457])).
% 2.64/2.89 tff(14459,plain,
% 2.64/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.64/2.89 inference(transitivity,[status(thm)],[14458, 14456])).
% 2.64/2.89 tff(14460,plain,
% 2.64/2.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.64/2.89 inference(quant_inst,[status(thm)],[])).
% 2.64/2.89 tff(14461,plain,
% 2.64/2.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[14460, 14459])).
% 2.64/2.89 tff(14462,plain,
% 2.64/2.89 ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[14461, 246, 14455, 14351, 14452])).
% 2.64/2.89 tff(14463,plain,
% 2.64/2.89 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[14462, 14449])).
% 2.64/2.89 tff(14464,plain,
% 2.64/2.89 (b(s(elem!1), z) <=> b(elem!1, z)),
% 2.64/2.89 inference(monotonicity,[status(thm)],[14428])).
% 2.64/2.89 tff(14465,plain,
% 2.64/2.89 (b(elem!1, z) <=> b(s(elem!1), z)),
% 2.64/2.89 inference(symmetry,[status(thm)],[14464])).
% 2.64/2.89 tff(14466,plain,
% 2.64/2.89 (b(s(elem!1), z)),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[14322, 14465])).
% 2.64/2.89 tff(14467,plain,
% 2.64/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(14468,plain,
% 2.64/2.89 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z))))))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(14469,plain,
% 2.64/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[14468])).
% 2.64/2.89 tff(14470,plain,
% 2.64/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.64/2.89 inference(transitivity,[status(thm)],[14469, 14467])).
% 2.64/2.89 tff(14471,plain,
% 2.64/2.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.64/2.89 inference(quant_inst,[status(thm)],[])).
% 2.64/2.89 tff(14472,plain,
% 2.64/2.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z))))))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[14471, 14470])).
% 2.64/2.89 tff(14473,plain,
% 2.64/2.89 (~b(s(s(s(s(z)))), z)),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[14472, 246, 13175, 14438, 14466, 14351, 14452])).
% 2.64/2.89 tff(14474,plain,
% 2.64/2.89 (r(s(s(s(s(z)))), z)),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[6040, 14473])).
% 2.64/2.89 tff(14475,plain,
% 2.64/2.89 (~b(s(s(s(z))), z)),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[12595, 246, 11962, 14322, 3697])).
% 2.64/2.89 tff(14476,plain,
% 2.64/2.89 (r(s(s(s(z))), z)),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[995, 14475])).
% 2.64/2.89 tff(14477,plain,
% 2.64/2.89 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[13400, 183, 14476, 14474])).
% 2.64/2.89 tff(14478,plain,
% 2.64/2.89 ($false),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[8213, 47, 8210, 14477, 14463])).
% 2.64/2.89 tff(14479,plain,((~(s(s(s(s(s(elem!1))))) = elem!1)) | (~b(s(s(s(z))), elem!1)) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.64/2.89 tff(14480,plain,
% 2.64/2.89 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[14479, 13730, 2232])).
% 2.64/2.89 tff(14481,plain,
% 2.64/2.89 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[86, 14480, 14321])).
% 2.64/2.89 tff(14482,plain,
% 2.64/2.89 (~r(elem!1, z)),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[13203, 14481, 13175, 14320, 14136])).
% 2.64/2.89 tff(14483,plain,
% 2.64/2.89 (~b(s(s(elem!1)), elem!1)),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[14364, 14482, 2232, 13730])).
% 2.64/2.89 tff(14484,plain,
% 2.64/2.89 (s(s(elem!1)) = elem!1),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[156, 14483, 2232])).
% 2.64/2.89 tff(14485,plain,
% 2.64/2.90 (s(s(s(elem!1))) = s(elem!1)),
% 2.64/2.90 inference(monotonicity,[status(thm)],[14484])).
% 2.64/2.90 tff(14486,plain,
% 2.64/2.90 (s(elem!1) = s(s(s(elem!1)))),
% 2.64/2.90 inference(symmetry,[status(thm)],[14485])).
% 2.64/2.90 tff(14487,plain,
% 2.64/2.90 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.64/2.90 inference(monotonicity,[status(thm)],[14485])).
% 2.64/2.90 tff(14488,plain,
% 2.64/2.90 (s(s(s(s(elem!1)))) = elem!1),
% 2.64/2.90 inference(transitivity,[status(thm)],[14487, 14484])).
% 2.64/2.90 tff(14489,plain,
% 2.64/2.90 (s(s(s(s(s(elem!1))))) = s(elem!1)),
% 2.64/2.90 inference(monotonicity,[status(thm)],[14488])).
% 2.64/2.90 tff(14490,plain,
% 2.64/2.90 (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 2.64/2.90 inference(transitivity,[status(thm)],[14489, 14486])).
% 2.64/2.90 tff(14491,plain,
% 2.64/2.90 (r(s(s(s(s(s(elem!1))))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 2.64/2.90 inference(monotonicity,[status(thm)],[14490])).
% 2.64/2.90 tff(14492,plain,
% 2.64/2.90 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(s(elem!1))))), s(z))),
% 2.64/2.90 inference(symmetry,[status(thm)],[14491])).
% 2.64/2.90 tff(14493,plain,
% 2.64/2.90 (r(s(elem!1), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 2.64/2.90 inference(monotonicity,[status(thm)],[14486])).
% 2.64/2.90 tff(14494,plain,
% 2.64/2.90 (r(s(elem!1), s(z)) <=> r(s(s(s(s(s(elem!1))))), s(z))),
% 2.64/2.90 inference(transitivity,[status(thm)],[14493, 14492])).
% 2.64/2.90 tff(14495,plain,
% 2.64/2.90 ((~r(s(elem!1), s(z))) <=> (~r(s(s(s(s(s(elem!1))))), s(z)))),
% 2.64/2.90 inference(monotonicity,[status(thm)],[14494])).
% 2.64/2.90 tff(14496,plain,
% 2.64/2.90 (r(s(s(s(s(s(elem!1))))), elem!1) <=> r(s(elem!1), elem!1)),
% 2.64/2.90 inference(monotonicity,[status(thm)],[14489])).
% 2.64/2.90 tff(14497,plain,
% 2.64/2.90 (r(s(elem!1), elem!1)),
% 2.64/2.90 inference(modus_ponens,[status(thm)],[14481, 14496])).
% 2.64/2.90 tff(14498,plain,
% 2.64/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)))),
% 2.64/2.90 inference(rewrite,[status(thm)],[])).
% 2.64/2.90 tff(14499,plain,
% 2.64/2.90 (((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)))),
% 2.64/2.90 inference(rewrite,[status(thm)],[])).
% 2.64/2.90 tff(14500,plain,
% 2.64/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1))))),
% 2.64/2.90 inference(monotonicity,[status(thm)],[14499])).
% 2.64/2.90 tff(14501,plain,
% 2.64/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)))),
% 2.64/2.90 inference(transitivity,[status(thm)],[14500, 14498])).
% 2.64/2.90 tff(14502,plain,
% 2.64/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))),
% 2.64/2.90 inference(quant_inst,[status(thm)],[])).
% 2.64/2.90 tff(14503,plain,
% 2.64/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1))),
% 2.64/2.90 inference(modus_ponens,[status(thm)],[14502, 14501])).
% 2.64/2.90 tff(14504,plain,
% 2.64/2.90 (~r(s(elem!1), s(z))),
% 2.64/2.90 inference(unit_resolution,[status(thm)],[14503, 183, 14320, 14497])).
% 2.64/2.90 tff(14505,plain,
% 2.64/2.90 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 2.64/2.90 inference(modus_ponens,[status(thm)],[14504, 14495])).
% 2.64/2.90 tff(14506,plain,
% 2.64/2.90 (b(s(s(s(s(s(elem!1))))), s(z))),
% 2.64/2.90 inference(unit_resolution,[status(thm)],[6447, 14505])).
% 2.64/2.90 tff(14507,plain,
% 2.64/2.90 (~b(s(z), s(s(s(z))))),
% 2.64/2.90 inference(unit_resolution,[status(thm)],[14052, 14506, 13175, 14017, 13532, 13730])).
% 2.74/2.90 tff(14508,plain,
% 2.74/2.90 (r(s(z), s(s(s(z))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[1291, 14507])).
% 2.74/2.90 tff(14509,plain,
% 2.74/2.90 (~(elem!1 = s(s(s(z))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[5785, 13730])).
% 2.74/2.90 tff(14510,plain,
% 2.74/2.90 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[14349, 14015, 13175, 13532, 13730])).
% 2.74/2.90 tff(14511,plain,
% 2.74/2.90 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[1702, 14510])).
% 2.74/2.90 tff(14512,plain,
% 2.74/2.90 (~b(elem!1, s(z))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[2262, 246, 11962, 14015, 14136])).
% 2.74/2.90 tff(14513,plain,
% 2.74/2.90 (r(elem!1, s(z))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[214, 14318, 14512])).
% 2.74/2.90 tff(14514,plain,
% 2.74/2.90 (~b(elem!1, s(s(s(z))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[13432, 14484, 13730, 14015, 14136, 14513, 13175, 14511])).
% 2.74/2.90 tff(14515,plain,
% 2.74/2.90 (r(elem!1, s(s(s(z))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[470, 14514, 14509])).
% 2.74/2.90 tff(14516,plain,
% 2.74/2.90 ($false),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[6194, 183, 14513, 14515, 14508])).
% 2.74/2.90 tff(14517,plain,(r(s(s(elem!1)), elem!1) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.90 tff(14518,plain,
% 2.74/2.90 (r(z, elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[14517, 2232])).
% 2.74/2.90 tff(14519,plain,
% 2.74/2.90 (~(s(s(s(z))) = elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[13536, 2214])).
% 2.74/2.90 tff(14520,plain,
% 2.74/2.90 (~r(s(s(s(z))), elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[6592, 13547, 267])).
% 2.74/2.90 tff(14521,plain,
% 2.74/2.90 ($false),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[647, 14520, 14519, 1])).
% 2.74/2.90 tff(14522,plain,(b(z, s(s(s(z)))) | b(s(s(s(z))), elem!1) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.90 tff(14523,plain,
% 2.74/2.90 (b(z, s(s(s(z))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[14522, 1, 14518])).
% 2.74/2.90 tff(14524,plain,
% 2.74/2.90 (~b(s(z), z)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[6174, 14523, 13175, 13532])).
% 2.74/2.90 tff(14525,plain,
% 2.74/2.90 (r(s(z), z)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[1069, 14524])).
% 2.74/2.90 tff(14526,plain,
% 2.74/2.90 (~r(s(z), elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[5432, 14525, 14518])).
% 2.74/2.90 tff(14527,plain,
% 2.74/2.90 (b(s(z), elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[1034, 14526, 5374])).
% 2.74/2.90 tff(14528,plain,
% 2.74/2.90 (~b(elem!1, z)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[13451, 14527, 13175])).
% 2.74/2.90 tff(14529,plain,
% 2.74/2.90 (r(elem!1, z)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[12008, 14528])).
% 2.74/2.90 tff(14530,plain,
% 2.74/2.90 (~b(elem!1, s(z))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[13509, 14527, 13175])).
% 2.74/2.90 tff(14531,plain,
% 2.74/2.90 (r(elem!1, s(z))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[214, 14530, 5375])).
% 2.74/2.90 tff(14532,plain,
% 2.74/2.90 ($false),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[1163, 14531, 14529, 14525])).
% 2.74/2.90 tff(14533,plain,(b(s(s(s(z))), elem!1) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.90 tff(14534,plain,
% 2.74/2.90 (b(s(s(s(z))), elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[14533, 2232])).
% 2.74/2.90 tff(14535,plain,
% 2.74/2.90 (b(elem!1, z)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[14014, 14534, 2232])).
% 2.74/2.90 tff(14536,plain,
% 2.74/2.90 (~b(s(z), elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[13451, 14535, 13175])).
% 2.74/2.90 tff(14537,plain,
% 2.74/2.90 (b(s(z), z)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[14135, 14534, 13175, 14535, 13532])).
% 2.74/2.90 tff(14538,plain,
% 2.74/2.90 (~(elem!1 = s(z))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[14317, 14537, 13175, 14535, 14534])).
% 2.74/2.90 tff(14539,plain,
% 2.74/2.90 (~(s(z) = elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[9, 14538])).
% 2.74/2.90 tff(14540,plain,
% 2.74/2.90 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[14479, 14534, 2232])).
% 2.74/2.90 tff(14541,plain,
% 2.74/2.90 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[13383, 14535, 14534])).
% 2.74/2.90 tff(14542,plain,
% 2.74/2.90 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[86, 14541, 14540])).
% 2.74/2.90 tff(14543,plain,
% 2.74/2.90 (~r(s(z), elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[5581, 14542, 14518, 13175])).
% 2.74/2.90 tff(14544,plain,
% 2.74/2.90 ($false),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[1034, 14543, 14539, 14536])).
% 2.74/2.90 tff(14545,plain,(r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.90 tff(14546,plain,
% 2.74/2.90 (r(s(s(s(z))), elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[647, 14519, 1])).
% 2.74/2.90 tff(14547,plain,
% 2.74/2.90 (~r(elem!1, s(z))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[1023, 14546, 430])).
% 2.74/2.90 tff(14548,plain,
% 2.74/2.90 (~r(s(z), elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[3017, 14546, 430])).
% 2.74/2.90 tff(14549,plain,
% 2.74/2.90 (~r(z, s(z))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[438, 13547, 430])).
% 2.74/2.90 tff(14550,plain,
% 2.74/2.90 (b(z, s(z))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[169, 14549])).
% 2.74/2.90 tff(14551,plain,
% 2.74/2.90 (b(s(z), elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[1034, 10, 6388])).
% 2.74/2.90 tff(14552,plain,
% 2.74/2.90 ($false),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[13509, 14551, 6419, 236])).
% 2.74/2.90 tff(14553,plain,((elem!1 = s(z)) | (~b(z, s(z))) | r(s(z), elem!1) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.90 tff(14554,plain,
% 2.74/2.90 (elem!1 = s(z)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[14553, 14550, 14548, 14547])).
% 2.74/2.90 tff(14555,plain,
% 2.74/2.90 (s(z) = elem!1),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[2279, 14554])).
% 2.74/2.90 tff(14556,plain,
% 2.74/2.90 (s(s(s(z))) = s(s(elem!1))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[121, 14555])).
% 2.74/2.90 tff(14557,plain,
% 2.74/2.90 ((s(s(s(s(s(elem!1))))) = s(s(s(z)))) <=> (s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[14556])).
% 2.74/2.90 tff(14558,plain,
% 2.74/2.90 ((s(s(s(s(s(elem!1))))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 2.74/2.90 inference(transitivity,[status(thm)],[14557, 1535])).
% 2.74/2.90 tff(14559,plain,
% 2.74/2.90 ((~(s(s(s(s(s(elem!1))))) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(s(s(elem!1)))))))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[14558])).
% 2.74/2.90 tff(14560,plain,
% 2.74/2.90 (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 2.74/2.90 inference(modus_ponens,[status(thm)],[1622, 14559])).
% 2.74/2.90 tff(14561,plain,
% 2.74/2.90 (b(s(s(s(s(s(elem!1))))), elem!1) <=> b(s(s(s(s(s(elem!1))))), s(z))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[14554])).
% 2.74/2.90 tff(14562,plain,
% 2.74/2.90 (~b(s(s(elem!1)), elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[5568, 14556, 1])).
% 2.74/2.90 tff(14563,plain,
% 2.74/2.90 (~r(z, elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[14522, 2214, 1])).
% 2.74/2.90 tff(14564,plain,
% 2.74/2.90 (s(z) = elem!1),
% 2.74/2.90 inference(symmetry,[status(thm)],[14554])).
% 2.74/2.90 tff(14565,plain,
% 2.74/2.90 (b(s(z), elem!1) <=> b(elem!1, elem!1)),
% 2.74/2.90 inference(monotonicity,[status(thm)],[14564])).
% 2.74/2.90 tff(14566,plain,
% 2.74/2.90 (b(elem!1, elem!1) <=> b(s(z), elem!1)),
% 2.74/2.90 inference(symmetry,[status(thm)],[14565])).
% 2.74/2.90 tff(14567,plain,
% 2.74/2.90 ((~b(elem!1, elem!1)) <=> (~b(s(z), elem!1))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[14566])).
% 2.74/2.90 tff(14568,plain,
% 2.74/2.90 (~b(s(z), elem!1)),
% 2.74/2.90 inference(modus_ponens,[status(thm)],[5691, 14567])).
% 2.74/2.90 tff(14569,plain,
% 2.74/2.90 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[86, 9095, 82])).
% 2.74/2.90 tff(14570,plain,
% 2.74/2.90 (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[1543, 183, 216, 14569])).
% 2.74/2.90 tff(14571,plain,
% 2.74/2.90 (b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[1547, 47, 14570, 9086])).
% 2.74/2.90 tff(14572,plain,
% 2.74/2.90 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[1551, 14569, 216])).
% 2.74/2.90 tff(14573,plain,
% 2.74/2.90 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[1557, 14572, 9189])).
% 2.74/2.90 tff(14574,plain,
% 2.74/2.90 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[3956, 367, 333])).
% 2.74/2.90 tff(14575,plain,
% 2.74/2.90 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[1795, 14574, 3410])).
% 2.74/2.90 tff(14576,plain,
% 2.74/2.90 (~r(s(s(elem!1)), s(elem!1))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[11073, 183, 216, 367])).
% 2.74/2.90 tff(14577,plain,
% 2.74/2.90 (b(s(s(elem!1)), s(elem!1))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[1949, 47, 14576, 5642])).
% 2.74/2.90 tff(14578,plain,
% 2.74/2.90 (b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[395, 47, 4462, 4037])).
% 2.74/2.90 tff(14579,plain,
% 2.74/2.90 ($false),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[4564, 14578, 14577, 946, 4520, 14575])).
% 2.74/2.90 tff(14580,plain,((~r(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (s(s(elem!1)) = s(elem!1)) | (~r(s(s(elem!1)), elem!1)) | (s(s(s(s(s(elem!1))))) = s(elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.90 tff(14581,plain,
% 2.74/2.90 (~r(s(elem!1), elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[14580, 14573, 14571, 9153, 216, 9119, 14569])).
% 2.74/2.90 tff(14582,plain,
% 2.74/2.90 (b(s(elem!1), elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[5655, 14581, 9117])).
% 2.74/2.90 tff(14583,plain,
% 2.74/2.90 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(s(z))) = s(elem!1))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[9129])).
% 2.74/2.90 tff(14584,plain,
% 2.74/2.90 ((s(s(elem!1)) = s(elem!1)) <=> (s(elem!1) = s(s(s(z))))),
% 2.74/2.90 inference(transitivity,[status(thm)],[14583, 2181])).
% 2.74/2.90 tff(14585,plain,
% 2.74/2.90 ((s(s(s(z))) = s(s(z))) <=> (s(elem!1) = s(s(s(z))))),
% 2.74/2.90 inference(transitivity,[status(thm)],[9151, 14584])).
% 2.74/2.90 tff(14586,plain,
% 2.74/2.90 ((~(s(s(s(z))) = s(s(z)))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[14585])).
% 2.74/2.90 tff(14587,plain,
% 2.74/2.90 (~(s(elem!1) = s(s(s(z))))),
% 2.74/2.90 inference(modus_ponens,[status(thm)],[8374, 14586])).
% 2.74/2.90 tff(14588,plain,
% 2.74/2.90 (~b(s(s(s(z))), elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[5770, 2266, 145])).
% 2.74/2.90 tff(14589,plain,
% 2.74/2.90 (~(s(elem!1) = s(s(elem!1)))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[6946, 5642])).
% 2.74/2.90 tff(14590,plain,
% 2.74/2.90 (b(elem!1, s(elem!1))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[2864, 3783, 3425])).
% 2.74/2.90 tff(14591,plain,
% 2.74/2.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(14592,plain,
% 2.74/2.90 (((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(14593,plain,
% 2.74/2.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[14592])).
% 2.74/2.90 tff(14594,plain,
% 2.74/2.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 2.74/2.90 inference(transitivity,[status(thm)],[14593, 14591])).
% 2.74/2.90 tff(14595,plain,
% 2.74/2.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 2.74/2.90 inference(quant_inst,[status(thm)],[])).
% 2.74/2.90 tff(14596,plain,
% 2.74/2.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))),
% 2.74/2.90 inference(modus_ponens,[status(thm)],[14595, 14594])).
% 2.74/2.90 tff(14597,plain,
% 2.74/2.90 (~b(s(elem!1), z)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[14596, 246, 2239, 1200, 14590])).
% 2.74/2.90 tff(14598,plain,
% 2.74/2.90 (r(s(elem!1), z)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[2581, 14597])).
% 2.74/2.90 tff(14599,plain,
% 2.74/2.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(14600,plain,
% 2.74/2.90 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1)))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(14601,plain,
% 2.74/2.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1)))))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[14600])).
% 2.74/2.90 tff(14602,plain,
% 2.74/2.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))))),
% 2.74/2.90 inference(transitivity,[status(thm)],[14601, 14599])).
% 2.74/2.90 tff(14603,plain,
% 2.74/2.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 2.74/2.90 inference(quant_inst,[status(thm)],[])).
% 2.74/2.90 tff(14604,plain,
% 2.74/2.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1)))),
% 2.74/2.90 inference(modus_ponens,[status(thm)],[14603, 14602])).
% 2.74/2.90 tff(14605,plain,
% 2.74/2.90 (~b(z, s(elem!1))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[14604, 246, 2239, 1200, 14590])).
% 2.74/2.90 tff(14606,plain,
% 2.74/2.90 (r(z, s(elem!1))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[2561, 14605])).
% 2.74/2.90 tff(14607,plain,
% 2.74/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(14608,plain,
% 2.74/2.90 (((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(z, s(s(s(s(s(elem!1)))))))) <=> ((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(14609,plain,
% 2.74/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1))))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[14608])).
% 2.74/2.90 tff(14610,plain,
% 2.74/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.74/2.90 inference(transitivity,[status(thm)],[14609, 14607])).
% 2.74/2.90 tff(14611,plain,
% 2.74/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(z, s(s(s(s(s(elem!1))))))))),
% 2.74/2.90 inference(quant_inst,[status(thm)],[])).
% 2.74/2.90 tff(14612,plain,
% 2.74/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 2.74/2.90 inference(modus_ponens,[status(thm)],[14611, 14610])).
% 2.74/2.90 tff(14613,plain,
% 2.74/2.90 (~r(z, s(s(s(s(s(elem!1))))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[14612, 183, 333, 1853, 14606])).
% 2.74/2.90 tff(14614,plain,
% 2.74/2.90 ((z = s(s(s(s(s(elem!1)))))) | b(z, s(s(s(s(s(elem!1))))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[2487, 47, 14613])).
% 2.74/2.90 tff(14615,plain,
% 2.74/2.90 (b(z, s(s(s(s(s(elem!1))))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[14614, 2477])).
% 2.74/2.90 tff(14616,plain,
% 2.74/2.90 (~r(s(s(s(s(s(elem!1))))), z)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[13296, 183, 1853, 14606])).
% 2.74/2.90 tff(14617,plain,
% 2.74/2.90 (b(s(s(s(s(s(elem!1))))), z)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[1601, 14616])).
% 2.74/2.90 tff(14618,plain,
% 2.74/2.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(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(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(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(elem!1)), s(s(s(s(s(elem!1))))))))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(14619,plain,
% 2.74/2.90 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), z))) <=> ((~b(z, elem!1)) | (~b(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(elem!1)), s(s(s(s(s(elem!1))))))))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(14620,plain,
% 2.74/2.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[14619])).
% 2.74/2.90 tff(14621,plain,
% 2.74/2.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 2.74/2.90 inference(transitivity,[status(thm)],[14620, 14618])).
% 2.74/2.90 tff(14622,plain,
% 2.74/2.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), z)))),
% 2.74/2.90 inference(quant_inst,[status(thm)],[])).
% 2.74/2.90 tff(14623,plain,
% 2.74/2.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(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(elem!1)), s(s(s(s(s(elem!1)))))))),
% 2.74/2.90 inference(modus_ponens,[status(thm)],[14622, 14621])).
% 2.74/2.90 tff(14624,plain,
% 2.74/2.90 ((~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(elem!1)))))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[14623, 246, 2239, 4520, 14617])).
% 2.74/2.90 tff(14625,plain,
% 2.74/2.90 (~b(s(s(elem!1)), z)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[14624, 14615])).
% 2.74/2.90 tff(14626,plain,
% 2.74/2.90 (r(s(s(elem!1)), z)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[523, 14625])).
% 2.74/2.90 tff(14627,plain,
% 2.74/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(14628,plain,
% 2.74/2.90 (((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(14629,plain,
% 2.74/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z))))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[14628])).
% 2.74/2.90 tff(14630,plain,
% 2.74/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)))),
% 2.74/2.90 inference(transitivity,[status(thm)],[14629, 14627])).
% 2.74/2.90 tff(14631,plain,
% 2.74/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1)))))),
% 2.74/2.90 inference(quant_inst,[status(thm)],[])).
% 2.74/2.90 tff(14632,plain,
% 2.74/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z))),
% 2.74/2.90 inference(modus_ponens,[status(thm)],[14631, 14630])).
% 2.74/2.90 tff(14633,plain,
% 2.74/2.90 (~r(s(elem!1), s(s(elem!1)))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[14632, 183, 14626, 14598])).
% 2.74/2.91 tff(14634,plain,
% 2.74/2.91 (b(s(elem!1), s(s(elem!1)))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[5561, 47, 14633, 14589])).
% 2.74/2.91 tff(14635,plain,
% 2.74/2.91 (~r(s(s(elem!1)), s(elem!1))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[12044, 183, 14626, 14598])).
% 2.74/2.91 tff(14636,plain,
% 2.74/2.91 (b(s(s(elem!1)), s(elem!1))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[1949, 47, 14635, 5642])).
% 2.74/2.91 tff(14637,plain,
% 2.74/2.91 ($false),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[1304, 14636, 14634, 1200, 947])).
% 2.74/2.91 tff(14638,plain,((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (s(s(elem!1)) = s(elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.91 tff(14639,plain,
% 2.74/2.91 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[14638, 947, 1200, 5642, 2239, 4520, 333, 3425])).
% 2.74/2.91 tff(14640,plain,
% 2.74/2.91 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[1795, 14639, 3410])).
% 2.74/2.91 tff(14641,plain,
% 2.74/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(14642,plain,
% 2.74/2.91 (((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(elem!1)))))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(14643,plain,
% 2.74/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1)))))))))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[14642])).
% 2.74/2.91 tff(14644,plain,
% 2.74/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 2.74/2.91 inference(transitivity,[status(thm)],[14643, 14641])).
% 2.74/2.91 tff(14645,plain,
% 2.74/2.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 2.74/2.91 inference(quant_inst,[status(thm)],[])).
% 2.74/2.91 tff(14646,plain,
% 2.74/2.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1)))))))),
% 2.74/2.91 inference(modus_ponens,[status(thm)],[14645, 14644])).
% 2.74/2.91 tff(14647,plain,
% 2.74/2.91 (~b(elem!1, s(s(s(s(s(elem!1))))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[14646, 246, 947, 946, 4520])).
% 2.74/2.91 tff(14648,plain,
% 2.74/2.91 (r(elem!1, s(s(s(s(s(elem!1))))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[5125, 14647, 5123])).
% 2.74/2.91 tff(14649,plain,
% 2.74/2.91 (~r(elem!1, s(elem!1))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[10769, 1951, 216])).
% 2.74/2.91 tff(14650,plain,
% 2.74/2.91 (b(elem!1, s(elem!1))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[2864, 14649, 3425])).
% 2.74/2.91 tff(14651,plain,
% 2.74/2.91 (~b(z, s(elem!1))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[14604, 246, 2239, 1200, 14650])).
% 2.74/2.91 tff(14652,plain,
% 2.74/2.91 (r(z, s(elem!1))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[2561, 14651])).
% 2.74/2.91 tff(14653,plain,
% 2.74/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(14654,plain,
% 2.74/2.91 (((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(14655,plain,
% 2.74/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1)))))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[14654])).
% 2.74/2.91 tff(14656,plain,
% 2.74/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))))),
% 2.74/2.91 inference(transitivity,[status(thm)],[14655, 14653])).
% 2.74/2.91 tff(14657,plain,
% 2.74/2.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)))),
% 2.74/2.91 inference(quant_inst,[status(thm)],[])).
% 2.74/2.91 tff(14658,plain,
% 2.74/2.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1)))),
% 2.74/2.91 inference(modus_ponens,[status(thm)],[14657, 14656])).
% 2.74/2.91 tff(14659,plain,
% 2.74/2.91 (~r(s(s(elem!1)), z)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[14658, 183, 14652, 1951])).
% 2.74/2.91 tff(14660,plain,
% 2.74/2.91 (b(s(s(elem!1)), z)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[523, 14659])).
% 2.74/2.91 tff(14661,plain,
% 2.74/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(14662,plain,
% 2.74/2.91 (((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(14663,plain,
% 2.74/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[14662])).
% 2.74/2.91 tff(14664,plain,
% 2.74/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 2.74/2.91 inference(transitivity,[status(thm)],[14663, 14661])).
% 2.74/2.91 tff(14665,plain,
% 2.74/2.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 2.74/2.91 inference(quant_inst,[status(thm)],[])).
% 2.74/2.91 tff(14666,plain,
% 2.74/2.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))),
% 2.74/2.91 inference(modus_ponens,[status(thm)],[14665, 14664])).
% 2.74/2.91 tff(14667,plain,
% 2.74/2.91 (~b(s(s(s(s(s(elem!1))))), z)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[14666, 246, 2239, 14660, 947, 946, 4520])).
% 2.74/2.91 tff(14668,plain,
% 2.74/2.91 (r(s(s(s(s(s(elem!1))))), z)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[1601, 14667])).
% 2.74/2.91 tff(14669,plain,
% 2.74/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(14670,plain,
% 2.74/2.91 (((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(14671,plain,
% 2.74/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1)))))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[14670])).
% 2.74/2.91 tff(14672,plain,
% 2.74/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))))),
% 2.74/2.91 inference(transitivity,[status(thm)],[14671, 14669])).
% 2.74/2.91 tff(14673,plain,
% 2.74/2.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))),
% 2.74/2.91 inference(quant_inst,[status(thm)],[])).
% 2.74/2.91 tff(14674,plain,
% 2.74/2.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1)))),
% 2.74/2.91 inference(modus_ponens,[status(thm)],[14673, 14672])).
% 2.74/2.91 tff(14675,plain,
% 2.74/2.91 (~r(z, s(s(elem!1)))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[14674, 183, 216, 14652, 1951])).
% 2.74/2.91 tff(14676,plain,
% 2.74/2.91 (b(z, s(s(elem!1)))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[264, 14675])).
% 2.74/2.91 tff(14677,plain,
% 2.74/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(14678,plain,
% 2.74/2.91 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(14679,plain,
% 2.74/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1))))))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[14678])).
% 2.74/2.91 tff(14680,plain,
% 2.74/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))))),
% 2.74/2.91 inference(transitivity,[status(thm)],[14679, 14677])).
% 2.74/2.91 tff(14681,plain,
% 2.74/2.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))),
% 2.74/2.91 inference(quant_inst,[status(thm)],[])).
% 2.74/2.91 tff(14682,plain,
% 2.74/2.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1))))),
% 2.74/2.91 inference(modus_ponens,[status(thm)],[14681, 14680])).
% 2.74/2.91 tff(14683,plain,
% 2.74/2.91 (~b(elem!1, z)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[14682, 246, 2239, 14660, 947, 14676])).
% 2.74/2.91 tff(14684,plain,
% 2.74/2.91 (r(elem!1, z)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[1143, 14683, 1438])).
% 2.74/2.91 tff(14685,plain,
% 2.74/2.91 ($false),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[9403, 183, 14684, 14668, 4837])).
% 2.74/2.91 tff(14686,plain,((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (elem!1 = z) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.91 tff(14687,plain,
% 2.74/2.91 (~r(s(s(elem!1)), s(elem!1))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[14686, 14648, 1438, 2239, 947, 946, 4520, 216, 1200, 3425])).
% 2.74/2.91 tff(14688,plain,
% 2.74/2.91 (b(s(s(elem!1)), s(elem!1))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[1949, 47, 14687, 5642])).
% 2.74/2.91 tff(14689,plain,
% 2.74/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(14690,plain,
% 2.74/2.91 (((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(14691,plain,
% 2.74/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[14690])).
% 2.74/2.91 tff(14692,plain,
% 2.74/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.74/2.92 inference(transitivity,[status(thm)],[14691, 14689])).
% 2.74/2.92 tff(14693,plain,
% 2.74/2.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 2.74/2.92 inference(quant_inst,[status(thm)],[])).
% 2.74/2.92 tff(14694,plain,
% 2.74/2.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[14693, 14692])).
% 2.74/2.92 tff(14695,plain,
% 2.74/2.92 ($false),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[14694, 246, 947, 14688, 946, 4520, 1200, 14640])).
% 2.74/2.92 tff(14696,plain,((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), elem!1)) | (s(s(elem!1)) = s(elem!1)) | (elem!1 = z) | (~b(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (elem!1 = s(elem!1)) | (s(s(s(s(s(elem!1))))) = s(elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (elem!1 = s(s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.92 tff(14697,plain,
% 2.74/2.92 (~b(elem!1, s(s(elem!1)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[14696, 14573, 14571, 14582, 9153, 1438, 2239, 216, 9228, 9119, 14569, 9397])).
% 2.74/2.92 tff(14698,plain,
% 2.74/2.92 (~b(elem!1, s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[13855, 14697, 9118])).
% 2.74/2.92 tff(14699,plain,
% 2.74/2.92 (b(z, s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[3497, 14698, 56, 1445, 9189, 14588, 9095, 14587])).
% 2.74/2.92 tff(14700,plain,
% 2.74/2.92 (b(z, s(s(elem!1)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[9374, 14699, 2266])).
% 2.74/2.92 tff(14701,plain,
% 2.74/2.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(14702,plain,
% 2.74/2.92 (((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(14703,plain,
% 2.74/2.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[14702])).
% 2.74/2.92 tff(14704,plain,
% 2.74/2.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 2.74/2.92 inference(transitivity,[status(thm)],[14703, 14701])).
% 2.74/2.92 tff(14705,plain,
% 2.74/2.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 2.74/2.92 inference(quant_inst,[status(thm)],[])).
% 2.74/2.92 tff(14706,plain,
% 2.74/2.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[14705, 14704])).
% 2.74/2.92 tff(14707,plain,
% 2.74/2.92 (~b(s(s(s(s(s(elem!1))))), z)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[14706, 246, 14700, 14573, 14571])).
% 2.74/2.92 tff(14708,plain,
% 2.74/2.92 (r(s(s(s(s(s(elem!1))))), z)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[1601, 14707])).
% 2.74/2.92 tff(14709,plain,
% 2.74/2.92 ($false),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[13296, 183, 1853, 14606, 5669])).
% 2.74/2.92 tff(14710,plain,((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (elem!1 = s(elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.92 tff(14711,plain,
% 2.74/2.92 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[14710, 14708, 2239, 14582, 9228, 14569])).
% 2.74/2.92 tff(14712,plain,
% 2.74/2.92 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[1795, 14711, 9119])).
% 2.74/2.92 tff(14713,plain,
% 2.74/2.92 (~(s(elem!1) = s(s(s(s(s(elem!1))))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[3920, 9119])).
% 2.74/2.92 tff(14714,plain,
% 2.74/2.92 (b(s(elem!1), s(z)) <=> b(s(elem!1), elem!1)),
% 2.74/2.92 inference(monotonicity,[status(thm)],[6])).
% 2.74/2.92 tff(14715,plain,
% 2.74/2.92 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(z))),
% 2.74/2.92 inference(symmetry,[status(thm)],[14714])).
% 2.74/2.92 tff(14716,plain,
% 2.74/2.92 (b(s(elem!1), s(z))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[14582, 14715])).
% 2.74/2.92 tff(14717,plain,
% 2.74/2.92 (elem!1 = s(z)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[9, 6])).
% 2.74/2.92 tff(14718,plain,
% 2.74/2.92 (~b(s(s(elem!1)), s(z))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[207, 14717, 145])).
% 2.74/2.92 tff(14719,plain,
% 2.74/2.92 (r(s(s(elem!1)), s(z))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[197, 14718])).
% 2.74/2.92 tff(14720,plain,
% 2.74/2.92 (~b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[4564, 363, 946, 4520, 2866])).
% 2.74/2.92 tff(14721,plain,
% 2.74/2.92 (r(s(elem!1), s(s(s(s(s(elem!1))))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[395, 47, 14720, 14713])).
% 2.74/2.92 tff(14722,plain,
% 2.74/2.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(14723,plain,
% 2.74/2.92 (((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(elem!1)))))))) <=> ((~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(14724,plain,
% 2.74/2.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[14723])).
% 2.74/2.92 tff(14725,plain,
% 2.74/2.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 2.74/2.92 inference(transitivity,[status(thm)],[14724, 14722])).
% 2.74/2.92 tff(14726,plain,
% 2.74/2.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 2.74/2.92 inference(quant_inst,[status(thm)],[])).
% 2.74/2.92 tff(14727,plain,
% 2.74/2.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[14726, 14725])).
% 2.74/2.92 tff(14728,plain,
% 2.74/2.92 (~b(z, s(s(s(s(s(elem!1))))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[14727, 246, 1099, 946, 4520])).
% 2.74/2.92 tff(14729,plain,
% 2.74/2.92 ((z = s(s(s(s(s(elem!1)))))) | r(z, s(s(s(s(s(elem!1))))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[2487, 47, 14728])).
% 2.74/2.92 tff(14730,plain,
% 2.74/2.92 (r(z, s(s(s(s(s(elem!1))))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[14729, 2477])).
% 2.74/2.92 tff(14731,plain,
% 2.74/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(14732,plain,
% 2.74/2.92 (((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), z))) <=> ((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(14733,plain,
% 2.74/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(elem!1)))))))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[14732])).
% 2.74/2.92 tff(14734,plain,
% 2.74/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 2.74/2.92 inference(transitivity,[status(thm)],[14733, 14731])).
% 2.74/2.92 tff(14735,plain,
% 2.74/2.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), z)))),
% 2.74/2.92 inference(quant_inst,[status(thm)],[])).
% 2.74/2.92 tff(14736,plain,
% 2.74/2.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(elem!1)))))))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[14735, 14734])).
% 2.74/2.92 tff(14737,plain,
% 2.74/2.92 (~r(s(elem!1), z)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[14736, 183, 14730, 14721])).
% 2.74/2.92 tff(14738,plain,
% 2.74/2.92 (b(s(elem!1), z)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[2581, 14737])).
% 2.74/2.92 tff(14739,assumption,(b(s(elem!1), s(z))), introduced(assumption)).
% 2.74/2.92 tff(14740,plain,
% 2.74/2.92 (b(elem!1, z)),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[1056, 9549])).
% 2.74/2.92 tff(14741,plain,
% 2.74/2.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(14742,plain,
% 2.74/2.92 (((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z)))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(14743,plain,
% 2.74/2.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z)))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[14742])).
% 2.74/2.92 tff(14744,plain,
% 2.74/2.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))),
% 2.74/2.92 inference(transitivity,[status(thm)],[14743, 14741])).
% 2.74/2.92 tff(14745,plain,
% 2.74/2.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))),
% 2.74/2.92 inference(quant_inst,[status(thm)],[])).
% 2.74/2.92 tff(14746,plain,
% 2.74/2.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z)))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[14745, 14744])).
% 2.74/2.92 tff(14747,plain,
% 2.74/2.92 ($false),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[14746, 246, 2239, 1051, 1056, 14739, 6012])).
% 2.74/2.92 tff(14748,plain,((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.92 tff(14749,plain,
% 2.74/2.92 (~b(elem!1, z)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[14748, 1056, 6012, 14739, 2239])).
% 2.74/2.92 tff(14750,plain,
% 2.74/2.92 ($false),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[14749, 14740])).
% 2.74/2.92 tff(14751,plain,((~b(s(z), z)) | (~(s(z) = elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.92 tff(14752,plain,
% 2.74/2.92 (~b(s(z), z)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[14751, 14738, 6, 14739, 2239])).
% 2.74/2.92 tff(14753,plain,
% 2.74/2.92 (r(s(z), z)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[1069, 14752])).
% 2.74/2.92 tff(14754,plain,
% 2.74/2.92 (~r(s(s(elem!1)), z)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[6720, 14753, 173])).
% 2.74/2.92 tff(14755,plain,
% 2.74/2.92 (b(s(s(elem!1)), z)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[523, 14754])).
% 2.74/2.92 tff(14756,plain,
% 2.74/2.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(14757,plain,
% 2.74/2.92 (((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(14758,plain,
% 2.74/2.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[14757])).
% 2.74/2.92 tff(14759,plain,
% 2.74/2.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)))),
% 2.74/2.92 inference(transitivity,[status(thm)],[14758, 14756])).
% 2.74/2.92 tff(14760,plain,
% 2.74/2.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.74/2.92 inference(quant_inst,[status(thm)],[])).
% 2.74/2.92 tff(14761,plain,
% 2.74/2.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[14760, 14759])).
% 2.74/2.92 tff(14762,plain,
% 2.74/2.92 ($false),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[14761, 246, 14755, 1099, 363, 14738])).
% 2.74/2.92 tff(14763,plain,((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~(s(z) = elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.92 tff(14764,plain,
% 2.74/2.92 (~b(s(s(elem!1)), s(elem!1))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[14763, 14700, 14719, 6, 14716, 2239, 14573, 14571, 14712])).
% 2.74/2.92 tff(14765,plain,
% 2.74/2.92 (r(s(s(elem!1)), s(elem!1))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[5644, 14764, 9153])).
% 2.74/2.92 tff(14766,plain,
% 2.74/2.92 (~r(elem!1, s(elem!1))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[10769, 14765, 216])).
% 2.74/2.92 tff(14767,plain,
% 2.74/2.92 (b(elem!1, s(elem!1))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[2864, 14766, 9228])).
% 2.74/2.92 tff(14768,plain,
% 2.74/2.92 (~b(s(elem!1), z)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[14596, 246, 2239, 14582, 14767])).
% 2.74/2.92 tff(14769,plain,
% 2.74/2.92 (r(s(elem!1), z)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[2581, 14768])).
% 2.74/2.92 tff(14770,plain,
% 2.74/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(14771,plain,
% 2.74/2.92 (((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(14772,plain,
% 2.74/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[14771])).
% 2.74/2.92 tff(14773,plain,
% 2.74/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.74/2.92 inference(transitivity,[status(thm)],[14772, 14770])).
% 2.74/2.92 tff(14774,plain,
% 2.74/2.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 2.74/2.92 inference(quant_inst,[status(thm)],[])).
% 2.74/2.92 tff(14775,plain,
% 2.74/2.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[14774, 14773])).
% 2.74/2.92 tff(14776,plain,
% 2.74/2.92 (~r(s(elem!1), s(s(s(s(s(elem!1))))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[14775, 183, 14569, 14769, 14708])).
% 2.74/2.92 tff(14777,plain,
% 2.74/2.92 (b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[395, 47, 14776, 14713])).
% 2.74/2.92 tff(14778,plain,
% 2.74/2.92 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(s(z)))), s(elem!1))),
% 2.74/2.92 inference(symmetry,[status(thm)],[9105])).
% 2.74/2.92 tff(14779,plain,
% 2.74/2.92 ((~r(s(s(s(elem!1))), s(elem!1))) <=> (~r(s(s(s(s(z)))), s(elem!1)))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[14778])).
% 2.74/2.92 tff(14780,plain,
% 2.74/2.92 (~b(z, s(elem!1))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[14604, 246, 2239, 14582, 14767])).
% 2.74/2.93 tff(14781,plain,
% 2.74/2.93 (r(z, s(elem!1))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[2561, 14780])).
% 2.74/2.93 tff(14782,plain,
% 2.74/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(14783,plain,
% 2.74/2.93 (((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(14784,plain,
% 2.74/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[14783])).
% 2.74/2.93 tff(14785,plain,
% 2.74/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)))),
% 2.74/2.93 inference(transitivity,[status(thm)],[14784, 14782])).
% 2.74/2.93 tff(14786,plain,
% 2.74/2.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(14787,plain,
% 2.74/2.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[14786, 14785])).
% 2.74/2.93 tff(14788,plain,
% 2.74/2.93 (~r(s(s(s(elem!1))), z)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[14787, 183, 820, 5864])).
% 2.74/2.93 tff(14789,plain,
% 2.74/2.93 (b(s(s(s(elem!1))), z)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[3086, 47, 355, 14788])).
% 2.74/2.93 tff(14790,plain,
% 2.74/2.93 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[3068, 97])).
% 2.74/2.93 tff(14791,plain,
% 2.74/2.93 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.93 inference(symmetry,[status(thm)],[14790])).
% 2.74/2.93 tff(14792,plain,
% 2.74/2.93 ((~r(s(s(s(elem!1))), s(s(elem!1)))) <=> (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[14791])).
% 2.74/2.93 tff(14793,plain,
% 2.74/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(14794,plain,
% 2.74/2.93 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(14795,plain,
% 2.74/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1)))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[14794])).
% 2.74/2.93 tff(14796,plain,
% 2.74/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.74/2.93 inference(transitivity,[status(thm)],[14795, 14793])).
% 2.74/2.93 tff(14797,plain,
% 2.74/2.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(14798,plain,
% 2.74/2.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1)))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[14797, 14796])).
% 2.74/2.93 tff(14799,plain,
% 2.74/2.93 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[14798, 183, 216, 820, 1951])).
% 2.74/2.93 tff(14800,plain,
% 2.74/2.93 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[14799, 14792])).
% 2.74/2.93 tff(14801,plain,
% 2.74/2.93 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1702, 14800])).
% 2.74/2.93 tff(14802,plain,
% 2.74/2.93 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[14801, 9442])).
% 2.74/2.93 tff(14803,plain,
% 2.74/2.93 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[3069])).
% 2.74/2.93 tff(14804,plain,
% 2.74/2.93 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 2.74/2.93 inference(transitivity,[status(thm)],[14803, 1825])).
% 2.74/2.93 tff(14805,plain,
% 2.74/2.93 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 2.74/2.93 inference(symmetry,[status(thm)],[14804])).
% 2.74/2.93 tff(14806,plain,
% 2.74/2.93 ((~(s(s(s(s(z)))) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[14805])).
% 2.74/2.93 tff(14807,plain,
% 2.74/2.93 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[98])).
% 2.74/2.93 tff(14808,plain,
% 2.74/2.93 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 2.74/2.93 inference(symmetry,[status(thm)],[14807])).
% 2.74/2.93 tff(14809,plain,
% 2.74/2.93 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(s(z)))) = s(s(elem!1))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[14808])).
% 2.74/2.93 tff(14810,plain,
% 2.74/2.93 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[1697, 14809])).
% 2.74/2.93 tff(14811,plain,
% 2.74/2.93 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[14810, 14806])).
% 2.74/2.93 tff(14812,plain,
% 2.74/2.93 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[3839, 183, 820, 1951])).
% 2.74/2.93 tff(14813,plain,
% 2.74/2.93 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[4455, 14812, 14811])).
% 2.74/2.93 tff(14814,plain,
% 2.74/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(14815,plain,
% 2.74/2.93 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(14816,plain,
% 2.74/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[14815])).
% 2.74/2.93 tff(14817,plain,
% 2.74/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))),
% 2.74/2.93 inference(transitivity,[status(thm)],[14816, 14814])).
% 2.74/2.93 tff(14818,plain,
% 2.74/2.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(14819,plain,
% 2.74/2.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[14818, 14817])).
% 2.74/2.93 tff(14820,plain,
% 2.74/2.93 ($false),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[14819, 246, 1099, 14813, 14802, 14789])).
% 2.74/2.93 tff(14821,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~(s(s(s(z))) = s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.93 tff(14822,plain,
% 2.74/2.93 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[14821, 14700, 2266, 216, 14765, 14781])).
% 2.74/2.93 tff(14823,plain,
% 2.74/2.93 (~r(s(s(s(s(z)))), s(elem!1))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[14822, 14779])).
% 2.74/2.93 tff(14824,plain,
% 2.74/2.93 (b(s(s(s(s(z)))), s(elem!1))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1728, 14823, 9109])).
% 2.74/2.93 tff(14825,plain,
% 2.74/2.93 (b(s(s(s(elem!1))), s(elem!1))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[14173, 14824, 2266])).
% 2.74/2.93 tff(14826,plain,
% 2.74/2.93 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[4047, 14825, 14777, 14712])).
% 2.74/2.93 tff(14827,plain,
% 2.74/2.93 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[3693, 14826, 9124])).
% 2.74/2.93 tff(14828,plain,
% 2.74/2.93 (~r(elem!1, s(s(s(elem!1))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[4270, 14827, 14569])).
% 2.74/2.93 tff(14829,plain,
% 2.74/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(14830,plain,
% 2.74/2.93 (((~b(s(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(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(14831,plain,
% 2.74/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[14830])).
% 2.74/2.93 tff(14832,plain,
% 2.74/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.74/2.93 inference(transitivity,[status(thm)],[14831, 14829])).
% 2.74/2.93 tff(14833,plain,
% 2.74/2.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(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))))))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(14834,plain,
% 2.74/2.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[14833, 14832])).
% 2.74/2.93 tff(14835,plain,
% 2.74/2.93 (~b(elem!1, s(s(s(elem!1))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[14834, 246, 14825, 14712, 14767, 14777])).
% 2.74/2.93 tff(14836,plain,
% 2.74/2.93 (elem!1 = s(s(s(elem!1)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[3104, 47, 14835, 14828])).
% 2.74/2.93 tff(14837,plain,
% 2.74/2.93 (s(s(s(elem!1))) = elem!1),
% 2.74/2.93 inference(symmetry,[status(thm)],[14836])).
% 2.74/2.93 tff(14838,plain,
% 2.74/2.93 (s(s(s(s(z)))) = elem!1),
% 2.74/2.93 inference(transitivity,[status(thm)],[9096, 14837])).
% 2.74/2.93 tff(14839,plain,
% 2.74/2.93 ($false),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[9103, 14838])).
% 2.74/2.93 tff(14840,plain,((~(s(z) = elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | r(z, elem!1) | b(s(z), elem!1) | (elem!1 = z) | b(s(s(s(s(s(elem!1))))), elem!1) | b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.93 tff(14841,plain,
% 2.74/2.93 ((~(s(z) = elem!1)) | (~r(s(s(elem!1)), elem!1)) | r(z, elem!1) | b(s(z), elem!1) | b(s(s(s(s(s(elem!1))))), elem!1) | b(s(s(elem!1)), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[14840, 11962, 11994])).
% 2.74/2.93 tff(14842,plain,
% 2.74/2.93 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[14841, 14568, 14563, 14545, 14555, 14562])).
% 2.74/2.93 tff(14843,plain,
% 2.74/2.93 (b(s(s(s(s(s(elem!1))))), s(z))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[14842, 14561])).
% 2.74/2.93 tff(14844,plain,
% 2.74/2.93 ((~(s(s(s(s(s(elem!1))))) = s(s(s(z))))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(elem!1))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[14557])).
% 2.74/2.93 tff(14845,plain,
% 2.74/2.93 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[1622, 14844])).
% 2.74/2.93 tff(14846,plain,
% 2.74/2.93 (r(z, s(s(s(z)))) <=> r(z, s(s(elem!1)))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[14556])).
% 2.74/2.93 tff(14847,plain,
% 2.74/2.93 (r(z, s(s(elem!1)))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[13547, 14846])).
% 2.74/2.93 tff(14848,plain,
% 2.74/2.93 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(elem!1)))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[14556])).
% 2.74/2.93 tff(14849,plain,
% 2.74/2.93 (b(elem!1, s(s(s(z)))) <=> b(s(z), s(s(s(z))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[14554])).
% 2.74/2.93 tff(14850,plain,
% 2.74/2.93 (b(elem!1, s(s(s(z)))) <=> b(s(z), s(s(elem!1)))),
% 2.74/2.93 inference(transitivity,[status(thm)],[14849, 14848])).
% 2.74/2.93 tff(14851,plain,
% 2.74/2.93 ((s(s(s(s(s(elem!1))))) = s(z)) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 2.74/2.93 inference(monotonicity,[status(thm)],[14564])).
% 2.74/2.93 tff(14852,plain,
% 2.74/2.93 ((~(s(s(s(s(s(elem!1))))) = s(z))) <=> (~(s(s(s(s(s(elem!1))))) = elem!1))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[14851])).
% 2.74/2.93 tff(14853,plain,
% 2.74/2.93 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[331, 14852])).
% 2.74/2.93 tff(14854,plain,
% 2.74/2.93 (b(elem!1, s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[3593, 14845, 14563, 1, 14853, 2214, 14568])).
% 2.74/2.93 tff(14855,plain,
% 2.74/2.93 (b(s(z), s(s(elem!1)))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[14854, 14850])).
% 2.74/2.93 tff(14856,plain,
% 2.74/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(14857,plain,
% 2.74/2.93 (((~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(14858,plain,
% 2.74/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[14857])).
% 2.74/2.93 tff(14859,plain,
% 2.74/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)))),
% 2.74/2.93 inference(transitivity,[status(thm)],[14858, 14856])).
% 2.74/2.93 tff(14860,plain,
% 2.74/2.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(14861,plain,
% 2.74/2.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[14860, 14859])).
% 2.74/2.93 tff(14862,plain,
% 2.74/2.93 ($false),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[14861, 183, 2246, 216, 172])).
% 2.74/2.93 tff(14863,plain,((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.93 tff(14864,plain,
% 2.74/2.93 (~r(s(s(elem!1)), z)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[14863, 13732, 14545])).
% 2.74/2.93 tff(14865,plain,
% 2.74/2.93 (b(s(s(elem!1)), z)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[523, 14864])).
% 2.74/2.93 tff(14866,assumption,(b(s(z), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 2.74/2.93 tff(14867,plain,
% 2.74/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(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))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(14868,plain,
% 2.74/2.93 (((~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(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(elem!1)))))))) <=> ((~b(z, s(z))) | (~b(z, s(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))))))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(14869,plain,
% 2.74/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(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)))))))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[14868])).
% 2.74/2.93 tff(14870,plain,
% 2.74/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(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))))))))),
% 2.74/2.93 inference(transitivity,[status(thm)],[14869, 14867])).
% 2.74/2.93 tff(14871,plain,
% 2.74/2.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(14872,plain,
% 2.74/2.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(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)))))))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[14871, 14870])).
% 2.74/2.93 tff(14873,plain,
% 2.74/2.93 (~b(z, s(s(s(s(s(elem!1))))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[14872, 246, 236, 6875, 14866])).
% 2.74/2.93 tff(14874,plain,
% 2.74/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(14875,plain,
% 2.74/2.94 (((~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(elem!1)))))))) <=> ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(14876,plain,
% 2.74/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(z), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1)))))))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[14875])).
% 2.74/2.94 tff(14877,plain,
% 2.74/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(z), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))))),
% 2.74/2.94 inference(transitivity,[status(thm)],[14876, 14874])).
% 2.74/2.94 tff(14878,plain,
% 2.74/2.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(elem!1))))))))),
% 2.74/2.94 inference(quant_inst,[status(thm)],[])).
% 2.74/2.94 tff(14879,plain,
% 2.74/2.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1)))))))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[14878, 14877])).
% 2.74/2.94 tff(14880,plain,
% 2.74/2.94 ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(elem!1)))))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[14879, 246, 1100, 236, 235, 6875])).
% 2.74/2.94 tff(14881,plain,
% 2.74/2.94 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[14880, 14866])).
% 2.74/2.94 tff(14882,plain,
% 2.74/2.94 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[1557, 14881, 1555])).
% 2.74/2.94 tff(14883,plain,
% 2.74/2.94 (~r(z, s(s(s(s(s(elem!1))))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[3325, 14882, 266])).
% 2.74/2.94 tff(14884,plain,
% 2.74/2.94 ($false),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[2487, 47, 14883, 5706, 14873])).
% 2.74/2.94 tff(14885,plain,((~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, s(s(elem!1)))) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.94 tff(14886,plain,
% 2.74/2.94 (~b(s(z), s(s(s(s(s(elem!1))))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[14885, 14865, 6875, 266, 10674, 236, 235])).
% 2.74/2.94 tff(14887,plain,
% 2.74/2.94 (~b(elem!1, s(s(s(s(s(elem!1))))))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[14886, 10610])).
% 2.74/2.94 tff(14888,plain,
% 2.74/2.94 (r(elem!1, s(s(s(s(s(elem!1))))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[5125, 14887, 10608])).
% 2.74/2.94 tff(14889,plain,
% 2.74/2.94 (r(s(z), s(s(s(s(s(elem!1))))))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[14888, 10604])).
% 2.74/2.94 tff(14890,plain,
% 2.74/2.94 (~b(s(z), z)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[13737, 13731, 202])).
% 2.74/2.94 tff(14891,plain,
% 2.74/2.94 (r(s(z), z)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[1069, 14890])).
% 2.74/2.94 tff(14892,assumption,(r(s(z), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 2.74/2.94 tff(14893,plain,
% 2.74/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(z), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(14894,plain,
% 2.74/2.94 (((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(z), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(14895,plain,
% 2.74/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(z), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(z), s(s(s(s(s(elem!1)))))))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[14894])).
% 2.74/2.94 tff(14896,plain,
% 2.74/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(z), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 2.74/2.94 inference(transitivity,[status(thm)],[14895, 14893])).
% 2.74/2.94 tff(14897,plain,
% 2.74/2.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 2.74/2.94 inference(quant_inst,[status(thm)],[])).
% 2.74/2.94 tff(14898,plain,
% 2.74/2.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(z), s(s(s(s(s(elem!1)))))))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[14897, 14896])).
% 2.74/2.94 tff(14899,plain,
% 2.74/2.94 ($false),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[14898, 183, 1114, 5669, 14892])).
% 2.74/2.94 tff(14900,plain,((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.94 tff(14901,plain,
% 2.74/2.94 (~r(s(s(s(s(s(elem!1))))), z)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[14900, 14891, 14889])).
% 2.74/2.94 tff(14902,plain,
% 2.74/2.94 (b(s(s(s(s(s(elem!1))))), z)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[1601, 14901])).
% 2.74/2.94 tff(14903,plain,
% 2.74/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), 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(elem!1))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), 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(elem!1))))), s(z))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(14904,plain,
% 2.74/2.94 (((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(elem!1)))))))) <=> ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), 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(elem!1))))), s(z))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(14905,plain,
% 2.74/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), 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(elem!1))))), s(z)))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[14904])).
% 2.74/2.94 tff(14906,plain,
% 2.74/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), 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(elem!1))))), s(z))))),
% 2.74/2.94 inference(transitivity,[status(thm)],[14905, 14903])).
% 2.74/2.94 tff(14907,plain,
% 2.74/2.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 2.74/2.94 inference(quant_inst,[status(thm)],[])).
% 2.74/2.94 tff(14908,plain,
% 2.74/2.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), 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(elem!1))))), s(z)))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[14907, 14906])).
% 2.74/2.94 tff(14909,plain,
% 2.74/2.94 (~b(z, s(s(s(s(s(elem!1))))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[14908, 246, 14865, 236, 235, 14902, 6875])).
% 2.74/2.94 tff(14910,plain,
% 2.74/2.94 (r(z, s(s(s(s(s(elem!1))))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[2487, 47, 5706, 14909])).
% 2.74/2.94 tff(14911,plain,
% 2.74/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(14912,plain,
% 2.74/2.94 (((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(14913,plain,
% 2.74/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1)))))))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[14912])).
% 2.74/2.94 tff(14914,plain,
% 2.74/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 2.74/2.94 inference(transitivity,[status(thm)],[14913, 14911])).
% 2.74/2.94 tff(14915,plain,
% 2.74/2.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), z)))),
% 2.74/2.94 inference(quant_inst,[status(thm)],[])).
% 2.74/2.94 tff(14916,plain,
% 2.74/2.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1)))))))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[14915, 14914])).
% 2.74/2.94 tff(14917,plain,
% 2.74/2.94 ($false),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[14916, 183, 14891, 14910, 14889])).
% 2.74/2.94 tff(14918,plain,(b(elem!1, z) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~(elem!1 = s(z))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.94 tff(14919,plain,
% 2.74/2.94 (b(elem!1, z)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[14918, 14550, 14855, 14843, 14554, 14847])).
% 2.74/2.94 tff(14920,plain,
% 2.74/2.94 (b(s(z), z)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[14060, 14919, 14555])).
% 2.74/2.94 tff(14921,plain,
% 2.74/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(14922,plain,
% 2.74/2.94 (((~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(elem!1)))))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(14923,plain,
% 2.74/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z)))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[14922])).
% 2.74/2.94 tff(14924,plain,
% 2.74/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 2.74/2.94 inference(transitivity,[status(thm)],[14923, 14921])).
% 2.74/2.94 tff(14925,plain,
% 2.74/2.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 2.74/2.94 inference(quant_inst,[status(thm)],[])).
% 2.74/2.94 tff(14926,plain,
% 2.74/2.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z)))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[14925, 14924])).
% 2.74/2.94 tff(14927,plain,
% 2.74/2.94 (~b(z, s(s(s(s(s(elem!1))))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[14926, 246, 14920, 14550, 14843])).
% 2.74/2.94 tff(14928,plain,
% 2.74/2.94 (r(z, s(s(s(s(s(elem!1))))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[2487, 47, 5706, 14927])).
% 2.74/2.94 tff(14929,plain,
% 2.74/2.94 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[3325, 14928, 14847])).
% 2.74/2.94 tff(14930,plain,
% 2.74/2.94 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[1557, 14929, 14845])).
% 2.74/2.94 tff(14931,plain,
% 2.74/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(14932,plain,
% 2.74/2.94 (((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z)))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(14933,plain,
% 2.74/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z)))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[14932])).
% 2.74/2.94 tff(14934,plain,
% 2.74/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 2.74/2.94 inference(transitivity,[status(thm)],[14933, 14931])).
% 2.74/2.94 tff(14935,plain,
% 2.74/2.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 2.74/2.94 inference(quant_inst,[status(thm)],[])).
% 2.74/2.94 tff(14936,plain,
% 2.74/2.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z)))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[14935, 14934])).
% 2.74/2.94 tff(14937,plain,
% 2.74/2.94 ($false),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[14936, 246, 235, 946, 4520, 6875])).
% 2.74/2.94 tff(14938,plain,((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.94 tff(14939,plain,
% 2.74/2.94 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[14938, 14855, 14930, 14843])).
% 2.74/2.94 tff(14940,plain,
% 2.74/2.94 (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[3314, 14928, 14847])).
% 2.74/2.94 tff(14941,plain,
% 2.74/2.94 ($false),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[1547, 47, 14940, 14939, 14560])).
% 2.74/2.94 tff(14942,plain,(b(z, s(s(s(z)))) | b(s(s(s(z))), elem!1) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.94 tff(14943,plain,
% 2.74/2.94 (b(z, s(s(s(z))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[14942, 53, 1])).
% 2.74/2.94 tff(14944,plain,
% 2.74/2.94 (~r(s(s(elem!1)), z)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[14863, 2246, 216])).
% 2.74/2.94 tff(14945,plain,
% 2.74/2.94 (b(s(s(elem!1)), z)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[523, 14944])).
% 2.74/2.94 tff(14946,plain,
% 2.74/2.94 (~r(s(s(s(z))), z)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[13540, 634, 2246])).
% 2.74/2.94 tff(14947,plain,
% 2.74/2.94 (b(s(s(s(z))), z)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[995, 14946])).
% 2.74/2.94 tff(14948,plain,
% 2.74/2.94 ($false),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[4659, 11056, 14947, 14945, 4651])).
% 2.74/2.94 tff(14949,plain,((~r(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.94 tff(14950,plain,
% 2.74/2.94 (~r(s(s(s(z))), elem!1)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[14949, 2246, 14943, 14545, 7736])).
% 2.74/2.94 tff(14951,plain,
% 2.74/2.94 (s(s(s(z))) = elem!1),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[647, 14950, 1])).
% 2.74/2.94 tff(14952,plain,
% 2.74/2.94 (~(elem!1 = s(s(s(z))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[6830, 12304, 2])).
% 2.74/2.94 tff(14953,plain,
% 2.74/2.94 ($false),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[1677, 14952, 14951])).
% 2.74/2.94 tff(14954,plain,((~r(elem!1, z)) | b(s(s(s(z))), s(z)) | b(s(s(s(z))), elem!1) | (elem!1 = s(z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.94 tff(14955,plain,
% 2.74/2.94 (~r(elem!1, z)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[14954, 11970, 1, 2, 170])).
% 2.74/2.94 tff(14956,plain,
% 2.74/2.94 (b(elem!1, z)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[12008, 14955])).
% 2.74/2.94 tff(14957,plain,
% 2.74/2.94 (~r(s(s(s(z))), elem!1)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[3017, 217, 430])).
% 2.74/2.94 tff(14958,plain,
% 2.74/2.94 (s(s(s(z))) = elem!1),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[647, 14957, 1])).
% 2.74/2.94 tff(14959,plain,
% 2.74/2.94 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[5623, 14958])).
% 2.74/2.94 tff(14960,plain,
% 2.74/2.94 (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[3815, 14959])).
% 2.74/2.94 tff(14961,plain,
% 2.74/2.94 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[7041, 14958])).
% 2.74/2.94 tff(14962,plain,
% 2.74/2.94 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[13340, 14958, 1051, 217, 14959])).
% 2.74/2.94 tff(14963,plain,
% 2.74/2.94 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[86, 14962, 14961])).
% 2.74/2.94 tff(14964,plain,
% 2.74/2.94 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[2307, 183, 217, 14963])).
% 2.74/2.94 tff(14965,plain,
% 2.74/2.94 (b(s(s(s(s(s(elem!1))))), s(z))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[6447, 14964])).
% 2.74/2.94 tff(14966,plain,
% 2.74/2.94 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[1551, 14963, 14545])).
% 2.74/2.94 tff(14967,plain,
% 2.74/2.94 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[1557, 14966, 14959])).
% 2.74/2.94 tff(14968,plain,
% 2.74/2.94 (~r(s(z), s(s(elem!1)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[223, 183, 217, 14545])).
% 2.74/2.94 tff(14969,plain,
% 2.74/2.94 (b(s(z), s(s(elem!1)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[233, 14968])).
% 2.74/2.94 tff(14970,plain,
% 2.74/2.94 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[14938, 14969, 14967, 14965])).
% 2.74/2.94 tff(14971,plain,
% 2.74/2.94 (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[1543, 183, 14545, 14963])).
% 2.74/2.94 tff(14972,plain,
% 2.74/2.94 ($false),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[1547, 47, 14971, 14970, 14960])).
% 2.74/2.94 tff(14973,plain,((~r(s(z), elem!1)) | (~b(elem!1, z)) | b(s(s(s(z))), elem!1) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.94 tff(14974,plain,
% 2.74/2.94 (~r(s(z), elem!1)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[14973, 14956, 1, 53])).
% 2.74/2.94 tff(14975,plain,
% 2.74/2.94 (b(s(z), elem!1)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[1034, 14974, 11971])).
% 2.74/2.94 tff(14976,plain,
% 2.74/2.94 (~b(s(s(s(s(z)))), elem!1)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[12741, 14975, 14956])).
% 2.74/2.94 tff(14977,plain,
% 2.74/2.94 (~b(s(z), z)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[12729, 246, 11962, 14956, 14975])).
% 2.74/2.94 tff(14978,plain,
% 2.74/2.94 (r(s(z), z)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[1069, 14977])).
% 2.74/2.94 tff(14979,plain,
% 2.74/2.94 (s(s(s(z))) = elem!1),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[647, 4189, 1])).
% 2.74/2.94 tff(14980,plain,
% 2.74/2.94 (s(s(s(s(z)))) = s(elem!1)),
% 2.74/2.94 inference(monotonicity,[status(thm)],[14979])).
% 2.74/2.95 tff(14981,plain,
% 2.74/2.95 (s(elem!1) = s(s(s(s(z))))),
% 2.74/2.95 inference(symmetry,[status(thm)],[14980])).
% 2.74/2.95 tff(14982,plain,
% 2.74/2.95 ((s(z) = s(elem!1)) <=> (s(z) = s(s(s(s(z)))))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[14981])).
% 2.74/2.95 tff(14983,plain,
% 2.74/2.95 ((s(z) = s(elem!1)) <=> (s(s(s(s(z)))) = s(z))),
% 2.74/2.95 inference(transitivity,[status(thm)],[14982, 5787])).
% 2.74/2.95 tff(14984,plain,
% 2.74/2.95 ((s(s(s(s(z)))) = s(z)) <=> (s(z) = s(elem!1))),
% 2.74/2.95 inference(symmetry,[status(thm)],[14983])).
% 2.74/2.95 tff(14985,plain,
% 2.74/2.95 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(z) = s(elem!1)))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[14984])).
% 2.74/2.95 tff(14986,plain,
% 2.74/2.95 (~(s(z) = s(elem!1))),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[1713, 14985])).
% 2.74/2.95 tff(14987,plain,
% 2.74/2.95 (b(s(s(s(s(z)))), s(z)) <=> b(s(elem!1), s(z))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[14980])).
% 2.74/2.95 tff(14988,plain,
% 2.74/2.95 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[11094, 14979, 9825])).
% 2.74/2.95 tff(14989,plain,
% 2.74/2.95 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[1702, 14988])).
% 2.74/2.95 tff(14990,plain,
% 2.74/2.95 (~r(s(s(s(s(z)))), s(z))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[8491, 14989, 430])).
% 2.74/2.95 tff(14991,plain,
% 2.74/2.95 (b(s(s(s(s(z)))), s(z))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[6103, 14990])).
% 2.74/2.95 tff(14992,plain,
% 2.74/2.95 (b(s(elem!1), s(z))),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[14991, 14987])).
% 2.74/2.95 tff(14993,plain,
% 2.74/2.95 (~(s(s(elem!1)) = elem!1)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[5385, 14979])).
% 2.74/2.95 tff(14994,plain,
% 2.74/2.95 (~(s(s(elem!1)) = s(elem!1))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[5640, 14993])).
% 2.74/2.95 tff(14995,plain,
% 2.74/2.95 (r(s(elem!1), elem!1)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[5548, 14989, 14979])).
% 2.74/2.95 tff(14996,plain,
% 2.74/2.95 (~r(s(s(elem!1)), s(elem!1))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[11073, 183, 14545, 14995])).
% 2.74/2.95 tff(14997,plain,
% 2.74/2.95 (b(s(s(elem!1)), s(elem!1))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[5644, 14996, 14994])).
% 2.74/2.95 tff(14998,plain,
% 2.74/2.95 (~r(s(s(elem!1)), s(z))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[11704, 474, 14545])).
% 2.74/2.95 tff(14999,plain,
% 2.74/2.95 (b(s(s(elem!1)), s(z))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[197, 14998])).
% 2.74/2.95 tff(15000,plain,
% 2.74/2.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(15001,plain,
% 2.74/2.95 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(15002,plain,
% 2.74/2.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1)))))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[15001])).
% 2.74/2.95 tff(15003,plain,
% 2.74/2.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))),
% 2.74/2.95 inference(transitivity,[status(thm)],[15002, 15000])).
% 2.74/2.95 tff(15004,plain,
% 2.74/2.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))))),
% 2.74/2.95 inference(quant_inst,[status(thm)],[])).
% 2.74/2.95 tff(15005,plain,
% 2.74/2.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1)))),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[15004, 15003])).
% 2.74/2.95 tff(15006,plain,
% 2.74/2.95 (~b(s(z), s(elem!1))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[15005, 246, 14999, 1044, 14997, 14992])).
% 2.74/2.95 tff(15007,plain,
% 2.74/2.95 (~(s(elem!1) = s(s(elem!1)))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[6946, 14994])).
% 2.74/2.95 tff(15008,plain,
% 2.74/2.95 (~r(s(elem!1), s(s(elem!1)))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[373, 183, 14545, 14995])).
% 2.74/2.95 tff(15009,plain,
% 2.74/2.95 (b(s(elem!1), s(s(elem!1)))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[5561, 47, 15008, 15007])).
% 2.74/2.95 tff(15010,plain,
% 2.74/2.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(15011,plain,
% 2.74/2.95 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(15012,plain,
% 2.74/2.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z)))))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[15011])).
% 2.74/2.95 tff(15013,plain,
% 2.74/2.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 2.74/2.95 inference(transitivity,[status(thm)],[15012, 15010])).
% 2.74/2.95 tff(15014,plain,
% 2.74/2.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 2.74/2.95 inference(quant_inst,[status(thm)],[])).
% 2.74/2.95 tff(15015,plain,
% 2.74/2.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z)))),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[15014, 15013])).
% 2.74/2.95 tff(15016,plain,
% 2.74/2.95 (~b(s(z), s(s(elem!1)))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[15015, 246, 14999, 1044, 15009, 14992])).
% 2.74/2.95 tff(15017,plain,
% 2.74/2.95 (r(s(z), s(s(elem!1)))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[233, 15016])).
% 2.74/2.95 tff(15018,plain,
% 2.74/2.95 (~r(z, s(s(elem!1)))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[6407, 15017, 171])).
% 2.74/2.95 tff(15019,plain,
% 2.74/2.95 (b(z, s(s(elem!1)))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[264, 15018])).
% 2.74/2.95 tff(15020,plain,
% 2.74/2.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(15021,plain,
% 2.74/2.95 (((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(15022,plain,
% 2.74/2.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z))))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[15021])).
% 2.74/2.95 tff(15023,plain,
% 2.74/2.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)))),
% 2.74/2.95 inference(transitivity,[status(thm)],[15022, 15020])).
% 2.74/2.95 tff(15024,plain,
% 2.74/2.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))),
% 2.74/2.95 inference(quant_inst,[status(thm)],[])).
% 2.74/2.95 tff(15025,plain,
% 2.74/2.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z))),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[15024, 15023])).
% 2.74/2.95 tff(15026,plain,
% 2.74/2.95 ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[15025, 246, 11962, 14999, 1044, 15009])).
% 2.74/2.95 tff(15027,plain,
% 2.74/2.95 (~b(s(elem!1), z)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[15026, 15019])).
% 2.74/2.95 tff(15028,plain,
% 2.74/2.95 (r(s(elem!1), z)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[2581, 15027])).
% 2.74/2.95 tff(15029,plain,
% 2.74/2.95 (~r(s(z), s(elem!1))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[2969, 183, 1114, 15028])).
% 2.74/2.95 tff(15030,plain,
% 2.74/2.95 ((s(z) = s(elem!1)) | b(s(z), s(elem!1))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[2973, 47, 15029])).
% 2.74/2.95 tff(15031,plain,
% 2.74/2.95 ($false),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[15030, 15006, 14986])).
% 2.74/2.95 tff(15032,plain,((~r(elem!1, s(z))) | (~b(s(z), elem!1)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | b(s(s(s(s(z)))), elem!1) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.95 tff(15033,plain,
% 2.74/2.95 (~r(elem!1, s(z))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[15032, 14975, 14978, 170, 53, 14976, 1])).
% 2.74/2.95 tff(15034,plain,
% 2.74/2.95 (b(elem!1, s(z))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[214, 15033, 11970])).
% 2.74/2.95 tff(15035,plain,
% 2.74/2.95 (~(elem!1 = s(s(s(z))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[6830, 15034, 2])).
% 2.74/2.95 tff(15036,plain,
% 2.74/2.95 (~(s(s(s(z))) = elem!1)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[1677, 15035])).
% 2.74/2.95 tff(15037,plain,
% 2.74/2.95 (r(s(s(s(z))), elem!1)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[647, 15036, 1])).
% 2.74/2.95 tff(15038,plain,
% 2.74/2.95 (~r(s(s(s(z))), z)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[11271, 183, 170, 53])).
% 2.74/2.95 tff(15039,plain,
% 2.74/2.95 (b(s(s(s(z))), z)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[995, 15038])).
% 2.74/2.95 tff(15040,plain,
% 2.74/2.95 (b(s(s(s(z))), s(s(elem!1)))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[689, 1647, 7736])).
% 2.74/2.95 tff(15041,plain,
% 2.74/2.95 (~b(s(s(elem!1)), z)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[4659, 15040, 2090, 4651])).
% 2.74/2.95 tff(15042,plain,
% 2.74/2.95 (r(s(s(elem!1)), z)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[523, 15041])).
% 2.74/2.95 tff(15043,plain,
% 2.74/2.95 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[7224, 183, 15042, 10484])).
% 2.74/2.95 tff(15044,plain,
% 2.74/2.95 (~r(s(s(s(s(z)))), s(z))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[9423, 10484, 1114])).
% 2.74/2.95 tff(15045,plain,
% 2.74/2.95 (b(s(s(s(s(z)))), s(z))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[6103, 15044])).
% 2.74/2.95 tff(15046,plain,
% 2.74/2.95 (b(s(s(elem!1)), s(s(s(z))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[454, 1638, 12305])).
% 2.74/2.95 tff(15047,plain,
% 2.74/2.95 (~r(s(z), s(s(elem!1)))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[1076, 183, 1114, 15042])).
% 2.74/2.95 tff(15048,plain,
% 2.74/2.95 (b(s(z), s(s(elem!1)))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[233, 15047])).
% 2.74/2.95 tff(15049,plain,
% 2.74/2.95 (~r(s(s(elem!1)), s(z))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[6720, 15042, 1114])).
% 2.74/2.95 tff(15050,plain,
% 2.74/2.95 (b(s(s(elem!1)), s(z))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[197, 15049])).
% 2.74/2.95 tff(15051,plain,
% 2.74/2.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(15052,plain,
% 2.74/2.95 (((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(15053,plain,
% 2.74/2.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[15052])).
% 2.74/2.95 tff(15054,plain,
% 2.74/2.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.74/2.95 inference(transitivity,[status(thm)],[15053, 15051])).
% 2.74/2.95 tff(15055,plain,
% 2.74/2.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.74/2.95 inference(quant_inst,[status(thm)],[])).
% 2.74/2.95 tff(15056,plain,
% 2.74/2.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[15055, 15054])).
% 2.74/2.95 tff(15057,plain,
% 2.74/2.95 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[15056, 246, 15050, 15048, 15046, 1833, 15045])).
% 2.74/2.95 tff(15058,plain,
% 2.74/2.95 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z))))))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(15059,plain,
% 2.74/2.95 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z))))))),
% 2.74/2.95 inference(quant_inst,[status(thm)],[])).
% 2.74/2.95 tff(15060,plain,
% 2.74/2.95 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[15059, 15058])).
% 2.74/2.95 tff(15061,plain,
% 2.74/2.95 ((s(s(elem!1)) = s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[15060, 47, 15057])).
% 2.74/2.95 tff(15062,plain,
% 2.74/2.95 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[15061, 15043])).
% 2.74/2.95 tff(15063,plain,
% 2.74/2.95 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(z)))))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[15062])).
% 2.74/2.95 tff(15064,plain,
% 2.74/2.95 (s(elem!1) = s(s(s(z)))),
% 2.74/2.95 inference(transitivity,[status(thm)],[108, 15063, 1491])).
% 2.74/2.95 tff(15065,plain,
% 2.74/2.95 (b(s(s(s(s(s(elem!1))))), s(elem!1)) <=> b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[15064])).
% 2.74/2.95 tff(15066,plain,
% 2.74/2.95 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 2.74/2.95 inference(symmetry,[status(thm)],[15063])).
% 2.74/2.95 tff(15067,plain,
% 2.74/2.95 (s(s(s(z))) = s(elem!1)),
% 2.74/2.95 inference(transitivity,[status(thm)],[1492, 15066, 92])).
% 2.74/2.95 tff(15068,plain,
% 2.74/2.95 ((s(s(s(s(s(elem!1))))) = s(s(s(z)))) <=> (s(s(s(s(s(elem!1))))) = s(elem!1))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[15067])).
% 2.74/2.95 tff(15069,plain,
% 2.74/2.95 ((~(s(s(s(s(s(elem!1))))) = s(s(s(z))))) <=> (~(s(s(s(s(s(elem!1))))) = s(elem!1)))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[15068])).
% 2.74/2.95 tff(15070,plain,
% 2.74/2.95 (~(s(s(s(s(s(elem!1))))) = s(elem!1))),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[1622, 15069])).
% 2.74/2.95 tff(15071,plain,
% 2.74/2.95 (r(s(elem!1), elem!1) <=> r(s(s(s(z))), elem!1)),
% 2.74/2.95 inference(monotonicity,[status(thm)],[15064])).
% 2.74/2.95 tff(15072,plain,
% 2.74/2.95 (r(s(s(s(z))), elem!1) <=> r(s(elem!1), elem!1)),
% 2.74/2.95 inference(symmetry,[status(thm)],[15071])).
% 2.74/2.95 tff(15073,plain,
% 2.74/2.95 (r(s(elem!1), elem!1)),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[634, 15072])).
% 2.74/2.95 tff(15074,plain,
% 2.74/2.95 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(s(z)))), s(elem!1))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[15062])).
% 2.74/2.95 tff(15075,plain,
% 2.74/2.95 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 2.74/2.95 inference(symmetry,[status(thm)],[15074])).
% 2.74/2.95 tff(15076,plain,
% 2.74/2.95 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[15064])).
% 2.74/2.95 tff(15077,plain,
% 2.74/2.95 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 2.74/2.95 inference(symmetry,[status(thm)],[15076])).
% 2.74/2.95 tff(15078,plain,
% 2.74/2.95 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(elem!1)), s(elem!1))),
% 2.74/2.95 inference(transitivity,[status(thm)],[15077, 15075])).
% 2.74/2.95 tff(15079,plain,
% 2.74/2.95 (b(s(s(elem!1)), s(elem!1))),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[1833, 15078])).
% 2.74/2.95 tff(15080,plain,
% 2.74/2.95 (b(z, s(elem!1)) <=> b(z, s(s(s(z))))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[15064])).
% 2.74/2.95 tff(15081,plain,
% 2.74/2.95 (b(z, s(s(s(z)))) <=> b(z, s(elem!1))),
% 2.74/2.95 inference(symmetry,[status(thm)],[15080])).
% 2.74/2.95 tff(15082,plain,
% 2.74/2.95 (b(z, s(elem!1))),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[4651, 15081])).
% 2.74/2.95 tff(15083,plain,
% 2.74/2.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(15084,plain,
% 2.74/2.95 (((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(15085,plain,
% 2.74/2.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z)))))))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[15084])).
% 2.74/2.96 tff(15086,plain,
% 2.74/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))))),
% 2.74/2.96 inference(transitivity,[status(thm)],[15085, 15083])).
% 2.74/2.96 tff(15087,plain,
% 2.74/2.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))))),
% 2.74/2.96 inference(quant_inst,[status(thm)],[])).
% 2.74/2.96 tff(15088,plain,
% 2.74/2.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z)))))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[15087, 15086])).
% 2.74/2.96 tff(15089,plain,
% 2.74/2.96 (~b(s(z), s(s(s(z))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[15088, 246, 201, 235, 11056])).
% 2.74/2.96 tff(15090,plain,
% 2.74/2.96 (r(s(z), s(s(s(z))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[1291, 15089])).
% 2.74/2.96 tff(15091,plain,
% 2.74/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(15092,plain,
% 2.74/2.96 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(15093,plain,
% 2.74/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z)))))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[15092])).
% 2.74/2.96 tff(15094,plain,
% 2.74/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))))),
% 2.74/2.96 inference(transitivity,[status(thm)],[15093, 15091])).
% 2.74/2.96 tff(15095,plain,
% 2.74/2.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))))),
% 2.74/2.96 inference(quant_inst,[status(thm)],[])).
% 2.74/2.96 tff(15096,plain,
% 2.74/2.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z)))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[15095, 15094])).
% 2.74/2.96 tff(15097,plain,
% 2.74/2.96 (~b(s(s(s(z))), s(z))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[15096, 246, 201, 1044, 235, 11056])).
% 2.74/2.96 tff(15098,plain,
% 2.74/2.96 (r(s(s(s(z))), s(z))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[52, 15097])).
% 2.74/2.96 tff(15099,plain,
% 2.74/2.96 (~r(z, s(s(s(z))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[438, 15098, 171])).
% 2.74/2.96 tff(15100,plain,
% 2.74/2.96 (b(z, s(s(s(z))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[6165, 15099])).
% 2.74/2.96 tff(15101,plain,
% 2.74/2.96 (~r(elem!1, s(z))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[1023, 15098, 634])).
% 2.74/2.96 tff(15102,plain,
% 2.74/2.96 (b(elem!1, s(z))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[214, 15101, 3])).
% 2.74/2.96 tff(15103,plain,
% 2.74/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(15104,plain,
% 2.74/2.96 (((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(15105,plain,
% 2.74/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z)))))))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[15104])).
% 2.74/2.96 tff(15106,plain,
% 2.74/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))))),
% 2.74/2.96 inference(transitivity,[status(thm)],[15105, 15103])).
% 2.74/2.96 tff(15107,plain,
% 2.74/2.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, elem!1)))),
% 2.74/2.96 inference(quant_inst,[status(thm)],[])).
% 2.74/2.96 tff(15108,plain,
% 2.74/2.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z)))))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[15107, 15106])).
% 2.74/2.96 tff(15109,plain,
% 2.74/2.96 (~b(elem!1, s(s(s(z))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[15108, 246, 2239, 201, 15102, 11056, 15100])).
% 2.74/2.96 tff(15110,plain,
% 2.74/2.96 (r(elem!1, s(s(s(z))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[470, 15109, 7868])).
% 2.74/2.96 tff(15111,plain,
% 2.74/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(15112,plain,
% 2.74/2.96 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(15113,plain,
% 2.74/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z))))))))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[15112])).
% 2.74/2.96 tff(15114,plain,
% 2.74/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.74/2.96 inference(transitivity,[status(thm)],[15113, 15111])).
% 2.74/2.96 tff(15115,plain,
% 2.74/2.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.74/2.96 inference(quant_inst,[status(thm)],[])).
% 2.74/2.96 tff(15116,plain,
% 2.74/2.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z))))))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[15115, 15114])).
% 2.74/2.96 tff(15117,plain,
% 2.74/2.96 ($false),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[15116, 246, 201, 2001, 235, 7169, 6725])).
% 2.74/2.96 tff(15118,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~(s(s(s(s(s(elem!1))))) = elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.96 tff(15119,plain,
% 2.74/2.96 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[15118, 15102, 201, 235, 7030, 15110, 15090])).
% 2.74/2.96 tff(15120,plain,
% 2.74/2.96 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[1702, 15119])).
% 2.74/2.96 tff(15121,plain,
% 2.74/2.96 (b(s(s(elem!1)), s(s(s(z))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[454, 1638, 4234])).
% 2.74/2.96 tff(15122,plain,
% 2.74/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(15123,plain,
% 2.74/2.96 (((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(15124,plain,
% 2.74/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[15123])).
% 2.74/2.96 tff(15125,plain,
% 2.74/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.74/2.96 inference(transitivity,[status(thm)],[15124, 15122])).
% 2.74/2.96 tff(15126,plain,
% 2.74/2.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.74/2.96 inference(quant_inst,[status(thm)],[])).
% 2.74/2.96 tff(15127,plain,
% 2.74/2.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[15126, 15125])).
% 2.74/2.96 tff(15128,plain,
% 2.74/2.96 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[15127, 246, 11056, 15121, 15120])).
% 2.74/2.96 tff(15129,plain,
% 2.74/2.96 (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z)))))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[15128, 11838])).
% 2.74/2.96 tff(15130,plain,
% 2.74/2.96 (r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z)))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[7230, 15129, 7215])).
% 2.74/2.96 tff(15131,plain,
% 2.74/2.96 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[15130, 11837])).
% 2.74/2.96 tff(15132,plain,
% 2.74/2.96 (~b(s(s(s(s(z)))), z)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[7194, 246, 11056, 15121, 15100, 15120])).
% 2.74/2.96 tff(15133,plain,
% 2.74/2.96 (r(s(s(s(s(z)))), z)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[6040, 15132])).
% 2.74/2.96 tff(15134,plain,
% 2.74/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(elem!1))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(15135,plain,
% 2.74/2.96 (((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(elem!1))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(15136,plain,
% 2.74/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(elem!1)))))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[15135])).
% 2.74/2.96 tff(15137,plain,
% 2.74/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(elem!1))))),
% 2.74/2.96 inference(transitivity,[status(thm)],[15136, 15134])).
% 2.74/2.96 tff(15138,plain,
% 2.74/2.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z)))),
% 2.74/2.96 inference(quant_inst,[status(thm)],[])).
% 2.74/2.96 tff(15139,plain,
% 2.74/2.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(elem!1)))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[15138, 15137])).
% 2.74/2.96 tff(15140,plain,
% 2.74/2.96 (~b(s(s(elem!1)), z)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[15139, 246, 11056, 15121, 363, 15100, 5939])).
% 2.74/2.96 tff(15141,plain,
% 2.74/2.96 (r(s(s(elem!1)), z)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[523, 15140])).
% 2.74/2.96 tff(15142,plain,
% 2.74/2.96 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[7224, 183, 15141, 15133])).
% 2.74/2.96 tff(15143,plain,
% 2.74/2.96 ($false),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[15142, 15131])).
% 2.74/2.96 tff(15144,plain,((~r(s(s(s(z))), elem!1)) | (~(s(s(s(s(s(elem!1))))) = elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (elem!1 = s(z)) | (~r(z, s(z))) | (~b(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (s(s(s(z))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.96 tff(15145,plain,
% 2.74/2.96 ((~r(s(s(s(z))), elem!1)) | (~(s(s(s(s(s(elem!1))))) = elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (elem!1 = s(z)) | (~r(z, s(z))) | (~b(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (s(s(s(z))) = s(s(elem!1)))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[15144, 11962])).
% 2.74/2.96 tff(15146,plain,
% 2.74/2.96 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[15145, 15082, 634, 15050, 15048, 15079, 3, 171, 1044, 216, 7736])).
% 2.74/2.96 tff(15147,plain,
% 2.74/2.96 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[15064])).
% 2.74/2.96 tff(15148,plain,
% 2.74/2.96 (elem!1 = s(s(z))),
% 2.74/2.96 inference(transitivity,[status(thm)],[3154, 15147, 24])).
% 2.74/2.96 tff(15149,plain,
% 2.74/2.96 (b(s(s(s(s(s(elem!1))))), elem!1) <=> b(s(s(s(s(s(elem!1))))), s(s(z)))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[15148])).
% 2.74/2.96 tff(15150,plain,
% 2.74/2.96 (b(s(s(s(s(s(elem!1))))), s(s(z))) <=> b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.74/2.96 inference(symmetry,[status(thm)],[15149])).
% 2.74/2.96 tff(15151,plain,
% 2.74/2.96 ((~b(s(s(s(s(s(elem!1))))), s(s(z)))) <=> (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[15150])).
% 2.74/2.96 tff(15152,plain,
% 2.74/2.96 (b(elem!1, z) <=> b(s(s(z)), z)),
% 2.74/2.96 inference(monotonicity,[status(thm)],[15148])).
% 2.74/2.96 tff(15153,plain,
% 2.74/2.96 (b(s(s(z)), z)),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[1051, 15152])).
% 2.74/2.96 tff(15154,plain,
% 2.74/2.96 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(s(z)))))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[15062])).
% 2.74/2.96 tff(15155,plain,
% 2.74/2.96 (b(s(z), s(s(s(s(z)))))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[15048, 15154])).
% 2.74/2.96 tff(15156,plain,
% 2.74/2.96 (b(s(z), elem!1) <=> b(s(z), s(s(z)))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[15148])).
% 2.74/2.96 tff(15157,plain,
% 2.74/2.96 (b(s(z), s(s(z)))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[1044, 15156])).
% 2.74/2.96 tff(15158,plain,
% 2.74/2.96 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[11863])).
% 2.74/2.96 tff(15159,plain,
% 2.74/2.96 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 2.74/2.96 inference(symmetry,[status(thm)],[15158])).
% 2.74/2.97 tff(15160,plain,
% 2.74/2.97 (s(s(z)) = elem!1),
% 2.74/2.97 inference(transitivity,[status(thm)],[25, 15159, 343])).
% 2.74/2.97 tff(15161,plain,
% 2.74/2.97 (b(z, s(s(z))) <=> b(z, elem!1)),
% 2.74/2.97 inference(monotonicity,[status(thm)],[15160])).
% 2.74/2.97 tff(15162,plain,
% 2.74/2.97 (b(z, elem!1) <=> b(z, s(s(z)))),
% 2.74/2.97 inference(symmetry,[status(thm)],[15161])).
% 2.74/2.97 tff(15163,plain,
% 2.74/2.97 (b(z, s(s(z)))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[11962, 15162])).
% 2.74/2.97 tff(15164,assumption,(b(s(s(z)), z)), introduced(assumption)).
% 2.74/2.97 tff(15165,plain,
% 2.74/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(15166,plain,
% 2.74/2.97 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(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(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(15167,plain,
% 2.74/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[15166])).
% 2.74/2.97 tff(15168,plain,
% 2.74/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 2.74/2.97 inference(transitivity,[status(thm)],[15167, 15165])).
% 2.74/2.97 tff(15169,plain,
% 2.74/2.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 2.74/2.97 inference(quant_inst,[status(thm)],[])).
% 2.74/2.97 tff(15170,plain,
% 2.74/2.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[15169, 15168])).
% 2.74/2.97 tff(15171,plain,
% 2.74/2.97 ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(z))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[15170, 246, 10944, 15164])).
% 2.74/2.97 tff(15172,plain,
% 2.74/2.97 (~b(s(s(s(s(s(elem!1))))), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[15171, 15163])).
% 2.74/2.97 tff(15173,plain,
% 2.74/2.97 (r(s(s(s(s(s(elem!1))))), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[1601, 15172])).
% 2.74/2.97 tff(15174,plain,
% 2.74/2.97 (b(s(s(z)), s(z)) <=> b(elem!1, s(z))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[15160])).
% 2.74/2.97 tff(15175,plain,
% 2.74/2.97 (b(elem!1, s(z)) <=> b(s(s(z)), s(z))),
% 2.74/2.97 inference(symmetry,[status(thm)],[15174])).
% 2.74/2.97 tff(15176,plain,
% 2.74/2.97 (b(s(s(z)), s(z))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[2001, 15175])).
% 2.74/2.97 tff(15177,plain,
% 2.74/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(15178,plain,
% 2.74/2.97 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), 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(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(15179,plain,
% 2.74/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), 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(X1, 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(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[15178])).
% 2.74/2.97 tff(15180,plain,
% 2.74/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), 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(X1, 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(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.74/2.97 inference(transitivity,[status(thm)],[15179, 15177])).
% 2.74/2.97 tff(15181,plain,
% 2.74/2.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 2.74/2.97 inference(quant_inst,[status(thm)],[])).
% 2.74/2.97 tff(15182,plain,
% 2.74/2.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[15181, 15180])).
% 2.74/2.97 tff(15183,plain,
% 2.74/2.97 ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(z)), s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[15182, 246, 10946, 9862, 10944])).
% 2.74/2.97 tff(15184,plain,
% 2.74/2.97 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[15183, 15176])).
% 2.74/2.97 tff(15185,plain,
% 2.74/2.97 (r(s(s(s(s(s(elem!1))))), s(z))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[6447, 15184])).
% 2.74/2.97 tff(15186,plain,
% 2.74/2.97 ($false),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[11167, 183, 1114, 15185, 15173])).
% 2.74/2.97 tff(15187,plain,((~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(elem!1, s(z))) | (~(s(s(elem!1)) = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.97 tff(15188,plain,
% 2.74/2.97 (~b(s(s(s(s(s(elem!1))))), s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[15187, 15157, 1114, 15155, 15153, 2001, 15062])).
% 2.74/2.97 tff(15189,plain,
% 2.74/2.97 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[15188, 15151])).
% 2.74/2.97 tff(15190,plain,
% 2.74/2.97 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[86, 15189, 15146])).
% 2.74/2.97 tff(15191,plain,
% 2.74/2.97 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[3956, 15190, 15073])).
% 2.74/2.97 tff(15192,plain,
% 2.74/2.97 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[1795, 15191, 15070])).
% 2.74/2.97 tff(15193,plain,
% 2.74/2.97 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[15192, 15065])).
% 2.74/2.97 tff(15194,plain,
% 2.74/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(15195,plain,
% 2.74/2.97 (((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(15196,plain,
% 2.74/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[15195])).
% 2.74/2.97 tff(15197,plain,
% 2.74/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 2.74/2.97 inference(transitivity,[status(thm)],[15196, 15194])).
% 2.74/2.97 tff(15198,plain,
% 2.74/2.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 2.74/2.97 inference(quant_inst,[status(thm)],[])).
% 2.74/2.97 tff(15199,plain,
% 2.74/2.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[15198, 15197])).
% 2.74/2.97 tff(15200,plain,
% 2.74/2.97 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[15199, 246, 4651, 2090, 1833, 15193])).
% 2.74/2.97 tff(15201,plain,
% 2.74/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(15202,plain,
% 2.74/2.97 (((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(15203,plain,
% 2.74/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z)))))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[15202])).
% 2.74/2.97 tff(15204,plain,
% 2.74/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))),
% 2.74/2.97 inference(transitivity,[status(thm)],[15203, 15201])).
% 2.74/2.97 tff(15205,plain,
% 2.74/2.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))))),
% 2.74/2.97 inference(quant_inst,[status(thm)],[])).
% 2.74/2.97 tff(15206,plain,
% 2.74/2.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z)))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[15205, 15204])).
% 2.74/2.97 tff(15207,plain,
% 2.74/2.97 (~b(elem!1, s(s(elem!1)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[15206, 246, 15050, 1044, 2001])).
% 2.74/2.97 tff(15208,plain,
% 2.74/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(15209,plain,
% 2.74/2.97 (((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(15210,plain,
% 2.74/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[15209])).
% 2.74/2.97 tff(15211,plain,
% 2.74/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.74/2.97 inference(transitivity,[status(thm)],[15210, 15208])).
% 2.74/2.97 tff(15212,plain,
% 2.74/2.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.74/2.97 inference(quant_inst,[status(thm)],[])).
% 2.74/2.97 tff(15213,plain,
% 2.74/2.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[15212, 15211])).
% 2.74/2.97 tff(15214,plain,
% 2.74/2.97 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[15213, 183, 216, 15042, 10484])).
% 2.74/2.97 tff(15215,plain,
% 2.74/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(15216,plain,
% 2.74/2.97 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(15217,plain,
% 2.74/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[15216])).
% 2.74/2.97 tff(15218,plain,
% 2.74/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.74/2.97 inference(transitivity,[status(thm)],[15217, 15215])).
% 2.74/2.97 tff(15219,plain,
% 2.74/2.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.74/2.97 inference(quant_inst,[status(thm)],[])).
% 2.74/2.97 tff(15220,plain,
% 2.74/2.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[15219, 15218])).
% 2.74/2.97 tff(15221,plain,
% 2.74/2.97 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[15220, 246, 15050, 15040, 15046, 1833])).
% 2.74/2.97 tff(15222,plain,
% 2.74/2.97 ((s(s(s(s(z)))) = s(s(elem!1))) | r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[6521, 47, 15221])).
% 2.74/2.97 tff(15223,plain,
% 2.74/2.97 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[15222, 15214])).
% 2.74/2.97 tff(15224,assumption,(s(s(s(s(z)))) = s(s(elem!1))), introduced(assumption)).
% 2.74/2.97 tff(15225,plain,
% 2.74/2.97 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[15224])).
% 2.74/2.97 tff(15226,plain,
% 2.74/2.97 (s(s(s(z))) = s(elem!1)),
% 2.74/2.97 inference(transitivity,[status(thm)],[1492, 15225, 92])).
% 2.74/2.97 tff(15227,plain,
% 2.74/2.97 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[15226])).
% 2.74/2.97 tff(15228,plain,
% 2.74/2.97 (s(s(z)) = elem!1),
% 2.74/2.97 inference(transitivity,[status(thm)],[25, 15227, 343])).
% 2.74/2.97 tff(15229,plain,
% 2.74/2.97 (b(s(s(z)), s(s(s(s(z))))) <=> b(elem!1, s(s(elem!1)))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[15228, 15224])).
% 2.74/2.97 tff(15230,plain,
% 2.74/2.97 (b(elem!1, s(s(elem!1))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 2.74/2.97 inference(symmetry,[status(thm)],[15229])).
% 2.74/2.97 tff(15231,plain,
% 2.74/2.97 ((~b(elem!1, s(s(elem!1)))) <=> (~b(s(s(z)), s(s(s(s(z))))))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[15230])).
% 2.74/2.97 tff(15232,plain,
% 2.74/2.97 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[13852, 15231])).
% 2.74/2.97 tff(15233,plain,
% 2.74/2.97 ($false),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[3457, 15232])).
% 2.74/2.97 tff(15234,plain,((~(s(s(s(s(z)))) = s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | b(elem!1, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.98 tff(15235,plain,
% 2.74/2.98 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[15234, 15223, 15207])).
% 2.74/2.98 tff(15236,plain,
% 2.74/2.98 (r(s(s(z)), s(s(s(s(z)))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[1531, 15235])).
% 2.74/2.98 tff(15237,plain,
% 2.74/2.98 (r(s(s(s(s(s(elem!1))))), elem!1) <=> r(s(s(s(s(s(elem!1))))), s(s(z)))),
% 2.74/2.98 inference(monotonicity,[status(thm)],[15148])).
% 2.74/2.98 tff(15238,plain,
% 2.74/2.98 (r(s(s(s(s(s(elem!1))))), s(s(z)))),
% 2.74/2.98 inference(modus_ponens,[status(thm)],[15190, 15237])).
% 2.74/2.98 tff(15239,plain,
% 2.74/2.98 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[1916, 15238, 15236])).
% 2.74/2.98 tff(15240,plain,
% 2.74/2.98 ($false),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[1897, 15239, 15200])).
% 2.74/2.98 tff(15241,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(s(z), z)) | (~b(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (elem!1 = s(z)) | (~r(z, s(z))) | (~b(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.98 tff(15242,plain,
% 2.74/2.98 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[15241, 15037, 15039, 14978, 14943, 15034, 11970, 170, 14975, 14545, 14956])).
% 2.74/2.98 tff(15243,plain,
% 2.74/2.98 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[1702, 15242])).
% 2.74/2.98 tff(15244,plain,
% 2.74/2.98 (s(s(s(s(z)))) = elem!1),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[9060, 15243, 53, 15034, 15037, 14975])).
% 2.74/2.98 tff(15245,plain,
% 2.74/2.98 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(z)), elem!1)),
% 2.74/2.98 inference(monotonicity,[status(thm)],[15244])).
% 2.74/2.98 tff(15246,plain,
% 2.74/2.98 (~r(s(s(s(s(z)))), s(z))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[8491, 15243, 53])).
% 2.74/2.98 tff(15247,plain,
% 2.74/2.98 (b(s(s(s(s(z)))), s(z))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[6103, 15246])).
% 2.74/2.98 tff(15248,plain,
% 2.74/2.98 (b(z, s(s(s(s(z))))) <=> b(z, elem!1)),
% 2.74/2.98 inference(monotonicity,[status(thm)],[15244])).
% 2.74/2.98 tff(15249,plain,
% 2.74/2.98 (b(z, elem!1) <=> b(z, s(s(s(s(z)))))),
% 2.74/2.98 inference(symmetry,[status(thm)],[15248])).
% 2.74/2.98 tff(15250,plain,
% 2.74/2.98 (b(z, s(s(s(s(z)))))),
% 2.74/2.98 inference(modus_ponens,[status(thm)],[11962, 15249])).
% 2.74/2.98 tff(15251,plain,
% 2.74/2.98 (b(s(s(s(s(z)))), z) <=> b(elem!1, z)),
% 2.74/2.98 inference(monotonicity,[status(thm)],[15244])).
% 2.74/2.98 tff(15252,plain,
% 2.74/2.98 (b(elem!1, z) <=> b(s(s(s(s(z)))), z)),
% 2.74/2.98 inference(symmetry,[status(thm)],[15251])).
% 2.74/2.98 tff(15253,plain,
% 2.74/2.98 (b(s(s(s(s(z)))), z)),
% 2.74/2.98 inference(modus_ponens,[status(thm)],[14956, 15252])).
% 2.74/2.98 tff(15254,plain,
% 2.74/2.98 (b(s(z), s(s(s(s(z))))) <=> b(s(z), elem!1)),
% 2.74/2.98 inference(monotonicity,[status(thm)],[15244])).
% 2.74/2.98 tff(15255,plain,
% 2.74/2.98 (b(s(z), elem!1) <=> b(s(z), s(s(s(s(z)))))),
% 2.74/2.98 inference(symmetry,[status(thm)],[15254])).
% 2.74/2.98 tff(15256,plain,
% 2.74/2.98 (b(s(z), s(s(s(s(z)))))),
% 2.74/2.98 inference(modus_ponens,[status(thm)],[14975, 15255])).
% 2.74/2.98 tff(15257,plain,
% 2.74/2.98 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[12662, 15256, 15253, 15250, 15247])).
% 2.74/2.98 tff(15258,plain,
% 2.74/2.98 (r(s(s(z)), s(s(s(s(z)))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[1531, 15257])).
% 2.74/2.98 tff(15259,plain,
% 2.74/2.98 (r(s(s(z)), elem!1)),
% 2.74/2.98 inference(modus_ponens,[status(thm)],[15258, 15245])).
% 2.74/2.98 tff(15260,plain,
% 2.74/2.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))))),
% 2.74/2.98 inference(rewrite,[status(thm)],[])).
% 2.74/2.98 tff(15261,plain,
% 2.74/2.98 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))))),
% 2.74/2.98 inference(rewrite,[status(thm)],[])).
% 2.74/2.98 tff(15262,plain,
% 2.74/2.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(elem!1))))))),
% 2.74/2.98 inference(monotonicity,[status(thm)],[15261])).
% 2.74/2.98 tff(15263,plain,
% 2.74/2.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))))),
% 2.74/2.98 inference(transitivity,[status(thm)],[15262, 15260])).
% 2.74/2.98 tff(15264,plain,
% 2.74/2.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))))),
% 2.74/2.98 inference(quant_inst,[status(thm)],[])).
% 2.74/2.98 tff(15265,plain,
% 2.74/2.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(elem!1))))),
% 2.74/2.98 inference(modus_ponens,[status(thm)],[15264, 15263])).
% 2.74/2.98 tff(15266,plain,
% 2.74/2.98 (~r(s(s(z)), s(s(elem!1)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[15265, 183, 14545, 15259])).
% 2.74/2.98 tff(15267,assumption,(s(s(z)) = s(s(elem!1))), introduced(assumption)).
% 2.74/2.98 tff(15268,plain,
% 2.74/2.98 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.74/2.98 inference(monotonicity,[status(thm)],[15267])).
% 2.74/2.98 tff(15269,plain,
% 2.74/2.98 (s(z) = s(elem!1)),
% 2.74/2.98 inference(transitivity,[status(thm)],[1523, 15268, 92])).
% 2.74/2.98 tff(15270,plain,
% 2.74/2.98 (inj_0(s(z)) = inj_0(s(elem!1))),
% 2.74/2.98 inference(monotonicity,[status(thm)],[15269])).
% 2.74/2.98 tff(15271,plain,
% 2.74/2.98 (z = inj_0(s(z))),
% 2.74/2.98 inference(symmetry,[status(thm)],[20])).
% 2.74/2.98 tff(15272,plain,
% 2.74/2.98 (z = elem!1),
% 2.74/2.98 inference(transitivity,[status(thm)],[15271, 15270, 343])).
% 2.74/2.98 tff(15273,plain,
% 2.74/2.98 (~(z = elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[1440, 11994])).
% 2.74/2.98 tff(15274,plain,
% 2.74/2.98 ($false),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[15273, 15272])).
% 2.74/2.98 tff(15275,plain,(~(s(s(z)) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.98 tff(15276,plain,
% 2.74/2.98 (b(s(s(z)), s(s(elem!1)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[10927, 47, 15275, 15266])).
% 2.74/2.98 tff(15277,plain,
% 2.74/2.98 (~r(s(s(s(z))), s(s(z)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[12512, 183, 15037, 15259])).
% 2.74/2.98 tff(15278,plain,
% 2.74/2.98 (b(s(s(s(z))), s(s(z)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[8991, 47, 8374, 15277])).
% 2.74/2.98 tff(15279,plain,
% 2.74/2.98 (~r(s(s(z)), s(s(s(z))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[12528, 183, 15037, 15259])).
% 2.74/2.98 tff(15280,plain,
% 2.74/2.98 (b(s(s(z)), s(s(s(z))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[8382, 15279])).
% 2.74/2.98 tff(15281,plain,
% 2.74/2.98 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[1637, 183, 14545, 15037])).
% 2.74/2.98 tff(15282,plain,
% 2.74/2.98 (b(s(s(elem!1)), s(s(s(z))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[454, 15281, 13043])).
% 2.74/2.98 tff(15283,plain,
% 2.74/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.74/2.98 inference(rewrite,[status(thm)],[])).
% 2.74/2.98 tff(15284,plain,
% 2.74/2.98 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.74/2.98 inference(rewrite,[status(thm)],[])).
% 2.74/2.98 tff(15285,plain,
% 2.74/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))))),
% 2.74/2.98 inference(monotonicity,[status(thm)],[15284])).
% 2.74/2.98 tff(15286,plain,
% 2.74/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.74/2.98 inference(transitivity,[status(thm)],[15285, 15283])).
% 2.74/2.98 tff(15287,plain,
% 2.74/2.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.74/2.98 inference(quant_inst,[status(thm)],[])).
% 2.74/2.98 tff(15288,plain,
% 2.74/2.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))),
% 2.74/2.98 inference(modus_ponens,[status(thm)],[15287, 15286])).
% 2.74/2.98 tff(15289,plain,
% 2.74/2.98 ($false),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[15288, 246, 15282, 15280, 15278, 15276])).
% 2.74/2.98 tff(15290,plain,(b(z, s(z)) | b(s(s(s(z))), elem!1) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.98 tff(15291,plain,
% 2.74/2.98 (b(z, s(z))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[15290, 2, 1])).
% 2.74/2.98 tff(15292,plain,
% 2.74/2.98 (~r(s(s(elem!1)), z)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[14863, 2246, 14545])).
% 2.74/2.98 tff(15293,plain,
% 2.74/2.98 (b(s(s(elem!1)), z)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[523, 15292])).
% 2.74/2.98 tff(15294,plain,
% 2.74/2.98 (elem!1 = s(s(s(z)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[1677, 14951])).
% 2.74/2.98 tff(15295,plain,
% 2.74/2.98 (~b(elem!1, s(z))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[6830, 15294, 2])).
% 2.74/2.98 tff(15296,plain,
% 2.74/2.98 (r(elem!1, s(z))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[214, 15295, 3])).
% 2.74/2.98 tff(15297,plain,
% 2.74/2.98 (~r(s(z), z)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[1163, 15296, 2246])).
% 2.74/2.98 tff(15298,plain,
% 2.74/2.98 (b(s(z), z)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[1069, 15297])).
% 2.74/2.98 tff(15299,plain,
% 2.74/2.98 (~r(s(s(elem!1)), s(z))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[11704, 15296, 14545])).
% 2.74/2.98 tff(15300,plain,
% 2.74/2.98 (b(s(s(elem!1)), s(z))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[197, 15299])).
% 2.74/2.98 tff(15301,plain,
% 2.74/2.98 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))),
% 2.74/2.98 inference(rewrite,[status(thm)],[])).
% 2.74/2.98 tff(15302,plain,
% 2.74/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z))))),
% 2.74/2.98 inference(monotonicity,[status(thm)],[15301])).
% 2.74/2.98 tff(15303,plain,
% 2.74/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))),
% 2.74/2.98 inference(transitivity,[status(thm)],[15302, 10372])).
% 2.74/2.98 tff(15304,plain,
% 2.74/2.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 2.74/2.98 inference(quant_inst,[status(thm)],[])).
% 2.74/2.98 tff(15305,plain,
% 2.74/2.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z))),
% 2.74/2.98 inference(modus_ponens,[status(thm)],[15304, 15303])).
% 2.74/2.98 tff(15306,plain,
% 2.74/2.98 ($false),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[15305, 246, 15300, 15298, 15293, 15291])).
% 2.74/2.98 tff(15307,plain,((~r(elem!1, z)) | (elem!1 = s(z)) | b(s(s(s(z))), s(z)) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.98 tff(15308,plain,
% 2.74/2.98 (~r(elem!1, z)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[15307, 3, 2, 1])).
% 2.74/2.98 tff(15309,plain,
% 2.74/2.98 (b(elem!1, z)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[12008, 15308])).
% 2.74/2.98 tff(15310,plain,
% 2.74/2.98 (~r(s(z), elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[14973, 15309, 1, 53])).
% 2.74/2.98 tff(15311,plain,
% 2.74/2.98 (~b(s(z), elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[13451, 15309, 15291])).
% 2.74/2.98 tff(15312,plain,
% 2.74/2.98 ($false),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[1034, 15311, 15310, 10])).
% 2.74/2.98 tff(15313,plain,((elem!1 = s(z)) | b(s(s(s(z))), elem!1) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.98 tff(15314,plain,
% 2.74/2.98 (elem!1 = s(z)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[15313, 2, 1])).
% 2.74/2.98 tff(15315,plain,
% 2.74/2.98 (s(z) = elem!1),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[2279, 15314])).
% 2.74/2.98 tff(15316,plain,
% 2.74/2.98 (s(s(s(z))) = s(s(elem!1))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[121, 15315])).
% 2.74/2.98 tff(15317,plain,
% 2.74/2.98 (~b(s(s(elem!1)), elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[5568, 15316, 1])).
% 2.74/2.98 tff(15318,plain,
% 2.74/2.98 (~b(s(s(elem!1)), s(z))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[207, 15317, 15314])).
% 2.74/2.98 tff(15319,plain,
% 2.74/2.98 (r(s(s(elem!1)), s(z))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[197, 15318])).
% 2.74/2.98 tff(15320,plain,
% 2.74/2.98 (b(z, s(s(elem!1)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[9374, 15316, 14943])).
% 2.74/2.98 tff(15321,plain,
% 2.74/2.98 (s(z) = elem!1),
% 2.74/2.98 inference(symmetry,[status(thm)],[15314])).
% 2.74/2.98 tff(15322,plain,
% 2.74/2.98 ((s(s(s(s(s(elem!1))))) = s(z)) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 2.74/2.98 inference(monotonicity,[status(thm)],[15321])).
% 2.74/2.98 tff(15323,plain,
% 2.74/2.98 ((~(s(s(s(s(s(elem!1))))) = s(z))) <=> (~(s(s(s(s(s(elem!1))))) = elem!1))),
% 2.74/2.98 inference(monotonicity,[status(thm)],[15322])).
% 2.74/2.98 tff(15324,plain,
% 2.74/2.98 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 2.74/2.98 inference(modus_ponens,[status(thm)],[331, 15323])).
% 2.74/2.98 tff(15325,plain,
% 2.74/2.98 (b(s(z), elem!1) <=> b(elem!1, elem!1)),
% 2.74/2.98 inference(monotonicity,[status(thm)],[15321])).
% 2.74/2.98 tff(15326,plain,
% 2.74/2.98 (b(elem!1, elem!1) <=> b(s(z), elem!1)),
% 2.74/2.98 inference(symmetry,[status(thm)],[15325])).
% 2.74/2.98 tff(15327,plain,
% 2.74/2.98 ((~b(elem!1, elem!1)) <=> (~b(s(z), elem!1))),
% 2.74/2.98 inference(monotonicity,[status(thm)],[15326])).
% 2.74/2.98 tff(15328,plain,
% 2.74/2.98 (~b(s(z), elem!1)),
% 2.74/2.98 inference(modus_ponens,[status(thm)],[5691, 15327])).
% 2.74/2.98 tff(15329,plain,
% 2.74/2.98 (r(s(s(s(z))), elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[11660, 15317, 15314])).
% 2.74/2.98 tff(15330,plain,
% 2.74/2.98 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[86, 82, 69])).
% 2.74/2.98 tff(15331,plain,
% 2.74/2.98 (r(z, elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[14841, 82, 6, 14545, 1445, 145])).
% 2.74/2.98 tff(15332,plain,
% 2.74/2.98 ($false),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[5485, 15331, 15330, 634])).
% 2.74/2.98 tff(15333,plain,(b(s(s(s(s(s(elem!1))))), elem!1) | (~r(s(s(s(z))), elem!1)) | (~(s(z) = elem!1)) | b(s(z), elem!1) | b(s(s(elem!1)), elem!1) | (s(s(s(s(s(elem!1))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.98 tff(15334,plain,
% 2.74/2.98 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[15333, 15329, 15315, 15328, 15317, 15324])).
% 2.74/2.98 tff(15335,plain,
% 2.74/2.98 (b(s(s(s(s(s(elem!1))))), s(z))),
% 2.74/2.98 inference(modus_ponens,[status(thm)],[714, 14258])).
% 2.74/2.98 tff(15336,plain,
% 2.74/2.98 ($false),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[6445, 15335])).
% 2.74/2.98 tff(15337,plain,((~b(s(s(s(s(s(elem!1))))), elem!1)) | b(s(s(s(s(s(elem!1))))), s(z)) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.98 tff(15338,plain,
% 2.74/2.98 (b(s(s(s(s(s(elem!1))))), s(z))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[15337, 15334, 15314])).
% 2.74/2.98 tff(15339,plain,
% 2.74/2.98 (~r(s(z), elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[3017, 15329, 53])).
% 2.74/2.98 tff(15340,plain,
% 2.74/2.98 (~r(elem!1, s(z))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[1023, 15329, 53])).
% 2.74/2.98 tff(15341,plain,
% 2.74/2.98 (~(s(s(s(s(z)))) = elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[13813, 15340, 15291, 15339])).
% 2.74/2.98 tff(15342,plain,
% 2.74/2.98 (~(elem!1 = s(s(s(elem!1))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[9194, 15341, 15316])).
% 2.74/2.98 tff(15343,plain,
% 2.74/2.98 (~b(s(s(s(elem!1))), z)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[8103, 246, 1056, 236, 8133])).
% 2.74/2.98 tff(15344,plain,
% 2.74/2.98 (r(s(s(s(elem!1))), z)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[3086, 47, 355, 15343])).
% 2.74/2.98 tff(15345,plain,
% 2.74/2.98 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 2.74/2.98 inference(rewrite,[status(thm)],[])).
% 2.74/2.98 tff(15346,plain,
% 2.74/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z)))))),
% 2.74/2.98 inference(monotonicity,[status(thm)],[15345])).
% 2.74/2.98 tff(15347,plain,
% 2.74/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 2.74/2.98 inference(transitivity,[status(thm)],[15346, 5573])).
% 2.74/2.98 tff(15348,plain,
% 2.74/2.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 2.74/2.98 inference(quant_inst,[status(thm)],[])).
% 2.74/2.98 tff(15349,plain,
% 2.74/2.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z)))),
% 2.74/2.98 inference(modus_ponens,[status(thm)],[15348, 15347])).
% 2.74/2.98 tff(15350,plain,
% 2.74/2.98 (~b(s(s(s(s(s(elem!1))))), z)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[15349, 246, 1056, 236, 6875])).
% 2.74/2.98 tff(15351,plain,
% 2.74/2.98 (r(s(s(s(s(s(elem!1))))), z)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[1601, 15350])).
% 2.74/2.98 tff(15352,plain,
% 2.74/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.74/2.98 inference(rewrite,[status(thm)],[])).
% 2.74/2.98 tff(15353,plain,
% 2.74/2.98 (((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.74/2.98 inference(rewrite,[status(thm)],[])).
% 2.74/2.98 tff(15354,plain,
% 2.74/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 2.74/2.98 inference(monotonicity,[status(thm)],[15353])).
% 2.74/2.98 tff(15355,plain,
% 2.74/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.74/2.98 inference(transitivity,[status(thm)],[15354, 15352])).
% 2.74/2.98 tff(15356,plain,
% 2.74/2.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.74/2.98 inference(quant_inst,[status(thm)],[])).
% 2.74/2.98 tff(15357,plain,
% 2.74/2.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))),
% 2.74/2.98 inference(modus_ponens,[status(thm)],[15356, 15355])).
% 2.74/2.98 tff(15358,plain,
% 2.74/2.98 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[15357, 246, 1056, 236, 8133, 6875])).
% 2.74/2.98 tff(15359,plain,
% 2.74/2.98 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[3693, 15358, 775])).
% 2.74/2.98 tff(15360,plain,
% 2.74/2.98 ($false),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[14315, 183, 15359, 15351, 15344])).
% 2.74/2.98 tff(15361,plain,((~b(s(s(s(elem!1))), s(z))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.98 tff(15362,plain,
% 2.74/2.98 (~b(s(s(s(elem!1))), s(z))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[15361, 1056, 10672, 236, 6875])).
% 2.74/2.98 tff(15363,plain,
% 2.74/2.98 (~b(s(s(s(s(z)))), s(z))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[10834, 15362, 3452])).
% 2.74/2.98 tff(15364,plain,
% 2.74/2.98 (r(s(s(s(s(z)))), s(z))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[6103, 15363])).
% 2.74/2.98 tff(15365,plain,
% 2.74/2.98 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[8491, 15364, 430])).
% 2.74/2.98 tff(15366,plain,
% 2.74/2.98 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[1702, 15365])).
% 2.74/2.98 tff(15367,plain,
% 2.74/2.98 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[9446, 15366, 3452])).
% 2.74/2.98 tff(15368,plain,
% 2.74/2.98 (~(s(s(s(elem!1))) = s(z))),
% 2.74/2.98 inference(modus_ponens,[status(thm)],[9481, 10681])).
% 2.74/2.98 tff(15369,plain,
% 2.74/2.98 ((s(s(s(elem!1))) = s(z)) | r(s(s(s(elem!1))), s(z))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[10692, 47, 15362])).
% 2.74/2.98 tff(15370,plain,
% 2.74/2.98 (r(s(s(s(elem!1))), s(z))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[15369, 15368])).
% 2.74/2.98 tff(15371,plain,
% 2.74/2.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.74/2.98 inference(rewrite,[status(thm)],[])).
% 2.74/2.98 tff(15372,plain,
% 2.74/2.98 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.74/2.98 inference(rewrite,[status(thm)],[])).
% 2.74/2.98 tff(15373,plain,
% 2.74/2.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))))),
% 2.74/2.98 inference(monotonicity,[status(thm)],[15372])).
% 2.74/2.98 tff(15374,plain,
% 2.74/2.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.74/2.98 inference(transitivity,[status(thm)],[15373, 15371])).
% 2.74/2.98 tff(15375,plain,
% 2.74/2.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.74/2.98 inference(quant_inst,[status(thm)],[])).
% 2.74/2.98 tff(15376,plain,
% 2.74/2.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))),
% 2.74/2.98 inference(modus_ponens,[status(thm)],[15375, 15374])).
% 2.74/2.98 tff(15377,plain,
% 2.74/2.98 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[15376, 183, 173, 15370])).
% 2.74/2.98 tff(15378,plain,
% 2.74/2.98 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[4455, 15377, 14297])).
% 2.74/2.98 tff(15379,plain,
% 2.74/2.98 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[5671, 172, 5669])).
% 2.74/2.98 tff(15380,plain,
% 2.74/2.98 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[1557, 15379, 1555])).
% 2.74/2.98 tff(15381,plain,
% 2.74/2.98 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[1667, 15380, 1657, 1659])).
% 2.74/2.98 tff(15382,plain,
% 2.74/2.98 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[3693, 15381, 775])).
% 2.74/2.98 tff(15383,plain,
% 2.74/2.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 2.74/2.99 inference(rewrite,[status(thm)],[])).
% 2.74/2.99 tff(15384,plain,
% 2.74/2.99 (((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 2.74/2.99 inference(rewrite,[status(thm)],[])).
% 2.74/2.99 tff(15385,plain,
% 2.74/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), z))))),
% 2.74/2.99 inference(monotonicity,[status(thm)],[15384])).
% 2.74/2.99 tff(15386,plain,
% 2.74/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 2.74/2.99 inference(transitivity,[status(thm)],[15385, 15383])).
% 2.74/2.99 tff(15387,plain,
% 2.74/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 2.74/2.99 inference(quant_inst,[status(thm)],[])).
% 2.74/2.99 tff(15388,plain,
% 2.74/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), z))),
% 2.74/2.99 inference(modus_ponens,[status(thm)],[15387, 15386])).
% 2.74/2.99 tff(15389,plain,
% 2.74/2.99 (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[15388, 183, 172, 15382, 5669])).
% 2.74/2.99 tff(15390,plain,
% 2.74/2.99 (b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[1547, 47, 15389, 4476])).
% 2.74/2.99 tff(15391,plain,
% 2.74/2.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(elem!1))), z)))),
% 2.74/2.99 inference(rewrite,[status(thm)],[])).
% 2.74/2.99 tff(15392,plain,
% 2.74/2.99 (((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(elem!1))), z)))),
% 2.74/2.99 inference(rewrite,[status(thm)],[])).
% 2.74/2.99 tff(15393,plain,
% 2.74/2.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(elem!1))), z))))),
% 2.74/2.99 inference(monotonicity,[status(thm)],[15392])).
% 2.74/2.99 tff(15394,plain,
% 2.74/2.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(elem!1))), z)))),
% 2.74/2.99 inference(transitivity,[status(thm)],[15393, 15391])).
% 2.74/2.99 tff(15395,plain,
% 2.74/2.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))),
% 2.74/2.99 inference(quant_inst,[status(thm)],[])).
% 2.74/2.99 tff(15396,plain,
% 2.74/2.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(elem!1))), z))),
% 2.74/2.99 inference(modus_ponens,[status(thm)],[15395, 15394])).
% 2.74/2.99 tff(15397,plain,
% 2.74/2.99 (~b(s(s(s(elem!1))), z)),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[15396, 246, 236, 1099, 15390, 1659, 6875])).
% 2.74/2.99 tff(15398,plain,
% 2.74/2.99 (r(s(s(s(elem!1))), z)),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[3086, 47, 355, 15397])).
% 2.74/2.99 tff(15399,plain,
% 2.74/2.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 2.74/2.99 inference(rewrite,[status(thm)],[])).
% 2.74/2.99 tff(15400,plain,
% 2.74/2.99 (((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 2.74/2.99 inference(rewrite,[status(thm)],[])).
% 2.74/2.99 tff(15401,plain,
% 2.74/2.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))))),
% 2.74/2.99 inference(monotonicity,[status(thm)],[15400])).
% 2.74/2.99 tff(15402,plain,
% 2.74/2.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 2.74/2.99 inference(transitivity,[status(thm)],[15401, 15399])).
% 2.74/2.99 tff(15403,plain,
% 2.74/2.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 2.74/2.99 inference(quant_inst,[status(thm)],[])).
% 2.74/2.99 tff(15404,plain,
% 2.74/2.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 2.74/2.99 inference(modus_ponens,[status(thm)],[15403, 15402])).
% 2.74/2.99 tff(15405,plain,
% 2.74/2.99 (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[15404, 246, 15380, 15390, 1659])).
% 2.74/2.99 tff(15406,plain,
% 2.74/2.99 (r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[913, 47, 785, 15405])).
% 2.74/2.99 tff(15407,plain,
% 2.74/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 2.74/2.99 inference(rewrite,[status(thm)],[])).
% 2.74/2.99 tff(15408,plain,
% 2.74/2.99 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 2.74/2.99 inference(rewrite,[status(thm)],[])).
% 2.74/2.99 tff(15409,plain,
% 2.74/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))))),
% 2.74/2.99 inference(monotonicity,[status(thm)],[15408])).
% 2.74/2.99 tff(15410,plain,
% 2.74/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 2.74/2.99 inference(transitivity,[status(thm)],[15409, 15407])).
% 2.74/2.99 tff(15411,plain,
% 2.74/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.74/2.99 inference(quant_inst,[status(thm)],[])).
% 2.74/2.99 tff(15412,plain,
% 2.74/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 2.74/2.99 inference(modus_ponens,[status(thm)],[15411, 15410])).
% 2.74/2.99 tff(15413,plain,
% 2.74/2.99 ($false),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[15412, 183, 15382, 5669, 15406, 15398])).
% 2.74/2.99 tff(15414,plain,((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(s(s(s(elem!1))))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.99 tff(15415,plain,
% 2.74/2.99 (~r(s(s(elem!1)), z)),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[15414, 15351, 10986, 236, 1099, 15367, 6875, 10668, 10672, 15378, 10674])).
% 2.74/2.99 tff(15416,plain,
% 2.74/2.99 (b(s(s(elem!1)), z)),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[523, 15415])).
% 2.74/2.99 tff(15417,plain,
% 2.74/2.99 (~b(s(s(s(elem!1))), z)),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[9440, 15416, 1099, 15367])).
% 2.74/2.99 tff(15418,plain,
% 2.74/2.99 (r(s(s(s(elem!1))), z)),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[3086, 47, 355, 15417])).
% 2.74/2.99 tff(15419,plain,
% 2.74/2.99 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[14315, 183, 15351, 15418])).
% 2.74/2.99 tff(15420,plain,
% 2.74/2.99 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[3693, 15419, 10672])).
% 2.74/2.99 tff(15421,plain,
% 2.74/2.99 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[1667, 15420, 15378, 15367])).
% 2.74/2.99 tff(15422,plain,
% 2.74/2.99 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[1557, 15421, 10674])).
% 2.74/2.99 tff(15423,plain,
% 2.74/2.99 (b(s(s(s(s(s(elem!1))))), s(elem!1)) <=> b(s(s(s(s(s(elem!1))))), s(s(z)))),
% 2.74/2.99 inference(monotonicity,[status(thm)],[3454])).
% 2.74/2.99 tff(15424,plain,
% 2.74/2.99 (b(s(s(s(s(s(elem!1))))), s(s(z))) <=> b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.74/2.99 inference(symmetry,[status(thm)],[15423])).
% 2.74/2.99 tff(15425,plain,
% 2.74/2.99 ((~b(s(s(s(s(s(elem!1))))), s(s(z)))) <=> (~b(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 2.74/2.99 inference(monotonicity,[status(thm)],[15424])).
% 2.74/2.99 tff(15426,plain,
% 2.74/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 2.74/2.99 inference(rewrite,[status(thm)],[])).
% 2.74/2.99 tff(15427,plain,
% 2.74/2.99 (((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 2.74/2.99 inference(rewrite,[status(thm)],[])).
% 2.74/2.99 tff(15428,plain,
% 2.74/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))))),
% 2.74/2.99 inference(monotonicity,[status(thm)],[15427])).
% 2.74/2.99 tff(15429,plain,
% 2.74/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 2.74/2.99 inference(transitivity,[status(thm)],[15428, 15426])).
% 2.74/2.99 tff(15430,plain,
% 2.74/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 2.74/2.99 inference(quant_inst,[status(thm)],[])).
% 2.74/2.99 tff(15431,plain,
% 2.74/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 2.74/2.99 inference(modus_ponens,[status(thm)],[15430, 15429])).
% 2.74/2.99 tff(15432,plain,
% 2.74/2.99 (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[15431, 183, 15351, 15418])).
% 2.74/2.99 tff(15433,plain,
% 2.74/2.99 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[913, 47, 10986, 15432])).
% 2.74/2.99 tff(15434,plain,
% 2.74/2.99 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 2.74/2.99 inference(monotonicity,[status(thm)],[3453])).
% 2.74/2.99 tff(15435,plain,
% 2.74/2.99 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(s(z)))))),
% 2.74/2.99 inference(monotonicity,[status(thm)],[10627])).
% 2.74/2.99 tff(15436,plain,
% 2.74/2.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(elem!1))))))),
% 2.74/2.99 inference(rewrite,[status(thm)],[])).
% 2.74/2.99 tff(15437,plain,
% 2.74/2.99 (((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z))) <=> ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(elem!1))))))),
% 2.74/2.99 inference(rewrite,[status(thm)],[])).
% 2.74/2.99 tff(15438,plain,
% 2.74/2.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(elem!1)))))))),
% 2.74/2.99 inference(monotonicity,[status(thm)],[15437])).
% 2.74/2.99 tff(15439,plain,
% 2.74/2.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(elem!1))))))),
% 2.74/3.00 inference(transitivity,[status(thm)],[15438, 15436])).
% 2.74/3.00 tff(15440,plain,
% 2.74/3.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 2.74/3.00 inference(quant_inst,[status(thm)],[])).
% 2.74/3.00 tff(15441,plain,
% 2.74/3.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(elem!1)))))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[15440, 15439])).
% 2.74/3.00 tff(15442,plain,
% 2.74/3.00 (~b(z, s(s(s(elem!1))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[15441, 246, 15416, 236, 15378, 6875, 15433])).
% 2.74/3.00 tff(15443,plain,
% 2.74/3.00 ((z = s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[9177, 47, 15442])).
% 2.74/3.00 tff(15444,plain,
% 2.74/3.00 (r(z, s(s(s(elem!1))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[15443, 5369])).
% 2.74/3.00 tff(15445,plain,
% 2.74/3.00 (r(z, s(s(s(s(z)))))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[15444, 15435])).
% 2.74/3.00 tff(15446,plain,
% 2.74/3.00 (~b(s(z), s(s(elem!1)))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[5746, 246, 1056, 15416, 236])).
% 2.74/3.00 tff(15447,plain,
% 2.74/3.00 (r(s(z), s(s(elem!1)))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[233, 15446])).
% 2.74/3.00 tff(15448,plain,
% 2.74/3.00 (r(s(z), s(s(s(z))))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[15447, 14208])).
% 2.74/3.00 tff(15449,plain,
% 2.74/3.00 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(s(s(z)))))),
% 2.74/3.00 inference(transitivity,[status(thm)],[11007, 11006])).
% 2.74/3.00 tff(15450,plain,
% 2.74/3.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.74/3.00 inference(rewrite,[status(thm)],[])).
% 2.74/3.00 tff(15451,plain,
% 2.74/3.00 (((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.74/3.00 inference(rewrite,[status(thm)],[])).
% 2.74/3.00 tff(15452,plain,
% 2.74/3.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[15451])).
% 2.74/3.00 tff(15453,plain,
% 2.74/3.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.74/3.00 inference(transitivity,[status(thm)],[15452, 15450])).
% 2.74/3.00 tff(15454,plain,
% 2.74/3.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 2.74/3.00 inference(quant_inst,[status(thm)],[])).
% 2.74/3.00 tff(15455,plain,
% 2.74/3.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[15454, 15453])).
% 2.74/3.00 tff(15456,plain,
% 2.74/3.00 (~b(s(z), s(s(s(elem!1))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[15455, 246, 1056, 15416, 15420, 15367, 6875])).
% 2.74/3.00 tff(15457,plain,
% 2.74/3.00 (~b(elem!1, s(s(s(elem!1))))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[15456, 11012])).
% 2.74/3.00 tff(15458,plain,
% 2.74/3.00 (r(elem!1, s(s(s(elem!1))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[9483, 15457, 9481])).
% 2.74/3.00 tff(15459,plain,
% 2.74/3.00 (r(s(z), s(s(s(elem!1))))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[15458, 11009])).
% 2.74/3.00 tff(15460,plain,
% 2.74/3.00 (r(s(z), s(s(s(s(z)))))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[15459, 15449])).
% 2.74/3.00 tff(15461,plain,
% 2.74/3.00 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[10158, 15460, 236, 15448, 15445, 1056])).
% 2.74/3.00 tff(15462,plain,
% 2.74/3.00 (b(s(s(z)), s(s(s(s(z)))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[1531, 15461])).
% 2.74/3.00 tff(15463,plain,
% 2.74/3.00 (b(s(s(z)), s(s(s(elem!1))))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[15462, 15434])).
% 2.74/3.00 tff(15464,plain,
% 2.74/3.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(elem!1))))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.74/3.00 inference(rewrite,[status(thm)],[])).
% 2.74/3.00 tff(15465,plain,
% 2.74/3.00 (((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z))))) <=> ((~b(s(s(s(elem!1))), s(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(elem!1))))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.74/3.00 inference(rewrite,[status(thm)],[])).
% 2.74/3.00 tff(15466,plain,
% 2.74/3.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[15465])).
% 2.74/3.00 tff(15467,plain,
% 2.74/3.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.74/3.00 inference(transitivity,[status(thm)],[15466, 15464])).
% 2.74/3.00 tff(15468,plain,
% 2.74/3.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))))),
% 2.74/3.00 inference(quant_inst,[status(thm)],[])).
% 2.74/3.00 tff(15469,plain,
% 2.74/3.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(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(elem!1))))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[15468, 15467])).
% 2.74/3.00 tff(15470,plain,
% 2.74/3.00 (~b(s(s(s(s(s(elem!1))))), s(s(z)))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[15469, 246, 15420, 15463, 15433])).
% 2.74/3.00 tff(15471,plain,
% 2.74/3.00 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[15470, 15425])).
% 2.74/3.00 tff(15472,plain,
% 2.74/3.00 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[1795, 15471, 10792])).
% 2.74/3.00 tff(15473,plain,
% 2.74/3.00 ((s(s(z)) = s(s(elem!1))) <=> (s(elem!1) = s(s(elem!1)))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[3455])).
% 2.74/3.00 tff(15474,plain,
% 2.74/3.00 ((s(s(z)) = s(s(elem!1))) <=> (s(s(elem!1)) = s(elem!1))),
% 2.74/3.00 inference(transitivity,[status(thm)],[15473, 5462])).
% 2.74/3.00 tff(15475,plain,
% 2.74/3.00 ((~(s(s(z)) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[15474])).
% 2.74/3.00 tff(15476,plain,
% 2.74/3.00 (~(s(s(elem!1)) = s(elem!1))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[15275, 15475])).
% 2.74/3.00 tff(15477,plain,
% 2.74/3.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(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(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.74/3.00 inference(rewrite,[status(thm)],[])).
% 2.74/3.00 tff(15478,plain,
% 2.74/3.00 (((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(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(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.74/3.00 inference(rewrite,[status(thm)],[])).
% 2.74/3.00 tff(15479,plain,
% 2.74/3.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z))))))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[15478])).
% 2.74/3.00 tff(15480,plain,
% 2.74/3.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.74/3.00 inference(transitivity,[status(thm)],[15479, 15477])).
% 2.74/3.00 tff(15481,plain,
% 2.74/3.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.74/3.00 inference(quant_inst,[status(thm)],[])).
% 2.74/3.00 tff(15482,plain,
% 2.74/3.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z))))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[15481, 15480])).
% 2.74/3.00 tff(15483,plain,
% 2.74/3.00 (~b(s(s(elem!1)), s(s(z)))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[15482, 246, 15420, 15378, 15463, 15433])).
% 2.74/3.00 tff(15484,plain,
% 2.74/3.00 (~b(s(s(elem!1)), s(elem!1))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[15483, 10732])).
% 2.74/3.00 tff(15485,plain,
% 2.74/3.00 (r(s(s(elem!1)), s(elem!1))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[5644, 15484, 15476])).
% 2.74/3.00 tff(15486,plain,
% 2.74/3.00 ($false),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[1959, 15485, 15472, 15422])).
% 2.74/3.00 tff(15487,plain,((~b(s(z), z)) | (~(elem!1 = s(z))) | (~b(z, s(z))) | (elem!1 = s(s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.00 tff(15488,plain,
% 2.74/3.00 (~b(s(z), z)),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[15487, 15314, 15291, 15342, 15338, 15320, 15319, 53])).
% 2.74/3.00 tff(15489,plain,
% 2.74/3.00 (r(s(z), z)),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[1069, 15488])).
% 2.74/3.00 tff(15490,plain,
% 2.74/3.00 (~b(elem!1, z)),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[14060, 15488, 15315])).
% 2.74/3.00 tff(15491,plain,
% 2.74/3.00 (r(elem!1, z)),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[12008, 15490])).
% 2.74/3.00 tff(15492,plain,
% 2.74/3.00 (~r(s(s(elem!1)), z)),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[6720, 15489, 15319])).
% 2.74/3.00 tff(15493,plain,
% 2.74/3.00 (b(s(s(elem!1)), z)),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[523, 15492])).
% 2.74/3.00 tff(15494,plain,
% 2.74/3.00 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[11385, 246, 1100, 1099, 9221])).
% 2.74/3.00 tff(15495,plain,
% 2.74/3.00 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[1557, 15494, 1555])).
% 2.74/3.00 tff(15496,plain,
% 2.74/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 2.74/3.00 inference(rewrite,[status(thm)],[])).
% 2.74/3.00 tff(15497,plain,
% 2.74/3.00 (((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 2.74/3.00 inference(rewrite,[status(thm)],[])).
% 2.74/3.00 tff(15498,plain,
% 2.74/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(elem!1)))))))))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[15497])).
% 2.74/3.00 tff(15499,plain,
% 2.74/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 2.74/3.00 inference(transitivity,[status(thm)],[15498, 15496])).
% 2.74/3.00 tff(15500,plain,
% 2.74/3.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 2.74/3.00 inference(quant_inst,[status(thm)],[])).
% 2.74/3.00 tff(15501,plain,
% 2.74/3.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(elem!1)))))))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[15500, 15499])).
% 2.74/3.00 tff(15502,plain,
% 2.74/3.00 (~r(s(z), s(s(s(s(s(elem!1))))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[15501, 183, 1113, 15495])).
% 2.74/3.00 tff(15503,plain,
% 2.74/3.00 ((s(z) = s(s(s(s(s(elem!1)))))) | b(s(z), s(s(s(s(s(elem!1))))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[6253, 47, 15502])).
% 2.74/3.00 tff(15504,plain,
% 2.74/3.00 (b(s(z), s(s(s(s(s(elem!1))))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[15503, 6243])).
% 2.74/3.00 tff(15505,plain,
% 2.74/3.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))))),
% 2.74/3.00 inference(rewrite,[status(thm)],[])).
% 2.74/3.00 tff(15506,plain,
% 2.74/3.00 (((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))))),
% 2.74/3.00 inference(rewrite,[status(thm)],[])).
% 2.74/3.00 tff(15507,plain,
% 2.74/3.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1)))))))))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[15506])).
% 2.74/3.00 tff(15508,plain,
% 2.74/3.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))))),
% 2.74/3.00 inference(transitivity,[status(thm)],[15507, 15505])).
% 2.74/3.00 tff(15509,plain,
% 2.74/3.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 2.74/3.00 inference(quant_inst,[status(thm)],[])).
% 2.74/3.00 tff(15510,plain,
% 2.74/3.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1)))))))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[15509, 15508])).
% 2.74/3.00 tff(15511,plain,
% 2.74/3.00 ($false),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[15510, 246, 236, 9221, 6875, 15504])).
% 2.74/3.00 tff(15512,plain,((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(z), s(s(elem!1)))) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.00 tff(15513,plain,
% 2.74/3.00 (~b(s(s(s(s(s(elem!1))))), z)),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[15512, 1113, 6875, 236, 10674, 1100, 1099])).
% 2.74/3.00 tff(15514,plain,
% 2.74/3.00 (r(s(s(s(s(s(elem!1))))), z)),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[1601, 15513])).
% 2.74/3.00 tff(15515,plain,
% 2.74/3.00 (~r(s(z), s(s(s(s(s(elem!1))))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[14900, 15514, 1114])).
% 2.74/3.00 tff(15516,plain,
% 2.74/3.00 ((s(z) = s(s(s(s(s(elem!1)))))) | b(s(z), s(s(s(s(s(elem!1))))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[6253, 47, 15515])).
% 2.74/3.00 tff(15517,plain,
% 2.74/3.00 (b(s(z), s(s(s(s(s(elem!1))))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[15516, 6243])).
% 2.74/3.00 tff(15518,plain,
% 2.74/3.00 (r(elem!1, s(s(s(z)))) <=> r(s(z), s(s(s(z))))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[202])).
% 2.74/3.00 tff(15519,plain,
% 2.74/3.00 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 2.74/3.00 inference(symmetry,[status(thm)],[15518])).
% 2.74/3.00 tff(15520,plain,
% 2.74/3.00 (r(s(z), s(s(elem!1))) <=> r(elem!1, s(s(s(z))))),
% 2.74/3.00 inference(transitivity,[status(thm)],[14208, 15519])).
% 2.74/3.00 tff(15521,plain,
% 2.74/3.00 (r(elem!1, s(s(s(z))))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[1113, 15520])).
% 2.74/3.00 tff(15522,plain,
% 2.74/3.00 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[202])).
% 2.74/3.00 tff(15523,plain,
% 2.74/3.00 (r(s(z), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.74/3.00 inference(symmetry,[status(thm)],[15522])).
% 2.74/3.00 tff(15524,plain,
% 2.74/3.00 (r(elem!1, s(s(elem!1)))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[1113, 15523])).
% 2.74/3.00 tff(15525,plain,
% 2.74/3.00 (b(s(s(s(elem!1))), s(z))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[10834, 8493, 97])).
% 2.74/3.00 tff(15526,plain,
% 2.74/3.00 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[5176, 13844, 959])).
% 2.74/3.00 tff(15527,plain,
% 2.74/3.00 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[3693, 15526, 13922])).
% 2.74/3.01 tff(15528,plain,
% 2.74/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(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(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(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(z))))),
% 2.74/3.01 inference(rewrite,[status(thm)],[])).
% 2.74/3.01 tff(15529,plain,
% 2.74/3.01 (((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(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(z))))),
% 2.74/3.01 inference(rewrite,[status(thm)],[])).
% 2.74/3.01 tff(15530,plain,
% 2.74/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 2.74/3.01 inference(monotonicity,[status(thm)],[15529])).
% 2.74/3.01 tff(15531,plain,
% 2.74/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.74/3.01 inference(transitivity,[status(thm)],[15530, 15528])).
% 2.74/3.01 tff(15532,plain,
% 2.74/3.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.74/3.01 inference(quant_inst,[status(thm)],[])).
% 2.74/3.01 tff(15533,plain,
% 2.74/3.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))),
% 2.74/3.01 inference(modus_ponens,[status(thm)],[15532, 15531])).
% 2.74/3.01 tff(15534,plain,
% 2.74/3.01 ($false),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[15533, 246, 15527, 15525, 6875, 14866])).
% 2.74/3.01 tff(15535,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~(s(s(s(z))) = s(s(elem!1)))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.01 tff(15536,plain,
% 2.74/3.01 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[15535, 959, 14866, 6875, 2266, 430])).
% 2.74/3.01 tff(15537,plain,
% 2.74/3.01 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[1702, 15536])).
% 2.74/3.01 tff(15538,plain,
% 2.74/3.01 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[9446, 15537, 2266])).
% 2.74/3.01 tff(15539,plain,
% 2.74/3.01 (~b(s(s(s(elem!1))), z)),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[13965, 15538, 2246, 413, 2266])).
% 2.74/3.01 tff(15540,plain,
% 2.74/3.01 (r(s(s(s(elem!1))), z)),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[3086, 47, 355, 15539])).
% 2.74/3.01 tff(15541,plain,
% 2.74/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 2.74/3.01 inference(rewrite,[status(thm)],[])).
% 2.74/3.01 tff(15542,plain,
% 2.74/3.01 (((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 2.74/3.01 inference(rewrite,[status(thm)],[])).
% 2.74/3.01 tff(15543,plain,
% 2.74/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))))),
% 2.74/3.01 inference(monotonicity,[status(thm)],[15542])).
% 2.74/3.01 tff(15544,plain,
% 2.74/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 2.74/3.01 inference(transitivity,[status(thm)],[15543, 15541])).
% 2.74/3.01 tff(15545,plain,
% 2.74/3.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 2.74/3.01 inference(quant_inst,[status(thm)],[])).
% 2.74/3.01 tff(15546,plain,
% 2.74/3.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 2.74/3.01 inference(modus_ponens,[status(thm)],[15545, 15544])).
% 2.74/3.01 tff(15547,plain,
% 2.74/3.01 (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[15546, 183, 959, 5669, 15540])).
% 2.74/3.01 tff(15548,plain,
% 2.74/3.01 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[913, 47, 9348, 15547])).
% 2.74/3.01 tff(15549,plain,
% 2.74/3.01 (~r(s(s(s(s(z)))), s(z))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[9582, 15538, 2246, 602, 6, 1099])).
% 2.74/3.01 tff(15550,plain,
% 2.74/3.01 (b(s(s(s(s(z)))), s(z))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[6103, 15549])).
% 2.74/3.01 tff(15551,plain,
% 2.74/3.01 (b(s(s(s(elem!1))), s(z))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[10834, 15550, 2266])).
% 2.74/3.01 tff(15552,plain,
% 2.74/3.01 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[14315, 183, 5669, 15540])).
% 2.74/3.01 tff(15553,plain,
% 2.74/3.01 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[3693, 15552, 9124])).
% 2.74/3.01 tff(15554,plain,
% 2.74/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(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(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(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(elem!1))), s(z))))),
% 2.74/3.01 inference(rewrite,[status(thm)],[])).
% 2.74/3.01 tff(15555,plain,
% 2.74/3.01 (((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.74/3.01 inference(rewrite,[status(thm)],[])).
% 2.74/3.01 tff(15556,plain,
% 2.74/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(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(elem!1))), s(z)))))),
% 2.74/3.01 inference(monotonicity,[status(thm)],[15555])).
% 2.74/3.01 tff(15557,plain,
% 2.74/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(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(elem!1))), s(z))))),
% 2.74/3.01 inference(transitivity,[status(thm)],[15556, 15554])).
% 2.74/3.01 tff(15558,plain,
% 2.74/3.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.74/3.01 inference(quant_inst,[status(thm)],[])).
% 2.74/3.01 tff(15559,plain,
% 2.74/3.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))),
% 2.74/3.01 inference(modus_ponens,[status(thm)],[15558, 15557])).
% 2.74/3.01 tff(15560,plain,
% 2.74/3.01 ($false),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[15559, 246, 15553, 15551, 15548, 14866])).
% 2.74/3.01 tff(15561,plain,((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(elem!1)))) | (~(s(z) = elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.01 tff(15562,plain,
% 2.74/3.01 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[15561, 15517, 15514, 2246, 15521, 15524, 3451, 1099, 6875, 430])).
% 2.74/3.01 tff(15563,plain,
% 2.74/3.01 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[1557, 15562, 10674])).
% 2.74/3.01 tff(15564,plain,
% 2.74/3.01 (~b(s(s(s(elem!1))), z)),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[13965, 1659, 2246, 413, 97])).
% 2.74/3.01 tff(15565,plain,
% 2.74/3.01 (r(s(s(s(elem!1))), z)),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[3086, 47, 355, 15564])).
% 2.74/3.01 tff(15566,plain,
% 2.74/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.74/3.01 inference(rewrite,[status(thm)],[])).
% 2.74/3.01 tff(15567,plain,
% 2.74/3.01 (((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.74/3.01 inference(rewrite,[status(thm)],[])).
% 2.74/3.01 tff(15568,plain,
% 2.74/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 2.74/3.01 inference(monotonicity,[status(thm)],[15567])).
% 2.74/3.01 tff(15569,plain,
% 2.74/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.74/3.01 inference(transitivity,[status(thm)],[15568, 15566])).
% 2.74/3.01 tff(15570,plain,
% 2.74/3.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.74/3.01 inference(quant_inst,[status(thm)],[])).
% 2.74/3.01 tff(15571,plain,
% 2.74/3.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 2.74/3.01 inference(modus_ponens,[status(thm)],[15570, 15569])).
% 2.74/3.01 tff(15572,plain,
% 2.74/3.01 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[15571, 246, 1100, 1099, 946, 1659])).
% 2.74/3.01 tff(15573,plain,
% 2.74/3.01 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[3693, 15572, 13922])).
% 2.74/3.01 tff(15574,plain,
% 2.74/3.01 ($false),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[14315, 183, 15573, 5669, 15565])).
% 2.74/3.01 tff(15575,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~(s(s(s(z))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.01 tff(15576,plain,
% 2.74/3.01 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[15575, 15514, 1100, 1099, 15563, 2246, 15521, 3452])).
% 2.74/3.01 tff(15577,plain,
% 2.74/3.01 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[9446, 15576, 3452])).
% 2.74/3.01 tff(15578,plain,
% 2.74/3.01 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[1702, 15577])).
% 2.74/3.01 tff(15579,plain,
% 2.74/3.01 (~r(s(s(s(s(z)))), s(z))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[8491, 15578, 430])).
% 2.74/3.01 tff(15580,plain,
% 2.74/3.01 (b(s(s(s(s(z)))), s(z))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[6103, 15579])).
% 2.74/3.01 tff(15581,plain,
% 2.74/3.01 (b(s(s(s(elem!1))), s(z))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[10834, 15580, 3452])).
% 2.74/3.01 tff(15582,plain,
% 2.74/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))),
% 2.74/3.01 inference(rewrite,[status(thm)],[])).
% 2.74/3.01 tff(15583,plain,
% 2.74/3.01 (((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))),
% 2.74/3.01 inference(rewrite,[status(thm)],[])).
% 2.74/3.01 tff(15584,plain,
% 2.74/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z))))),
% 2.74/3.01 inference(monotonicity,[status(thm)],[15583])).
% 2.74/3.01 tff(15585,plain,
% 2.74/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))),
% 2.74/3.01 inference(transitivity,[status(thm)],[15584, 15582])).
% 2.74/3.01 tff(15586,plain,
% 2.74/3.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))),
% 2.74/3.01 inference(quant_inst,[status(thm)],[])).
% 2.74/3.01 tff(15587,plain,
% 2.74/3.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z))),
% 2.74/3.01 inference(modus_ponens,[status(thm)],[15586, 15585])).
% 2.74/3.01 tff(15588,plain,
% 2.74/3.01 (~b(s(s(s(elem!1))), z)),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[15587, 246, 236, 1099, 15563, 15581, 15517])).
% 2.74/3.01 tff(15589,plain,
% 2.74/3.01 (r(s(s(s(elem!1))), z)),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[3086, 47, 355, 15588])).
% 2.74/3.01 tff(15590,plain,
% 2.74/3.01 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[15533, 246, 15581, 6875, 15517])).
% 2.74/3.01 tff(15591,plain,
% 2.74/3.01 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[3693, 15590, 10672])).
% 2.74/3.01 tff(15592,plain,
% 2.74/3.01 ($false),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[14315, 183, 15591, 15514, 15589])).
% 2.74/3.02 tff(15593,plain,((~r(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.02 tff(15594,plain,
% 2.74/3.02 (~r(s(z), s(s(elem!1)))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[15593, 15338, 15291, 15320, 53, 15493, 15491, 15489, 15314])).
% 2.74/3.02 tff(15595,plain,
% 2.74/3.02 (b(s(z), s(s(elem!1)))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[233, 15594])).
% 2.74/3.02 tff(15596,plain,
% 2.74/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))))),
% 2.74/3.02 inference(rewrite,[status(thm)],[])).
% 2.74/3.02 tff(15597,plain,
% 2.74/3.02 (((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))))),
% 2.74/3.02 inference(rewrite,[status(thm)],[])).
% 2.74/3.02 tff(15598,plain,
% 2.74/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1))))))),
% 2.74/3.02 inference(monotonicity,[status(thm)],[15597])).
% 2.74/3.02 tff(15599,plain,
% 2.74/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))))),
% 2.74/3.02 inference(transitivity,[status(thm)],[15598, 15596])).
% 2.74/3.02 tff(15600,plain,
% 2.74/3.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))),
% 2.74/3.02 inference(quant_inst,[status(thm)],[])).
% 2.74/3.02 tff(15601,plain,
% 2.74/3.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1))))),
% 2.74/3.02 inference(modus_ponens,[status(thm)],[15600, 15599])).
% 2.74/3.02 tff(15602,plain,
% 2.74/3.02 ($false),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[15601, 246, 15493, 15291, 15320, 15595])).
% 2.74/3.02 tff(15603,plain,(b(s(s(s(z))), s(z)) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/3.02 tff(15604,plain,
% 2.74/3.02 (b(s(s(s(z))), s(z))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[15603, 1])).
% 2.74/3.02 tff(15605,plain,
% 2.74/3.02 (~(s(z) = elem!1)),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[2290, 15604, 1])).
% 2.74/3.02 tff(15606,plain,
% 2.74/3.02 (~(elem!1 = s(z))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[2279, 15605])).
% 2.74/3.02 tff(15607,plain,
% 2.74/3.02 (b(elem!1, s(z))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[214, 12303, 15606])).
% 2.74/3.02 tff(15608,plain,
% 2.74/3.02 (~r(s(z), elem!1)),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[2725, 2246, 1114])).
% 2.74/3.02 tff(15609,plain,
% 2.74/3.02 (b(s(z), elem!1)),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[1034, 15608, 10])).
% 2.74/3.02 tff(15610,plain,
% 2.74/3.02 (~r(s(s(s(z))), elem!1)),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[14949, 4651, 119, 216, 2246])).
% 2.74/3.02 tff(15611,plain,
% 2.74/3.02 (s(s(s(z))) = elem!1),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[647, 15610, 1])).
% 2.74/3.02 tff(15612,plain,
% 2.74/3.02 (b(s(z), s(s(s(z)))) <=> b(s(z), elem!1)),
% 2.74/3.02 inference(monotonicity,[status(thm)],[15611])).
% 2.74/3.02 tff(15613,plain,
% 2.74/3.02 (b(s(z), elem!1) <=> b(s(z), s(s(s(z))))),
% 2.74/3.02 inference(symmetry,[status(thm)],[15612])).
% 2.74/3.02 tff(15614,plain,
% 2.74/3.02 (b(s(z), s(s(s(z))))),
% 2.74/3.02 inference(modus_ponens,[status(thm)],[1044, 15613])).
% 2.74/3.02 tff(15615,plain,
% 2.74/3.02 (~r(s(s(s(z))), z)),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[13364, 53, 1114])).
% 2.74/3.02 tff(15616,plain,
% 2.74/3.02 (b(s(s(s(z))), z)),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[995, 15615])).
% 2.74/3.02 tff(15617,plain,
% 2.74/3.02 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[4659, 15616, 1100, 12832])).
% 2.74/3.02 tff(15618,plain,
% 2.74/3.02 (~(elem!1 = s(s(s(z))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[6830, 2, 2001])).
% 2.74/3.02 tff(15619,plain,
% 2.74/3.02 (~(s(s(s(z))) = elem!1)),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[1677, 15618])).
% 2.74/3.02 tff(15620,plain,
% 2.74/3.02 (r(s(s(s(z))), elem!1)),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[647, 15619, 1])).
% 2.74/3.02 tff(15621,plain,
% 2.74/3.02 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[642, 15620, 216])).
% 2.74/3.02 tff(15622,plain,
% 2.74/3.02 ($false),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[689, 15621, 15617, 119])).
% 2.74/3.02 tff(15623,plain,(b(s(s(s(z))), s(z)) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | b(s(s(s(z))), elem!1) | (~r(s(z), z)) | (~r(z, s(z))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.02 tff(15624,plain,
% 2.74/3.02 (b(s(s(s(z))), s(z))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[15623, 14945, 216, 119, 1, 1114, 171, 2001])).
% 2.74/3.02 tff(15625,plain,
% 2.74/3.02 (elem!1 = s(s(s(z)))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[1677, 15611])).
% 2.74/3.02 tff(15626,plain,
% 2.74/3.02 (s(s(s(z))) = elem!1),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[3013, 2292])).
% 2.74/3.02 tff(15627,plain,
% 2.74/3.02 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[5623, 15626])).
% 2.74/3.02 tff(15628,plain,
% 2.74/3.02 (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[3815, 15627])).
% 2.74/3.02 tff(15629,plain,
% 2.74/3.02 (r(s(s(s(s(s(elem!1))))), elem!1) <=> r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.74/3.02 inference(monotonicity,[status(thm)],[2292])).
% 2.74/3.02 tff(15630,plain,
% 2.74/3.02 (r(s(s(s(s(s(elem!1))))), s(s(s(z)))) <=> r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.74/3.02 inference(symmetry,[status(thm)],[15629])).
% 2.74/3.02 tff(15631,plain,
% 2.74/3.02 (b(s(s(s(z))), s(z))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[6830, 2292, 2001])).
% 2.74/3.02 tff(15632,plain,
% 2.74/3.02 (b(s(z), elem!1) <=> b(s(z), s(s(s(z))))),
% 2.74/3.02 inference(monotonicity,[status(thm)],[2292])).
% 2.74/3.02 tff(15633,plain,
% 2.74/3.02 (b(s(z), s(s(s(z))))),
% 2.74/3.02 inference(modus_ponens,[status(thm)],[1044, 15632])).
% 2.74/3.02 tff(15634,plain,
% 2.74/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.74/3.02 inference(rewrite,[status(thm)],[])).
% 2.74/3.02 tff(15635,plain,
% 2.74/3.02 (((~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), z))) <=> ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.74/3.02 inference(rewrite,[status(thm)],[])).
% 2.74/3.02 tff(15636,plain,
% 2.74/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 2.74/3.02 inference(monotonicity,[status(thm)],[15635])).
% 2.74/3.02 tff(15637,plain,
% 2.74/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.74/3.02 inference(transitivity,[status(thm)],[15636, 15634])).
% 2.74/3.02 tff(15638,plain,
% 2.74/3.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 2.74/3.02 inference(quant_inst,[status(thm)],[])).
% 2.74/3.02 tff(15639,plain,
% 2.74/3.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 2.74/3.02 inference(modus_ponens,[status(thm)],[15638, 15637])).
% 2.74/3.02 tff(15640,plain,
% 2.74/3.02 (~b(s(s(s(s(s(elem!1))))), z)),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[15639, 246, 2401, 2003, 4651, 1885])).
% 2.74/3.02 tff(15641,plain,
% 2.74/3.02 (r(s(s(s(s(s(elem!1))))), z)),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[1601, 15640])).
% 2.74/3.02 tff(15642,plain,
% 2.74/3.02 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[2935, 246, 2401, 2003, 1885])).
% 2.74/3.02 tff(15643,plain,
% 2.74/3.02 (r(s(s(s(s(s(elem!1))))), s(z))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[6447, 15642])).
% 2.74/3.02 tff(15644,plain,
% 2.74/3.02 ($false),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[11167, 183, 1114, 15643, 15641])).
% 2.74/3.02 tff(15645,plain,((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.02 tff(15646,plain,
% 2.74/3.02 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[15645, 15633, 1114, 15631, 4651])).
% 2.74/3.02 tff(15647,plain,
% 2.74/3.02 (r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[1626, 15646])).
% 2.74/3.02 tff(15648,plain,
% 2.74/3.02 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.74/3.02 inference(modus_ponens,[status(thm)],[15647, 15630])).
% 2.74/3.02 tff(15649,plain,
% 2.74/3.02 (s(elem!1) = s(s(s(s(z))))),
% 2.74/3.02 inference(monotonicity,[status(thm)],[2292])).
% 2.74/3.02 tff(15650,plain,
% 2.74/3.02 ((s(s(s(s(s(elem!1))))) = s(elem!1)) <=> (s(s(s(s(s(elem!1))))) = s(s(s(s(z)))))),
% 2.74/3.02 inference(monotonicity,[status(thm)],[15649])).
% 2.74/3.02 tff(15651,plain,
% 2.74/3.02 ((s(s(s(s(s(elem!1))))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))),
% 2.74/3.02 inference(transitivity,[status(thm)],[15650, 1483])).
% 2.74/3.02 tff(15652,plain,
% 2.74/3.02 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(elem!1))),
% 2.74/3.02 inference(symmetry,[status(thm)],[15651])).
% 2.74/3.02 tff(15653,plain,
% 2.74/3.02 ((~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(s(elem!1))))) = s(elem!1)))),
% 2.74/3.02 inference(monotonicity,[status(thm)],[15652])).
% 2.74/3.02 tff(15654,plain,
% 2.74/3.02 (~(s(s(s(s(s(elem!1))))) = s(elem!1))),
% 2.74/3.02 inference(modus_ponens,[status(thm)],[1501, 15653])).
% 2.74/3.02 tff(15655,plain,
% 2.74/3.02 (r(s(elem!1), elem!1)),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[5548, 15626, 2593])).
% 2.74/3.02 tff(15656,plain,
% 2.74/3.02 (~(s(s(elem!1)) = elem!1)),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[8772, 2292, 8770])).
% 2.74/3.02 tff(15657,plain,
% 2.74/3.02 (~(s(s(elem!1)) = s(elem!1))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[5640, 15656])).
% 2.74/3.02 tff(15658,plain,
% 2.74/3.02 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(s(s(z))))),
% 2.74/3.02 inference(monotonicity,[status(thm)],[2292])).
% 2.74/3.02 tff(15659,plain,
% 2.74/3.02 (r(s(s(elem!1)), s(s(s(z))))),
% 2.74/3.02 inference(modus_ponens,[status(thm)],[216, 15658])).
% 2.74/3.02 tff(15660,plain,
% 2.74/3.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.74/3.02 inference(rewrite,[status(thm)],[])).
% 2.74/3.02 tff(15661,plain,
% 2.74/3.02 (((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.74/3.02 inference(rewrite,[status(thm)],[])).
% 2.74/3.02 tff(15662,plain,
% 2.74/3.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 2.74/3.02 inference(monotonicity,[status(thm)],[15661])).
% 2.74/3.02 tff(15663,plain,
% 2.74/3.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.74/3.02 inference(transitivity,[status(thm)],[15662, 15660])).
% 2.74/3.02 tff(15664,plain,
% 2.74/3.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.74/3.02 inference(quant_inst,[status(thm)],[])).
% 2.74/3.02 tff(15665,plain,
% 2.74/3.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 2.74/3.02 inference(modus_ponens,[status(thm)],[15664, 15663])).
% 2.74/3.02 tff(15666,plain,
% 2.74/3.02 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[15665, 183, 15659, 15647])).
% 2.74/3.02 tff(15667,plain,
% 2.74/3.02 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[1557, 15666, 15627])).
% 2.74/3.02 tff(15668,plain,
% 2.74/3.02 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[14580, 15667, 216, 15657, 15655, 15654, 15648])).
% 2.74/3.02 tff(15669,plain,
% 2.74/3.02 (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[10519, 183, 15659, 15647])).
% 2.74/3.02 tff(15670,plain,
% 2.74/3.02 ($false),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[1547, 47, 15669, 15668, 15628])).
% 2.74/3.02 tff(15671,plain,((~(elem!1 = s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(z))) | (s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.02 tff(15672,plain,
% 2.74/3.02 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[15671, 15625, 1114, 4651, 1044, 216, 2001, 4234])).
% 2.74/3.02 tff(15673,plain,
% 2.74/3.02 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[1702, 15672])).
% 2.74/3.02 tff(15674,plain,
% 2.74/3.02 (~b(s(z), s(s(s(z))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[7450, 15673, 171, 4651, 15624])).
% 2.74/3.02 tff(15675,plain,
% 2.74/3.02 ($false),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[15674, 15614])).
% 2.74/3.02 tff(15676,plain,((~b(z, s(s(s(z))))) | (~b(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | b(s(s(s(z))), elem!1) | (s(s(s(z))) = s(s(elem!1))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.02 tff(15677,plain,
% 2.74/3.02 (~b(z, s(s(s(z))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[15676, 15609, 171, 1114, 216, 12325, 1, 7736, 2246])).
% 2.74/3.02 tff(15678,plain,
% 2.74/3.02 (~(s(s(s(z))) = elem!1)),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[13536, 15677])).
% 2.74/3.02 tff(15679,plain,
% 2.74/3.02 (b(s(s(s(z))), s(z))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[15623, 14945, 216, 7736, 1, 1114, 171, 12325])).
% 2.74/3.02 tff(15680,plain,
% 2.74/3.02 (r(z, s(s(s(z))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[6165, 15677])).
% 2.74/3.02 tff(15681,plain,
% 2.74/3.02 (elem!1 = s(s(s(z)))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[12329, 15680, 15609, 1114, 3, 15679, 2246])).
% 2.74/3.02 tff(15682,plain,
% 2.74/3.02 ($false),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[3013, 15681, 15678])).
% 2.74/3.02 tff(15683,plain,((~r(elem!1, z)) | (~r(s(z), z)) | (elem!1 = s(z)) | (~r(z, s(z))) | (~r(s(s(elem!1)), elem!1)) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/3.02 tff(15684,plain,
% 2.74/3.02 (~r(s(z), z)),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[15683, 2246, 15606, 171, 14545, 1])).
% 2.74/3.02 tff(15685,plain,
% 2.74/3.02 (b(s(z), z)),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[1069, 15684])).
% 2.74/3.02 tff(15686,plain,
% 2.74/3.02 (~r(s(s(elem!1)), s(z))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[11730, 217, 14545])).
% 2.74/3.02 tff(15687,plain,
% 2.74/3.02 (b(s(s(elem!1)), s(z))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[197, 15686])).
% 2.74/3.02 tff(15688,plain,
% 2.74/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 2.74/3.02 inference(rewrite,[status(thm)],[])).
% 2.74/3.02 tff(15689,plain,
% 2.74/3.02 (((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 2.74/3.02 inference(rewrite,[status(thm)],[])).
% 2.74/3.02 tff(15690,plain,
% 2.74/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z)))))),
% 2.86/3.02 inference(monotonicity,[status(thm)],[15689])).
% 2.86/3.02 tff(15691,plain,
% 2.86/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 2.86/3.02 inference(transitivity,[status(thm)],[15690, 15688])).
% 2.86/3.02 tff(15692,plain,
% 2.86/3.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))),
% 2.86/3.02 inference(quant_inst,[status(thm)],[])).
% 2.86/3.02 tff(15693,plain,
% 2.86/3.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z)))),
% 2.86/3.02 inference(modus_ponens,[status(thm)],[15692, 15691])).
% 2.86/3.02 tff(15694,plain,
% 2.86/3.02 (~b(s(z), s(s(elem!1)))),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[15693, 246, 11962, 15687, 1056, 2001, 1100])).
% 2.86/3.02 tff(15695,plain,
% 2.86/3.02 ($false),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[233, 15694, 14968])).
% 2.86/3.02 tff(15696,plain,((~r(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.02 tff(15697,plain,
% 2.86/3.02 (~r(s(z), elem!1)),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[15696, 15685, 15607, 15293])).
% 2.86/3.02 tff(15698,plain,
% 2.86/3.02 (b(s(z), elem!1)),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[1034, 15697, 15605])).
% 2.86/3.02 tff(15699,plain,
% 2.86/3.02 ($false),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[12312, 246, 11962, 15685, 15698, 15607])).
% 2.86/3.02 tff(15700,plain,((~r(elem!1, z)) | (~r(z, s(z))) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.86/3.02 tff(15701,plain,
% 2.86/3.02 (~r(elem!1, z)),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[15700, 170, 1])).
% 2.86/3.02 tff(15702,plain,
% 2.86/3.02 (b(elem!1, z)),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[12008, 15701])).
% 2.86/3.02 tff(15703,plain,
% 2.86/3.02 (~r(elem!1, z)),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[15700, 171, 1])).
% 2.86/3.02 tff(15704,plain,
% 2.86/3.02 (b(elem!1, z)),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[12008, 15703])).
% 2.86/3.02 tff(15705,plain,
% 2.86/3.02 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[5804, 15605])).
% 2.86/3.02 tff(15706,plain,
% 2.86/3.02 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[12070, 246, 201, 235, 15604])).
% 2.86/3.02 tff(15707,plain,
% 2.86/3.02 (r(s(s(s(z))), s(s(elem!1)))),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[689, 15706, 15705])).
% 2.86/3.02 tff(15708,plain,
% 2.86/3.02 (~r(s(s(s(z))), elem!1)),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[642, 15707, 14545])).
% 2.86/3.02 tff(15709,plain,
% 2.86/3.02 (s(s(s(z))) = elem!1),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[647, 15708, 1])).
% 2.86/3.02 tff(15710,plain,
% 2.86/3.02 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(elem!1)), elem!1)),
% 2.86/3.02 inference(monotonicity,[status(thm)],[15709])).
% 2.86/3.02 tff(15711,plain,
% 2.86/3.02 ((~b(s(s(elem!1)), s(s(s(z))))) <=> (~b(s(s(elem!1)), elem!1))),
% 2.86/3.02 inference(monotonicity,[status(thm)],[15710])).
% 2.86/3.02 tff(15712,plain,
% 2.86/3.02 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[3488, 246, 201, 235, 15604])).
% 2.86/3.02 tff(15713,plain,
% 2.86/3.02 (~b(s(s(elem!1)), elem!1)),
% 2.86/3.02 inference(modus_ponens,[status(thm)],[15712, 15711])).
% 2.86/3.02 tff(15714,plain,
% 2.86/3.02 (~(s(s(elem!1)) = s(s(s(z))))),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[421, 15705])).
% 2.86/3.02 tff(15715,plain,
% 2.86/3.02 (elem!1 = s(s(s(z)))),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[1677, 15709])).
% 2.86/3.02 tff(15716,plain,
% 2.86/3.02 (b(elem!1, s(z))),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[2297, 15715, 15604])).
% 2.86/3.02 tff(15717,plain,
% 2.86/3.02 ($false),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[2262, 246, 11962, 1051, 1056, 2001])).
% 2.86/3.02 tff(15718,plain,((~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.02 tff(15719,plain,
% 2.86/3.02 (~b(s(z), z)),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[15718, 2001, 1051])).
% 2.86/3.02 tff(15720,plain,
% 2.86/3.02 (r(s(z), z)),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[1069, 15719])).
% 2.86/3.02 tff(15721,plain,
% 2.86/3.02 (b(z, s(s(s(z))))),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[13536, 1673])).
% 2.86/3.02 tff(15722,plain,
% 2.86/3.02 (elem!1 = s(s(s(z)))),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[1677, 1673])).
% 2.86/3.02 tff(15723,plain,
% 2.86/3.02 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[15671, 1044, 15722, 15721, 15720, 14545, 2001, 8770])).
% 2.86/3.02 tff(15724,plain,
% 2.86/3.02 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[11094, 13050, 1673])).
% 2.86/3.02 tff(15725,plain,
% 2.86/3.02 ($false),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[1702, 15724, 15723])).
% 2.86/3.02 tff(15726,plain,((~b(s(z), elem!1)) | (~(s(s(s(z))) = elem!1)) | (~b(elem!1, s(z))) | (s(s(elem!1)) = s(s(s(z)))) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.02 tff(15727,plain,
% 2.86/3.02 (~b(s(z), elem!1)),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[15726, 15709, 15716, 15714, 1051])).
% 2.86/3.02 tff(15728,plain,
% 2.86/3.02 (r(s(z), elem!1)),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[1034, 15727, 15605])).
% 2.86/3.02 tff(15729,plain,
% 2.86/3.02 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[5623, 15709])).
% 2.86/3.02 tff(15730,plain,
% 2.86/3.02 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[13340, 15728, 1051, 15709, 15729])).
% 2.86/3.02 tff(15731,plain,
% 2.86/3.02 (r(s(s(elem!1)), elem!1)),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[156, 5457, 145])).
% 2.86/3.02 tff(15732,plain,
% 2.86/3.02 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[1551, 7043, 15731])).
% 2.86/3.02 tff(15733,plain,
% 2.86/3.02 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[2307, 183, 217, 7043])).
% 2.86/3.02 tff(15734,plain,
% 2.86/3.02 (b(s(s(s(s(s(elem!1))))), s(z))),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[2311, 47, 331, 15733])).
% 2.86/3.02 tff(15735,plain,
% 2.86/3.02 (~r(s(z), s(s(elem!1)))),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[223, 183, 217, 15731])).
% 2.86/3.02 tff(15736,plain,
% 2.86/3.02 (b(s(z), s(s(elem!1)))),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[233, 15735])).
% 2.86/3.02 tff(15737,plain,
% 2.86/3.02 (b(elem!1, s(z))),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[2297, 15722, 2003])).
% 2.86/3.02 tff(15738,plain,
% 2.86/3.02 (b(s(s(elem!1)), s(z))),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[2141, 15737, 145, 217])).
% 2.86/3.02 tff(15739,plain,
% 2.86/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 2.86/3.02 inference(rewrite,[status(thm)],[])).
% 2.86/3.02 tff(15740,plain,
% 2.86/3.02 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 2.86/3.02 inference(rewrite,[status(thm)],[])).
% 2.86/3.02 tff(15741,plain,
% 2.86/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z)))))),
% 2.86/3.03 inference(monotonicity,[status(thm)],[15740])).
% 2.86/3.03 tff(15742,plain,
% 2.86/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 2.86/3.03 inference(transitivity,[status(thm)],[15741, 15739])).
% 2.86/3.03 tff(15743,plain,
% 2.86/3.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.86/3.03 inference(quant_inst,[status(thm)],[])).
% 2.86/3.03 tff(15744,plain,
% 2.86/3.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z)))),
% 2.86/3.03 inference(modus_ponens,[status(thm)],[15743, 15742])).
% 2.86/3.03 tff(15745,plain,
% 2.86/3.03 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[15744, 246, 15738, 15736, 15734])).
% 2.86/3.03 tff(15746,plain,
% 2.86/3.03 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[1557, 15745, 15732])).
% 2.86/3.03 tff(15747,plain,
% 2.86/3.03 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(elem!1)))),
% 2.86/3.03 inference(monotonicity,[status(thm)],[15746])).
% 2.86/3.03 tff(15748,plain,
% 2.86/3.03 (s(s(s(s(elem!1)))) = s(elem!1)),
% 2.86/3.03 inference(transitivity,[status(thm)],[326, 15747, 92])).
% 2.86/3.03 tff(15749,plain,
% 2.86/3.03 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(elem!1))),
% 2.86/3.03 inference(monotonicity,[status(thm)],[15748])).
% 2.86/3.03 tff(15750,plain,
% 2.86/3.03 (inj_0(s(elem!1)) = inj_0(s(s(s(s(elem!1)))))),
% 2.86/3.03 inference(symmetry,[status(thm)],[15749])).
% 2.86/3.03 tff(15751,plain,
% 2.86/3.03 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.86/3.03 inference(transitivity,[status(thm)],[1673, 3154, 15750, 351])).
% 2.86/3.03 tff(15752,plain,
% 2.86/3.03 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 2.86/3.03 inference(monotonicity,[status(thm)],[15751])).
% 2.86/3.03 tff(15753,plain,
% 2.86/3.03 (s(s(z)) = s(s(elem!1))),
% 2.86/3.03 inference(transitivity,[status(thm)],[25, 15752, 103])).
% 2.86/3.03 tff(15754,plain,
% 2.86/3.03 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.86/3.03 inference(monotonicity,[status(thm)],[15753])).
% 2.86/3.03 tff(15755,plain,
% 2.86/3.03 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.86/3.03 inference(symmetry,[status(thm)],[15754])).
% 2.86/3.03 tff(15756,plain,
% 2.86/3.03 (s(s(s(s(z)))) = s(z)),
% 2.86/3.03 inference(transitivity,[status(thm)],[5378, 108, 15755, 1486])).
% 2.86/3.03 tff(15757,plain,
% 2.86/3.03 ($false),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[1713, 15756])).
% 2.86/3.03 tff(15758,plain,((~(s(s(s(z))) = elem!1)) | (~r(s(z), elem!1)) | b(s(s(elem!1)), elem!1) | (~b(s(s(s(z))), s(z))) | b(s(s(s(s(s(elem!1))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.86/3.03 tff(15759,plain,
% 2.86/3.03 ($false),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[15758, 15730, 15728, 15604, 15709, 15713])).
% 2.86/3.03 tff(15760,plain,((~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | b(s(s(s(z))), elem!1) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.03 tff(15761,plain,
% 2.86/3.03 (~b(s(s(elem!1)), s(z))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[15760, 11974, 1, 1051])).
% 2.86/3.03 tff(15762,plain,
% 2.86/3.03 (r(s(s(elem!1)), s(z))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[197, 15761])).
% 2.86/3.03 tff(15763,plain,
% 2.86/3.03 (~r(elem!1, s(z))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[11704, 15762, 14545])).
% 2.86/3.03 tff(15764,plain,
% 2.86/3.03 (~r(s(z), elem!1)),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[11730, 15762, 14545])).
% 2.86/3.03 tff(15765,plain,
% 2.86/3.03 (~b(s(s(elem!1)), elem!1)),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[6397, 15764, 15605, 11974, 15763])).
% 2.86/3.03 tff(15766,plain,
% 2.86/3.03 (~r(elem!1, s(z))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[4199, 2133, 602])).
% 2.86/3.03 tff(15767,plain,
% 2.86/3.03 (b(elem!1, s(z))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[214, 15766, 2339])).
% 2.86/3.03 tff(15768,plain,
% 2.86/3.03 (~b(elem!1, s(z))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[2141, 2124, 145, 217])).
% 2.86/3.03 tff(15769,plain,
% 2.86/3.03 ($false),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[214, 15766, 15768, 3])).
% 2.86/3.03 tff(15770,plain,(b(s(s(elem!1)), s(z)) | (elem!1 = s(z)) | (~r(elem!1, s(s(elem!1)))) | b(s(s(elem!1)), elem!1) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.03 tff(15771,plain,
% 2.86/3.03 (~r(s(z), elem!1)),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[15770, 2124, 602, 145, 2339])).
% 2.86/3.03 tff(15772,plain,
% 2.86/3.03 (b(s(z), elem!1)),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[1034, 15771, 2277])).
% 2.86/3.03 tff(15773,plain,
% 2.86/3.03 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z)))) <=> ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))))),
% 2.86/3.03 inference(rewrite,[status(thm)],[])).
% 2.86/3.03 tff(15774,plain,
% 2.86/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z)))))),
% 2.86/3.03 inference(monotonicity,[status(thm)],[15773])).
% 2.86/3.03 tff(15775,plain,
% 2.86/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))))),
% 2.86/3.03 inference(transitivity,[status(thm)],[15774, 13502])).
% 2.86/3.03 tff(15776,plain,
% 2.86/3.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 2.86/3.03 inference(quant_inst,[status(thm)],[])).
% 2.86/3.03 tff(15777,plain,
% 2.86/3.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z)))),
% 2.86/3.03 inference(modus_ponens,[status(thm)],[15776, 15775])).
% 2.86/3.03 tff(15778,plain,
% 2.86/3.03 (~b(z, s(z))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[15777, 246, 2239, 15772, 15767])).
% 2.86/3.03 tff(15779,plain,
% 2.86/3.03 (r(z, s(z))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[169, 15778])).
% 2.86/3.03 tff(15780,plain,
% 2.86/3.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))))),
% 2.86/3.03 inference(rewrite,[status(thm)],[])).
% 2.86/3.03 tff(15781,plain,
% 2.86/3.03 (((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))))),
% 2.86/3.03 inference(rewrite,[status(thm)],[])).
% 2.86/3.03 tff(15782,plain,
% 2.86/3.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z)))))),
% 2.86/3.03 inference(monotonicity,[status(thm)],[15781])).
% 2.86/3.03 tff(15783,plain,
% 2.86/3.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))))),
% 2.86/3.03 inference(transitivity,[status(thm)],[15782, 15780])).
% 2.86/3.03 tff(15784,plain,
% 2.86/3.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))),
% 2.86/3.03 inference(quant_inst,[status(thm)],[])).
% 2.86/3.03 tff(15785,plain,
% 2.86/3.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z)))),
% 2.86/3.03 inference(modus_ponens,[status(thm)],[15784, 15783])).
% 2.86/3.03 tff(15786,plain,
% 2.86/3.03 ($false),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[15785, 183, 2133, 15779, 266])).
% 2.86/3.03 tff(15787,plain,(b(s(s(elem!1)), s(z)) | (~r(z, s(s(elem!1)))) | (~b(z, elem!1)) | (s(z) = elem!1) | (~r(elem!1, s(s(elem!1)))) | b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.86/3.03 tff(15788,plain,
% 2.86/3.03 (b(s(s(elem!1)), s(z)) | (~r(z, s(s(elem!1)))) | (s(z) = elem!1) | (~r(elem!1, s(s(elem!1)))) | b(s(s(elem!1)), elem!1)),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[15787, 11962])).
% 2.86/3.03 tff(15789,plain,
% 2.86/3.03 (~r(elem!1, s(s(elem!1)))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[15788, 15765, 15605, 15761, 11972])).
% 2.86/3.03 tff(15790,plain,
% 2.86/3.03 (b(elem!1, s(s(elem!1)))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[1268, 15789, 11983])).
% 2.86/3.03 tff(15791,plain,
% 2.86/3.03 (~r(s(s(elem!1)), z)),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[191, 15762, 171])).
% 2.86/3.03 tff(15792,plain,
% 2.86/3.03 (b(s(s(elem!1)), z)),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[523, 15791])).
% 2.86/3.03 tff(15793,plain,
% 2.86/3.03 (b(elem!1, s(z))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[214, 15763, 15606])).
% 2.86/3.03 tff(15794,plain,
% 2.86/3.03 (b(s(z), elem!1)),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[1034, 15764, 15605])).
% 2.86/3.03 tff(15795,plain,
% 2.86/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 2.86/3.03 inference(rewrite,[status(thm)],[])).
% 2.86/3.03 tff(15796,plain,
% 2.86/3.03 (((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 2.86/3.03 inference(rewrite,[status(thm)],[])).
% 2.86/3.03 tff(15797,plain,
% 2.86/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z)))))),
% 2.86/3.03 inference(monotonicity,[status(thm)],[15796])).
% 2.86/3.03 tff(15798,plain,
% 2.86/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 2.86/3.03 inference(transitivity,[status(thm)],[15797, 15795])).
% 2.86/3.03 tff(15799,plain,
% 2.86/3.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 2.86/3.03 inference(quant_inst,[status(thm)],[])).
% 2.86/3.03 tff(15800,plain,
% 2.86/3.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z)))),
% 2.86/3.03 inference(modus_ponens,[status(thm)],[15799, 15798])).
% 2.86/3.03 tff(15801,plain,
% 2.86/3.03 ($false),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[15800, 246, 11962, 15794, 15793, 15792, 15790, 11974])).
% 2.86/3.03 tff(15802,plain,(b(z, s(s(elem!1))) | (~r(z, s(z))) | b(s(s(s(z))), elem!1) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.03 tff(15803,plain,
% 2.86/3.03 (b(z, s(s(elem!1)))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[15802, 15704, 1, 171])).
% 2.86/3.03 tff(15804,plain,
% 2.86/3.03 (~(elem!1 = s(s(s(z))))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[2297, 210, 15604])).
% 2.86/3.03 tff(15805,plain,
% 2.86/3.03 (~(s(s(s(z))) = elem!1)),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[1677, 15804])).
% 2.86/3.03 tff(15806,plain,
% 2.86/3.03 (r(s(s(s(z))), elem!1)),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[647, 15805, 1])).
% 2.86/3.03 tff(15807,plain,
% 2.86/3.03 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[1637, 183, 14545, 15806])).
% 2.86/3.03 tff(15808,plain,
% 2.86/3.03 (b(s(s(elem!1)), s(s(s(z))))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[454, 15807, 15714])).
% 2.86/3.03 tff(15809,plain,
% 2.86/3.03 (r(elem!1, s(z))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[214, 210, 15606])).
% 2.86/3.03 tff(15810,plain,
% 2.86/3.03 (~r(s(s(elem!1)), s(z))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[11704, 15809, 14545])).
% 2.86/3.03 tff(15811,plain,
% 2.86/3.03 (b(s(s(elem!1)), s(z))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[197, 15810])).
% 2.86/3.03 tff(15812,plain,
% 2.86/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.86/3.03 inference(rewrite,[status(thm)],[])).
% 2.86/3.03 tff(15813,plain,
% 2.86/3.03 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.86/3.03 inference(rewrite,[status(thm)],[])).
% 2.86/3.03 tff(15814,plain,
% 2.86/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 2.86/3.03 inference(monotonicity,[status(thm)],[15813])).
% 2.86/3.03 tff(15815,plain,
% 2.86/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.86/3.03 inference(transitivity,[status(thm)],[15814, 15812])).
% 2.86/3.03 tff(15816,plain,
% 2.86/3.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(z))))),
% 2.86/3.03 inference(quant_inst,[status(thm)],[])).
% 2.86/3.03 tff(15817,plain,
% 2.86/3.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 2.86/3.03 inference(modus_ponens,[status(thm)],[15816, 15815])).
% 2.86/3.03 tff(15818,plain,
% 2.86/3.03 (~b(s(z), s(s(s(z))))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[15817, 246, 15811, 1044, 15808, 15604])).
% 2.86/3.03 tff(15819,plain,
% 2.86/3.03 (r(s(z), s(s(s(z))))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[1291, 15818])).
% 2.86/3.03 tff(15820,plain,
% 2.86/3.03 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[642, 15806, 14545])).
% 2.86/3.03 tff(15821,plain,
% 2.86/3.03 (b(s(s(s(z))), s(s(elem!1)))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[689, 15820, 15705])).
% 2.86/3.03 tff(15822,plain,
% 2.86/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.86/3.03 inference(rewrite,[status(thm)],[])).
% 2.86/3.03 tff(15823,plain,
% 2.86/3.03 (((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.86/3.03 inference(rewrite,[status(thm)],[])).
% 2.86/3.03 tff(15824,plain,
% 2.86/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 2.86/3.03 inference(monotonicity,[status(thm)],[15823])).
% 2.86/3.03 tff(15825,plain,
% 2.86/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.86/3.03 inference(transitivity,[status(thm)],[15824, 15822])).
% 2.86/3.03 tff(15826,plain,
% 2.86/3.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))))),
% 2.86/3.03 inference(quant_inst,[status(thm)],[])).
% 2.86/3.03 tff(15827,plain,
% 2.86/3.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 2.86/3.03 inference(modus_ponens,[status(thm)],[15826, 15825])).
% 2.86/3.03 tff(15828,plain,
% 2.86/3.03 (~b(z, s(s(s(z))))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[15827, 246, 1099, 15821, 15808])).
% 2.86/3.03 tff(15829,plain,
% 2.86/3.03 (r(z, s(s(s(z))))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[6165, 15828])).
% 2.86/3.03 tff(15830,plain,
% 2.86/3.03 ($false),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[6607, 15829, 15819, 171])).
% 2.86/3.03 tff(15831,plain,(b(elem!1, s(z)) | (~r(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), elem!1)) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.86/3.03 tff(15832,plain,
% 2.86/3.03 (~b(s(z), elem!1)),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[15831, 210, 171, 15803, 1])).
% 2.86/3.03 tff(15833,plain,
% 2.86/3.03 (r(s(z), elem!1)),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[1034, 15832, 15605])).
% 2.86/3.03 tff(15834,plain,
% 2.86/3.03 (~r(s(s(s(z))), s(z))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[3017, 634, 217])).
% 2.86/3.03 tff(15835,plain,
% 2.86/3.03 (b(s(s(s(z))), s(z))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[52, 15834])).
% 2.86/3.03 tff(15836,plain,
% 2.86/3.03 ($false),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[12070, 246, 201, 234, 11056, 15835])).
% 2.86/3.03 tff(15837,plain,((~r(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(z))) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.03 tff(15838,plain,
% 2.86/3.03 ($false),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[15837, 15806, 15811, 14545, 15705, 15833])).
% 2.86/3.03 tff(15839,plain,(b(elem!1, s(z)) | b(s(s(s(z))), elem!1) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.03 tff(15840,plain,
% 2.86/3.03 (b(elem!1, s(z))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[15839, 170, 1])).
% 2.86/3.03 tff(15841,plain,
% 2.86/3.03 (~b(s(z), z)),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[15718, 15840, 15702])).
% 2.86/3.03 tff(15842,plain,
% 2.86/3.03 (~r(s(s(s(z))), elem!1)),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[15837, 15687, 14545, 15705, 217])).
% 2.86/3.03 tff(15843,plain,
% 2.86/3.03 (s(s(s(z))) = elem!1),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[647, 15842, 1])).
% 2.86/3.03 tff(15844,plain,
% 2.86/3.03 (~(s(s(elem!1)) = elem!1)),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[5385, 15843])).
% 2.86/3.03 tff(15845,plain,
% 2.86/3.03 (~(s(s(elem!1)) = s(elem!1))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[5640, 15844])).
% 2.86/3.03 tff(15846,plain,
% 2.86/3.03 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[5623, 15843])).
% 2.86/3.03 tff(15847,plain,
% 2.86/3.03 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[13340, 15843, 1051, 217, 15846])).
% 2.86/3.03 tff(15848,plain,
% 2.86/3.03 (b(s(s(elem!1)), elem!1)),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[15758, 15847, 15604, 217, 15843])).
% 2.86/3.03 tff(15849,plain,
% 2.86/3.03 (~b(s(s(elem!1)), z)),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[12483, 15848, 1051])).
% 2.86/3.03 tff(15850,plain,
% 2.86/3.03 (r(s(s(elem!1)), z)),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[523, 15849])).
% 2.86/3.03 tff(15851,plain,
% 2.86/3.03 (~b(s(elem!1), elem!1)),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[12046, 15850, 1051, 15848, 15845])).
% 2.86/3.03 tff(15852,plain,
% 2.86/3.03 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[7041, 15843])).
% 2.86/3.03 tff(15853,plain,
% 2.86/3.03 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[86, 15847, 15852])).
% 2.86/3.03 tff(15854,plain,
% 2.86/3.03 (~r(s(elem!1), elem!1)),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[12151, 15853, 217, 15843])).
% 2.86/3.03 tff(15855,plain,
% 2.86/3.03 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[5548, 15854, 15843])).
% 2.86/3.03 tff(15856,plain,
% 2.86/3.03 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[1702, 15855])).
% 2.86/3.03 tff(15857,plain,
% 2.86/3.03 ($false),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[5677, 15856, 15851, 15843])).
% 2.86/3.03 tff(15858,plain,((~r(s(z), elem!1)) | (~b(elem!1, z)) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.86/3.03 tff(15859,plain,
% 2.86/3.03 (~r(s(z), elem!1)),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[15858, 15702, 1])).
% 2.86/3.03 tff(15860,plain,
% 2.86/3.03 (b(s(z), elem!1)),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[1034, 15859, 15605])).
% 2.86/3.03 tff(15861,plain,
% 2.86/3.03 (~(s(s(s(z))) = elem!1)),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[15726, 15860, 15702, 15714, 15840])).
% 2.86/3.03 tff(15862,plain,
% 2.86/3.03 (r(s(s(s(z))), elem!1)),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[647, 15861, 1])).
% 2.86/3.03 tff(15863,plain,
% 2.86/3.03 (~b(elem!1, s(z))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[12805, 1100, 1044, 2362, 2239])).
% 2.86/3.03 tff(15864,plain,
% 2.86/3.03 (r(elem!1, s(z))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[214, 15863, 3])).
% 2.86/3.03 tff(15865,plain,
% 2.86/3.03 (~r(s(s(s(z))), s(z))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[1023, 15864, 634])).
% 2.86/3.03 tff(15866,plain,
% 2.86/3.03 (b(s(s(s(z))), s(z))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[52, 15865])).
% 2.86/3.03 tff(15867,plain,
% 2.86/3.03 (~b(elem!1, z)),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[2370, 1100, 2362, 2239])).
% 2.86/3.03 tff(15868,plain,
% 2.86/3.03 (r(elem!1, z)),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[1143, 15867, 1438])).
% 2.86/3.03 tff(15869,plain,
% 2.86/3.03 (~r(z, s(z))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[2351, 15864, 15868])).
% 2.86/3.03 tff(15870,plain,
% 2.86/3.03 (b(z, s(z))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[169, 15869])).
% 2.86/3.03 tff(15871,plain,
% 2.86/3.03 (~r(s(z), z)),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[1163, 15864, 15868])).
% 2.86/3.03 tff(15872,plain,
% 2.86/3.03 (b(s(z), z)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[1069, 15871])).
% 2.86/3.04 tff(15873,plain,
% 2.86/3.04 (~b(s(s(s(z))), z)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[2525, 246, 2239, 15872, 15870, 15866])).
% 2.86/3.04 tff(15874,plain,
% 2.86/3.04 (r(s(s(s(z))), z)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[993, 47, 80, 15873])).
% 2.86/3.04 tff(15875,plain,
% 2.86/3.04 ($false),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[2533, 183, 15868, 634, 15874])).
% 2.86/3.04 tff(15876,plain,((~b(s(s(elem!1)), z)) | (~r(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (elem!1 = s(z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.86/3.04 tff(15877,plain,
% 2.86/3.04 (~b(s(s(elem!1)), z)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[15876, 2239, 634, 3, 1044, 2362, 1438])).
% 2.86/3.04 tff(15878,plain,
% 2.86/3.04 (r(s(s(elem!1)), z)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[523, 15877])).
% 2.86/3.04 tff(15879,plain,
% 2.86/3.04 (~r(z, s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[12004, 474, 1044, 2362, 1438, 172, 2239])).
% 2.86/3.04 tff(15880,plain,
% 2.86/3.04 (b(z, s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[169, 15879])).
% 2.86/3.04 tff(15881,plain,
% 2.86/3.04 (~r(elem!1, z)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[2535, 15880, 2239, 634, 474])).
% 2.86/3.04 tff(15882,plain,
% 2.86/3.04 (b(elem!1, z)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[1143, 15881, 1438])).
% 2.86/3.04 tff(15883,plain,
% 2.86/3.04 ($false),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[13449, 246, 2239, 15882, 1044, 15880])).
% 2.86/3.04 tff(15884,plain,((~r(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (elem!1 = z) | (~r(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.04 tff(15885,plain,
% 2.86/3.04 (~r(elem!1, s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[15884, 2239, 1044, 1438, 634, 2362, 15878])).
% 2.86/3.04 tff(15886,plain,
% 2.86/3.04 (b(elem!1, s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[214, 15885, 3])).
% 2.86/3.04 tff(15887,plain,
% 2.86/3.04 (~b(s(s(elem!1)), s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[3799, 15886, 1044, 2362])).
% 2.86/3.04 tff(15888,plain,
% 2.86/3.04 (r(s(s(elem!1)), s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[197, 15887])).
% 2.86/3.04 tff(15889,plain,
% 2.86/3.04 (~r(z, s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[191, 15888, 15878])).
% 2.86/3.04 tff(15890,plain,
% 2.86/3.04 (b(z, s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[169, 15889])).
% 2.86/3.04 tff(15891,plain,
% 2.86/3.04 ($false),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[15777, 246, 2239, 1044, 15886, 15890])).
% 2.86/3.04 tff(15892,plain,((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (elem!1 = s(z)) | (elem!1 = z) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.04 tff(15893,plain,
% 2.86/3.04 ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (elem!1 = s(z)) | (~r(s(s(s(z))), elem!1))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[15892, 11962, 11994])).
% 2.86/3.04 tff(15894,plain,
% 2.86/3.04 (~b(s(s(elem!1)), elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[15893, 15862, 15860, 15606])).
% 2.86/3.04 tff(15895,plain,
% 2.86/3.04 (r(s(z), z)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[1069, 15841])).
% 2.86/3.04 tff(15896,plain,
% 2.86/3.04 (~r(z, elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[11231, 15860, 14545, 170, 15895, 15702])).
% 2.86/3.04 tff(15897,plain,
% 2.86/3.04 (~b(s(z), s(s(elem!1)))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[15760, 12049, 1, 15704])).
% 2.86/3.04 tff(15898,plain,
% 2.86/3.04 (r(s(z), s(s(elem!1)))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[233, 15897])).
% 2.86/3.04 tff(15899,plain,
% 2.86/3.04 (b(elem!1, s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[15839, 171, 1])).
% 2.86/3.04 tff(15900,plain,
% 2.86/3.04 (~b(s(z), z)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[15718, 15899, 15704])).
% 2.86/3.04 tff(15901,plain,
% 2.86/3.04 (r(s(z), z)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[1069, 15900])).
% 2.86/3.04 tff(15902,plain,
% 2.86/3.04 ($false),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[1076, 183, 15901, 172, 15898])).
% 2.86/3.04 tff(15903,plain,((~r(s(s(elem!1)), z)) | b(s(s(s(z))), elem!1) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.04 tff(15904,plain,
% 2.86/3.04 (~r(s(s(elem!1)), z)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[15903, 170, 1])).
% 2.86/3.04 tff(15905,plain,
% 2.86/3.04 (b(s(s(elem!1)), z)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[523, 15904])).
% 2.86/3.04 tff(15906,plain,
% 2.86/3.04 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[1637, 183, 14545, 15862])).
% 2.86/3.04 tff(15907,plain,
% 2.86/3.04 (b(s(s(elem!1)), s(s(s(z))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[454, 15906, 15714])).
% 2.86/3.04 tff(15908,plain,
% 2.86/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.86/3.04 inference(rewrite,[status(thm)],[])).
% 2.86/3.04 tff(15909,plain,
% 2.86/3.04 (((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z))) <=> ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.86/3.04 inference(rewrite,[status(thm)],[])).
% 2.86/3.04 tff(15910,plain,
% 2.86/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 2.86/3.04 inference(monotonicity,[status(thm)],[15909])).
% 2.86/3.04 tff(15911,plain,
% 2.86/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.86/3.04 inference(transitivity,[status(thm)],[15910, 15908])).
% 2.86/3.04 tff(15912,plain,
% 2.86/3.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z)))),
% 2.86/3.04 inference(quant_inst,[status(thm)],[])).
% 2.86/3.04 tff(15913,plain,
% 2.86/3.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 2.86/3.04 inference(modus_ponens,[status(thm)],[15912, 15911])).
% 2.86/3.04 tff(15914,plain,
% 2.86/3.04 ((~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z)))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[15913, 246, 11962, 15860, 15907, 15604])).
% 2.86/3.04 tff(15915,plain,
% 2.86/3.04 (~b(z, s(s(s(z))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[15914, 15905])).
% 2.86/3.04 tff(15916,plain,
% 2.86/3.04 (~b(z, elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[2242, 1673, 2214])).
% 2.86/3.04 tff(15917,plain,
% 2.86/3.04 (z = elem!1),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[60, 15916, 56])).
% 2.86/3.04 tff(15918,plain,
% 2.86/3.04 (elem!1 = z),
% 2.86/3.04 inference(symmetry,[status(thm)],[15917])).
% 2.86/3.04 tff(15919,plain,
% 2.86/3.04 (s(s(s(z))) = elem!1),
% 2.86/3.04 inference(symmetry,[status(thm)],[15722])).
% 2.86/3.04 tff(15920,plain,
% 2.86/3.04 (s(s(s(z))) = z),
% 2.86/3.04 inference(transitivity,[status(thm)],[15919, 15918])).
% 2.86/3.04 tff(15921,plain,
% 2.86/3.04 ($false),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[80, 15920])).
% 2.86/3.04 tff(15922,plain,((~(s(s(s(z))) = elem!1)) | r(z, elem!1) | b(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.04 tff(15923,plain,
% 2.86/3.04 (~(s(s(s(z))) = elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[15922, 2214, 56])).
% 2.86/3.04 tff(15924,plain,
% 2.86/3.04 (~(elem!1 = s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[11660, 10369, 145])).
% 2.86/3.04 tff(15925,plain,
% 2.86/3.04 (~(s(z) = elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[9, 15924])).
% 2.86/3.04 tff(15926,plain,
% 2.86/3.04 (r(s(z), elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[1034, 15925, 1445])).
% 2.86/3.04 tff(15927,plain,
% 2.86/3.04 (~r(elem!1, z)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[2725, 15926, 1114])).
% 2.86/3.04 tff(15928,plain,
% 2.86/3.04 (b(s(s(s(z))), elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[647, 10369, 3011])).
% 2.86/3.04 tff(15929,plain,
% 2.86/3.04 (z = elem!1),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[60, 55, 56])).
% 2.86/3.04 tff(15930,plain,
% 2.86/3.04 (b(z, s(z)) <=> b(elem!1, s(z))),
% 2.86/3.04 inference(monotonicity,[status(thm)],[15929])).
% 2.86/3.04 tff(15931,plain,
% 2.86/3.04 (b(elem!1, s(z)) <=> b(z, s(z))),
% 2.86/3.04 inference(symmetry,[status(thm)],[15930])).
% 2.86/3.04 tff(15932,plain,
% 2.86/3.04 (~r(s(s(elem!1)), s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[2139, 183, 217, 216])).
% 2.86/3.04 tff(15933,plain,
% 2.86/3.04 (b(s(s(elem!1)), s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[197, 15932])).
% 2.86/3.04 tff(15934,plain,
% 2.86/3.04 (b(elem!1, s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[1029, 55, 217, 145, 216, 15933])).
% 2.86/3.04 tff(15935,plain,
% 2.86/3.04 (b(z, s(z))),
% 2.86/3.04 inference(modus_ponens,[status(thm)],[15934, 15931])).
% 2.86/3.04 tff(15936,plain,
% 2.86/3.04 ($false),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[54, 15935])).
% 2.86/3.04 tff(15937,plain,(b(z, elem!1) | b(z, s(z)) | (~r(s(z), elem!1)) | b(s(s(elem!1)), elem!1) | (~r(s(s(elem!1)), elem!1)) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.86/3.04 tff(15938,plain,
% 2.86/3.04 (b(z, elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[15937, 15926, 54, 145, 216, 56])).
% 2.86/3.04 tff(15939,plain,
% 2.86/3.04 (~b(elem!1, z)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[13382, 15938, 15928, 714])).
% 2.86/3.04 tff(15940,plain,
% 2.86/3.04 (elem!1 = z),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[1143, 15939, 15927])).
% 2.86/3.04 tff(15941,plain,
% 2.86/3.04 (b(z, elem!1) <=> b(z, z)),
% 2.86/3.04 inference(monotonicity,[status(thm)],[15940])).
% 2.86/3.04 tff(15942,plain,
% 2.86/3.04 (b(z, z) <=> b(z, elem!1)),
% 2.86/3.04 inference(symmetry,[status(thm)],[15941])).
% 2.86/3.04 tff(15943,plain,
% 2.86/3.04 ((~b(z, z)) <=> (~b(z, elem!1))),
% 2.86/3.04 inference(monotonicity,[status(thm)],[15942])).
% 2.86/3.04 tff(15944,plain,
% 2.86/3.04 (~b(z, elem!1)),
% 2.86/3.04 inference(modus_ponens,[status(thm)],[11990, 15943])).
% 2.86/3.04 tff(15945,plain,
% 2.86/3.04 ($false),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[15938, 15944])).
% 2.86/3.04 tff(15946,plain,(r(s(s(s(z))), elem!1) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | b(z, s(z)) | b(s(s(elem!1)), elem!1) | (~r(s(s(elem!1)), elem!1)) | r(z, elem!1) | (~r(s(z), z)) | b(s(z), elem!1) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.86/3.04 tff(15947,plain,
% 2.86/3.04 (r(s(s(s(z))), elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[15946, 216, 54, 145, 714, 56, 1114, 1445, 3011])).
% 2.86/3.04 tff(15948,plain,
% 2.86/3.04 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[1637, 183, 216, 15947])).
% 2.86/3.04 tff(15949,plain,
% 2.86/3.04 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[115, 15929])).
% 2.86/3.04 tff(15950,plain,
% 2.86/3.04 (~r(s(z), elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[15937, 55, 54, 145, 216, 56])).
% 2.86/3.04 tff(15951,plain,
% 2.86/3.04 (s(z) = elem!1),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[1034, 15950, 1445])).
% 2.86/3.04 tff(15952,plain,
% 2.86/3.04 ($false),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[121, 15951, 15949])).
% 2.86/3.04 tff(15953,plain,(b(z, elem!1) | b(s(z), elem!1) | b(z, s(z)) | b(s(s(elem!1)), elem!1) | (~r(s(s(elem!1)), elem!1)) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.86/3.04 tff(15954,plain,
% 2.86/3.04 (b(z, elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[15953, 216, 54, 145, 1445, 56])).
% 2.86/3.04 tff(15955,plain,
% 2.86/3.04 (~(elem!1 = s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[11968, 15954, 54])).
% 2.86/3.04 tff(15956,plain,
% 2.86/3.04 (~(s(z) = elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[9, 15955])).
% 2.86/3.04 tff(15957,plain,
% 2.86/3.04 (r(s(z), elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[1034, 15956, 1445])).
% 2.86/3.04 tff(15958,plain,
% 2.86/3.04 (~r(s(s(s(z))), s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[3017, 15957, 15947])).
% 2.86/3.04 tff(15959,plain,
% 2.86/3.04 (b(s(s(s(z))), s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[52, 15958])).
% 2.86/3.04 tff(15960,plain,
% 2.86/3.04 (~r(s(z), s(s(elem!1)))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[223, 183, 15957, 216])).
% 2.86/3.04 tff(15961,plain,
% 2.86/3.04 (b(s(z), s(s(elem!1)))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[233, 15960])).
% 2.86/3.04 tff(15962,plain,
% 2.86/3.04 (~r(s(s(elem!1)), s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[2139, 183, 15957, 216])).
% 2.86/3.04 tff(15963,plain,
% 2.86/3.04 (b(s(s(elem!1)), s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[197, 15962])).
% 2.86/3.04 tff(15964,plain,
% 2.86/3.04 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[3488, 246, 15963, 15961, 15959])).
% 2.86/3.04 tff(15965,plain,
% 2.86/3.04 (s(s(elem!1)) = s(s(s(z)))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[454, 15964, 15948])).
% 2.86/3.04 tff(15966,plain,
% 2.86/3.04 (inj_0(s(s(elem!1))) = inj_0(s(s(s(z))))),
% 2.86/3.04 inference(monotonicity,[status(thm)],[15965])).
% 2.86/3.04 tff(15967,plain,
% 2.86/3.04 (s(elem!1) = s(s(z))),
% 2.86/3.04 inference(transitivity,[status(thm)],[108, 15966, 24])).
% 2.86/3.04 tff(15968,plain,
% 2.86/3.04 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 2.86/3.04 inference(monotonicity,[status(thm)],[15967])).
% 2.86/3.04 tff(15969,plain,
% 2.86/3.04 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 2.86/3.04 inference(symmetry,[status(thm)],[15968])).
% 2.86/3.04 tff(15970,plain,
% 2.86/3.04 (s(z) = elem!1),
% 2.86/3.04 inference(transitivity,[status(thm)],[1523, 15969, 343])).
% 2.86/3.04 tff(15971,plain,
% 2.86/3.04 ($false),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[15956, 15970])).
% 2.86/3.04 tff(15972,plain,((~r(s(s(elem!1)), elem!1)) | b(s(z), elem!1) | b(z, s(z)) | b(s(s(elem!1)), elem!1) | r(z, elem!1) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(z), z)) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.86/3.04 tff(15973,plain,
% 2.86/3.04 (~r(s(s(elem!1)), elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[15972, 1445, 54, 145, 56, 714, 1114, 15923])).
% 2.86/3.04 tff(15974,plain,
% 2.86/3.04 (s(s(elem!1)) = elem!1),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[156, 15973, 145])).
% 2.86/3.04 tff(15975,plain,
% 2.86/3.04 (s(s(s(elem!1))) = s(elem!1)),
% 2.86/3.04 inference(monotonicity,[status(thm)],[15974])).
% 2.86/3.04 tff(15976,plain,
% 2.86/3.04 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.86/3.04 inference(monotonicity,[status(thm)],[15975])).
% 2.86/3.04 tff(15977,plain,
% 2.86/3.04 (s(s(s(s(elem!1)))) = elem!1),
% 2.86/3.04 inference(transitivity,[status(thm)],[15976, 15974])).
% 2.86/3.04 tff(15978,plain,
% 2.86/3.04 (s(s(s(s(s(elem!1))))) = s(elem!1)),
% 2.86/3.04 inference(monotonicity,[status(thm)],[15977])).
% 2.86/3.04 tff(15979,plain,
% 2.86/3.04 (b(s(s(s(s(s(elem!1))))), elem!1) <=> b(s(elem!1), elem!1)),
% 2.86/3.04 inference(monotonicity,[status(thm)],[15978])).
% 2.86/3.04 tff(15980,plain,
% 2.86/3.04 (b(s(elem!1), elem!1)),
% 2.86/3.04 inference(modus_ponens,[status(thm)],[714, 15979])).
% 2.86/3.04 tff(15981,plain,
% 2.86/3.04 ((s(s(elem!1)) = z) <=> (elem!1 = z)),
% 2.86/3.04 inference(monotonicity,[status(thm)],[15974])).
% 2.86/3.04 tff(15982,plain,
% 2.86/3.04 ((s(s(elem!1)) = z) <=> (z = elem!1)),
% 2.86/3.04 inference(transitivity,[status(thm)],[15981, 1037])).
% 2.86/3.04 tff(15983,plain,
% 2.86/3.04 ((s(s(elem!1)) = z) <=> (elem!1 = z)),
% 2.86/3.04 inference(transitivity,[status(thm)],[15982, 1436])).
% 2.86/3.04 tff(15984,plain,
% 2.86/3.04 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = z))),
% 2.86/3.04 inference(monotonicity,[status(thm)],[15983])).
% 2.86/3.04 tff(15985,plain,
% 2.86/3.04 (~(elem!1 = z)),
% 2.86/3.04 inference(modus_ponens,[status(thm)],[139, 15984])).
% 2.86/3.04 tff(15986,plain,
% 2.86/3.04 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(z))),
% 2.86/3.04 inference(monotonicity,[status(thm)],[15974])).
% 2.86/3.04 tff(15987,plain,
% 2.86/3.04 ((s(s(elem!1)) = s(z)) <=> (s(z) = elem!1)),
% 2.86/3.04 inference(transitivity,[status(thm)],[15986, 4])).
% 2.86/3.04 tff(15988,plain,
% 2.86/3.04 ((~(s(s(elem!1)) = s(z))) <=> (~(s(z) = elem!1))),
% 2.86/3.04 inference(monotonicity,[status(thm)],[15987])).
% 2.86/3.04 tff(15989,plain,
% 2.86/3.04 (~(s(z) = elem!1)),
% 2.86/3.04 inference(modus_ponens,[status(thm)],[113, 15988])).
% 2.86/3.04 tff(15990,plain,
% 2.86/3.04 (r(s(z), elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[1034, 15989, 1445])).
% 2.86/3.04 tff(15991,plain,
% 2.86/3.04 (~r(elem!1, z)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[2725, 15990, 1114])).
% 2.86/3.04 tff(15992,plain,
% 2.86/3.04 (b(elem!1, z)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[1143, 15991, 15985])).
% 2.86/3.04 tff(15993,plain,
% 2.86/3.04 ((~(s(s(elem!1)) = z)) <=> (~(z = elem!1))),
% 2.86/3.04 inference(monotonicity,[status(thm)],[15982])).
% 2.86/3.04 tff(15994,plain,
% 2.86/3.04 (~(z = elem!1)),
% 2.86/3.04 inference(modus_ponens,[status(thm)],[139, 15993])).
% 2.86/3.04 tff(15995,plain,
% 2.86/3.04 (b(z, elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[60, 15994, 56])).
% 2.86/3.04 tff(15996,plain,
% 2.86/3.04 (~b(z, s(elem!1))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[2551, 246, 15995, 15992, 15980])).
% 2.86/3.04 tff(15997,plain,
% 2.86/3.04 (r(z, s(elem!1))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[2561, 15996])).
% 2.86/3.04 tff(15998,plain,
% 2.86/3.04 ((s(s(s(s(s(elem!1))))) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 2.86/3.04 inference(monotonicity,[status(thm)],[15978])).
% 2.86/3.04 tff(15999,plain,
% 2.86/3.04 ((s(s(s(s(s(elem!1))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 2.86/3.04 inference(transitivity,[status(thm)],[15998, 2182])).
% 2.86/3.04 tff(16000,plain,
% 2.86/3.04 ((~(s(s(s(s(s(elem!1))))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 2.86/3.04 inference(monotonicity,[status(thm)],[15999])).
% 2.86/3.04 tff(16001,plain,
% 2.86/3.04 (~(s(s(s(z))) = s(elem!1))),
% 2.86/3.04 inference(modus_ponens,[status(thm)],[1622, 16000])).
% 2.86/3.04 tff(16002,plain,
% 2.86/3.04 (s(elem!1) = s(s(s(s(s(elem!1)))))),
% 2.86/3.04 inference(symmetry,[status(thm)],[15978])).
% 2.86/3.04 tff(16003,plain,
% 2.86/3.04 ((s(z) = s(elem!1)) <=> (s(z) = s(s(s(s(s(elem!1))))))),
% 2.86/3.04 inference(monotonicity,[status(thm)],[16002])).
% 2.86/3.04 tff(16004,plain,
% 2.86/3.04 ((s(z) = s(elem!1)) <=> (s(s(s(s(s(elem!1))))) = s(z))),
% 2.86/3.04 inference(transitivity,[status(thm)],[16003, 317])).
% 2.86/3.04 tff(16005,plain,
% 2.86/3.04 ((s(s(s(s(s(elem!1))))) = s(z)) <=> (s(z) = s(elem!1))),
% 2.86/3.04 inference(symmetry,[status(thm)],[16004])).
% 2.86/3.04 tff(16006,plain,
% 2.86/3.04 ((~(s(s(s(s(s(elem!1))))) = s(z))) <=> (~(s(z) = s(elem!1)))),
% 2.86/3.04 inference(monotonicity,[status(thm)],[16005])).
% 2.86/3.04 tff(16007,plain,
% 2.86/3.04 (~(s(z) = s(elem!1))),
% 2.86/3.04 inference(modus_ponens,[status(thm)],[331, 16006])).
% 2.86/3.04 tff(16008,plain,
% 2.86/3.04 (~b(s(elem!1), z)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[2961, 246, 15995, 15992, 15980])).
% 2.86/3.04 tff(16009,plain,
% 2.86/3.04 (r(s(elem!1), z)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[2581, 16008])).
% 2.86/3.04 tff(16010,plain,
% 2.86/3.04 (~r(s(z), s(elem!1))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[2969, 183, 1114, 16009])).
% 2.86/3.04 tff(16011,plain,
% 2.86/3.04 ((s(z) = s(elem!1)) | b(s(z), s(elem!1))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[2973, 47, 16010])).
% 2.86/3.04 tff(16012,plain,
% 2.86/3.04 (b(s(z), s(elem!1))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[16011, 16007])).
% 2.86/3.04 tff(16013,plain,
% 2.86/3.04 ((s(elem!1) = s(z)) <=> (s(s(s(s(s(elem!1))))) = s(z))),
% 2.86/3.04 inference(monotonicity,[status(thm)],[16002])).
% 2.86/3.04 tff(16014,plain,
% 2.86/3.04 ((s(s(s(s(s(elem!1))))) = s(z)) <=> (s(elem!1) = s(z))),
% 2.86/3.04 inference(symmetry,[status(thm)],[16013])).
% 2.86/3.04 tff(16015,plain,
% 2.86/3.04 ((~(s(s(s(s(s(elem!1))))) = s(z))) <=> (~(s(elem!1) = s(z)))),
% 2.86/3.04 inference(monotonicity,[status(thm)],[16014])).
% 2.86/3.04 tff(16016,plain,
% 2.86/3.04 (~(s(elem!1) = s(z))),
% 2.86/3.04 inference(modus_ponens,[status(thm)],[331, 16015])).
% 2.86/3.04 tff(16017,plain,
% 2.86/3.04 (~r(s(elem!1), s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[2985, 183, 1114, 16009])).
% 2.86/3.04 tff(16018,plain,
% 2.86/3.04 ((s(elem!1) = s(z)) | b(s(elem!1), s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[2989, 47, 16017])).
% 2.86/3.04 tff(16019,plain,
% 2.86/3.04 (b(s(elem!1), s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[16018, 16016])).
% 2.86/3.04 tff(16020,plain,
% 2.86/3.04 (~b(s(s(s(z))), elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[13382, 15992, 15995, 714])).
% 2.86/3.04 tff(16021,plain,
% 2.86/3.04 (r(s(s(s(z))), elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[647, 16020, 15923])).
% 2.86/3.04 tff(16022,plain,
% 2.86/3.04 (~r(s(s(s(z))), s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[2713, 16021, 1445, 15973])).
% 2.86/3.04 tff(16023,plain,
% 2.86/3.04 (b(s(s(s(z))), s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[52, 16022])).
% 2.86/3.04 tff(16024,plain,
% 2.86/3.04 (~b(s(s(s(z))), s(elem!1))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[2997, 246, 16023, 16019, 16012])).
% 2.86/3.04 tff(16025,plain,
% 2.86/3.04 (r(s(s(s(z))), s(elem!1))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[2675, 16024, 16001])).
% 2.86/3.04 tff(16026,plain,
% 2.86/3.04 (r(z, s(s(s(z))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[2221, 47, 2214, 5476])).
% 2.86/3.04 tff(16027,plain,
% 2.86/3.04 ($false),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[3005, 183, 16026, 16025, 15997])).
% 2.86/3.04 tff(16028,plain,(b(s(z), elem!1) | (~r(s(z), z)) | b(z, s(s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | r(z, elem!1) | b(s(s(elem!1)), elem!1) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.04 tff(16029,plain,
% 2.86/3.04 (b(s(z), elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[16028, 714, 2214, 14018, 56, 145, 54])).
% 2.86/3.04 tff(16030,plain,
% 2.86/3.04 (~(z = elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[2120, 16029, 2118])).
% 2.86/3.04 tff(16031,plain,
% 2.86/3.04 (~(elem!1 = z)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[1041, 16030])).
% 2.86/3.04 tff(16032,plain,
% 2.86/3.04 (b(z, elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[60, 16030, 56])).
% 2.86/3.04 tff(16033,plain,
% 2.86/3.04 (~(elem!1 = s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[11968, 16032, 54])).
% 2.86/3.04 tff(16034,plain,
% 2.86/3.04 (~(elem!1 = s(s(s(z))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[3013, 15923])).
% 2.86/3.04 tff(16035,plain,
% 2.86/3.04 (~r(s(s(s(z))), s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[438, 16026, 170])).
% 2.86/3.04 tff(16036,plain,
% 2.86/3.04 (b(s(s(s(z))), s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[52, 16035])).
% 2.86/3.04 tff(16037,plain,
% 2.86/3.04 (~r(elem!1, z)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[12329, 16029, 16036, 16034, 16033, 16026, 14018])).
% 2.86/3.04 tff(16038,plain,
% 2.86/3.04 (b(elem!1, z)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[1143, 16037, 16031])).
% 2.86/3.04 tff(16039,plain,
% 2.86/3.04 (~b(s(s(s(s(s(elem!1))))), z)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[2359, 246, 16032, 16038, 714])).
% 2.86/3.04 tff(16040,plain,
% 2.86/3.04 (r(s(s(s(s(s(elem!1))))), z)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[1601, 16039])).
% 2.86/3.04 tff(16041,plain,
% 2.86/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.86/3.04 inference(rewrite,[status(thm)],[])).
% 2.86/3.04 tff(16042,plain,
% 2.86/3.04 (((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(z)))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.86/3.04 inference(rewrite,[status(thm)],[])).
% 2.86/3.04 tff(16043,plain,
% 2.86/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(elem!1))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 2.86/3.04 inference(monotonicity,[status(thm)],[16042])).
% 2.86/3.04 tff(16044,plain,
% 2.86/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(elem!1))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.86/3.04 inference(transitivity,[status(thm)],[16043, 16041])).
% 2.86/3.04 tff(16045,plain,
% 2.86/3.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 2.86/3.04 inference(quant_inst,[status(thm)],[])).
% 2.86/3.04 tff(16046,plain,
% 2.86/3.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 2.86/3.04 inference(modus_ponens,[status(thm)],[16045, 16044])).
% 2.86/3.04 tff(16047,plain,
% 2.86/3.04 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[16046, 246, 16032, 16038, 16029, 714])).
% 2.86/3.04 tff(16048,plain,
% 2.86/3.04 (r(s(s(s(s(s(elem!1))))), s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[2311, 47, 331, 16047])).
% 2.86/3.04 tff(16049,plain,
% 2.86/3.04 ($false),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[11167, 183, 14018, 16048, 16040])).
% 2.86/3.04 tff(16050,plain,((~b(s(s(s(s(s(elem!1))))), elem!1)) | b(z, s(s(s(z)))) | b(z, s(z)) | r(z, elem!1) | b(s(z), z) | b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.86/3.04 tff(16051,plain,
% 2.86/3.04 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[16050, 15915, 54, 15896, 15894, 15841])).
% 2.86/3.04 tff(16052,plain,
% 2.86/3.04 (elem!1 = s(s(s(z)))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[1677, 15843])).
% 2.86/3.04 tff(16053,plain,
% 2.86/3.04 (b(elem!1, s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[2297, 16052, 15604])).
% 2.86/3.04 tff(16054,plain,
% 2.86/3.04 (~b(s(z), z)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[15718, 16053, 1051])).
% 2.86/3.04 tff(16055,plain,
% 2.86/3.04 (~r(s(z), z)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[14064, 15853, 4064, 217])).
% 2.86/3.04 tff(16056,plain,
% 2.86/3.04 ($false),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[1069, 16055, 16054])).
% 2.86/3.04 tff(16057,plain,((~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~b(elem!1, z)) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.86/3.04 tff(16058,plain,
% 2.86/3.04 (~r(s(z), elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[16057, 1051, 4064, 1])).
% 2.86/3.04 tff(16059,plain,
% 2.86/3.04 (b(s(z), elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[1034, 16058, 15605])).
% 2.86/3.04 tff(16060,plain,
% 2.86/3.04 (~b(s(z), z)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[12729, 246, 11962, 1051, 16059])).
% 2.86/3.04 tff(16061,plain,
% 2.86/3.04 (b(z, s(s(elem!1)))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[15802, 1051, 1, 170])).
% 2.86/3.04 tff(16062,plain,
% 2.86/3.04 (b(elem!1, s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[15831, 16061, 170, 16059, 1])).
% 2.86/3.04 tff(16063,plain,
% 2.86/3.04 (~(s(s(s(z))) = elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[15726, 16062, 16059, 15714, 1051])).
% 2.86/3.04 tff(16064,plain,
% 2.86/3.04 (r(s(s(s(z))), elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[647, 16063, 1])).
% 2.86/3.04 tff(16065,plain,
% 2.86/3.04 (~b(s(s(elem!1)), elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[15893, 16064, 16059, 15606])).
% 2.86/3.04 tff(16066,plain,
% 2.86/3.04 (r(s(z), z)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[1069, 16060])).
% 2.86/3.04 tff(16067,plain,
% 2.86/3.04 (~r(z, elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[11231, 16066, 14545, 170, 16059, 1051])).
% 2.86/3.04 tff(16068,plain,
% 2.86/3.04 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[1637, 183, 14545, 16064])).
% 2.86/3.04 tff(16069,plain,
% 2.86/3.04 (b(s(s(elem!1)), s(s(s(z))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[454, 16068, 15714])).
% 2.86/3.04 tff(16070,plain,
% 2.86/3.04 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[642, 16064, 14545])).
% 2.86/3.04 tff(16071,plain,
% 2.86/3.04 (b(s(s(s(z))), s(s(elem!1)))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[689, 16070, 15705])).
% 2.86/3.04 tff(16072,plain,
% 2.86/3.04 (~b(z, s(s(s(z))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[15827, 246, 16061, 16071, 16069])).
% 2.86/3.04 tff(16073,plain,
% 2.86/3.04 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[16050, 16072, 54, 16067, 16065, 16060])).
% 2.86/3.04 tff(16074,plain,
% 2.86/3.04 (~b(s(s(s(s(z)))), elem!1)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[12741, 16059, 1051])).
% 2.86/3.04 tff(16075,plain,
% 2.86/3.04 (r(z, s(s(s(z))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[6165, 16072])).
% 2.86/3.04 tff(16076,plain,
% 2.86/3.04 (~r(s(z), s(s(s(z))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[6607, 16075, 170])).
% 2.86/3.04 tff(16077,plain,
% 2.86/3.04 (b(s(z), s(s(s(z))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[1291, 16076])).
% 2.86/3.04 tff(16078,plain,
% 2.86/3.04 ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z)))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[15817, 246, 16059, 16069, 15604])).
% 2.86/3.04 tff(16079,plain,
% 2.86/3.04 (~b(s(s(elem!1)), s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[16078, 16077])).
% 2.86/3.04 tff(16080,plain,
% 2.86/3.04 (r(s(s(elem!1)), s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[197, 16079])).
% 2.86/3.04 tff(16081,plain,
% 2.86/3.04 (~r(s(s(elem!1)), z)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[191, 16080, 170])).
% 2.86/3.04 tff(16082,plain,
% 2.86/3.04 (b(s(s(elem!1)), z)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[523, 16081])).
% 2.86/3.04 tff(16083,plain,
% 2.86/3.04 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[4092, 16080, 170, 4064, 16061])).
% 2.86/3.04 tff(16084,plain,
% 2.86/3.04 (~(s(elem!1) = s(s(s(z))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[11452, 16083])).
% 2.86/3.04 tff(16085,plain,
% 2.86/3.04 ($false),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[1749, 11863])).
% 2.86/3.04 tff(16086,plain,((~(s(s(elem!1)) = s(s(s(s(z)))))) | (s(elem!1) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.04 tff(16087,plain,
% 2.86/3.04 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[16086, 16084])).
% 2.86/3.04 tff(16088,plain,
% 2.86/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.86/3.04 inference(rewrite,[status(thm)],[])).
% 2.86/3.04 tff(16089,plain,
% 2.86/3.04 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.86/3.05 inference(rewrite,[status(thm)],[])).
% 2.86/3.05 tff(16090,plain,
% 2.86/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.86/3.05 inference(monotonicity,[status(thm)],[16089])).
% 2.86/3.05 tff(16091,plain,
% 2.86/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.86/3.05 inference(transitivity,[status(thm)],[16090, 16088])).
% 2.86/3.05 tff(16092,plain,
% 2.86/3.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.86/3.05 inference(quant_inst,[status(thm)],[])).
% 2.86/3.05 tff(16093,plain,
% 2.86/3.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.86/3.05 inference(modus_ponens,[status(thm)],[16092, 16091])).
% 2.86/3.05 tff(16094,plain,
% 2.86/3.05 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[16093, 246, 2401, 963, 2003, 1833])).
% 2.86/3.05 tff(16095,assumption,(~(s(s(elem!1)) = s(s(s(s(z)))))), introduced(assumption)).
% 2.86/3.05 tff(16096,plain,
% 2.86/3.05 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[15060, 47, 16095, 16094])).
% 2.86/3.05 tff(16097,plain,
% 2.86/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.86/3.05 inference(rewrite,[status(thm)],[])).
% 2.86/3.05 tff(16098,plain,
% 2.86/3.05 (((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.86/3.05 inference(rewrite,[status(thm)],[])).
% 2.86/3.05 tff(16099,plain,
% 2.86/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.86/3.05 inference(monotonicity,[status(thm)],[16098])).
% 2.86/3.05 tff(16100,plain,
% 2.86/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.86/3.05 inference(transitivity,[status(thm)],[16099, 16097])).
% 2.86/3.05 tff(16101,plain,
% 2.86/3.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.86/3.05 inference(quant_inst,[status(thm)],[])).
% 2.86/3.05 tff(16102,plain,
% 2.86/3.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.86/3.05 inference(modus_ponens,[status(thm)],[16101, 16100])).
% 2.86/3.05 tff(16103,plain,
% 2.86/3.05 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[16102, 246, 1100, 4327, 963, 1833])).
% 2.86/3.05 tff(16104,plain,
% 2.86/3.05 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 2.86/3.05 inference(modus_ponens,[status(thm)],[16095, 11836])).
% 2.86/3.05 tff(16105,plain,
% 2.86/3.05 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[6521, 47, 16104, 16103])).
% 2.86/3.05 tff(16106,plain,
% 2.86/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.86/3.05 inference(rewrite,[status(thm)],[])).
% 2.86/3.05 tff(16107,plain,
% 2.86/3.05 (((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.86/3.05 inference(rewrite,[status(thm)],[])).
% 2.86/3.05 tff(16108,plain,
% 2.86/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.86/3.05 inference(monotonicity,[status(thm)],[16107])).
% 2.86/3.05 tff(16109,plain,
% 2.86/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.86/3.05 inference(transitivity,[status(thm)],[16108, 16106])).
% 2.86/3.05 tff(16110,plain,
% 2.86/3.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.86/3.05 inference(quant_inst,[status(thm)],[])).
% 2.86/3.05 tff(16111,plain,
% 2.86/3.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.86/3.05 inference(modus_ponens,[status(thm)],[16110, 16109])).
% 2.86/3.05 tff(16112,plain,
% 2.86/3.05 (~b(s(s(s(s(z)))), s(z))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[16111, 246, 4327, 2401, 963, 1833])).
% 2.86/3.05 tff(16113,plain,
% 2.86/3.05 (r(s(s(s(s(z)))), s(z))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[6103, 16112])).
% 2.86/3.05 tff(16114,plain,
% 2.86/3.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.86/3.05 inference(rewrite,[status(thm)],[])).
% 2.86/3.05 tff(16115,plain,
% 2.86/3.05 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.86/3.05 inference(rewrite,[status(thm)],[])).
% 2.86/3.05 tff(16116,plain,
% 2.86/3.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 2.86/3.05 inference(monotonicity,[status(thm)],[16115])).
% 2.86/3.05 tff(16117,plain,
% 2.86/3.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.86/3.05 inference(transitivity,[status(thm)],[16116, 16114])).
% 2.86/3.05 tff(16118,plain,
% 2.86/3.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.86/3.05 inference(quant_inst,[status(thm)],[])).
% 2.86/3.05 tff(16119,plain,
% 2.86/3.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 2.86/3.05 inference(modus_ponens,[status(thm)],[16118, 16117])).
% 2.86/3.05 tff(16120,plain,
% 2.86/3.05 ($false),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[16119, 183, 173, 16113, 16105, 16096])).
% 2.86/3.05 tff(16121,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(z))) | (s(s(elem!1)) = s(s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.05 tff(16122,plain,
% 2.86/3.05 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[16121, 16080, 16087, 16077, 16069, 15604, 16071, 16082])).
% 2.86/3.05 tff(16123,plain,
% 2.86/3.05 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[1702, 16122])).
% 2.86/3.05 tff(16124,plain,
% 2.86/3.05 (~b(elem!1, s(s(s(z))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[2011, 16062, 15604, 16059])).
% 2.86/3.05 tff(16125,plain,
% 2.86/3.05 (~(elem!1 = s(s(s(z))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[3013, 16063])).
% 2.86/3.05 tff(16126,plain,
% 2.86/3.05 (r(elem!1, s(s(s(z))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[470, 16125, 16124])).
% 2.86/3.05 tff(16127,plain,
% 2.86/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.86/3.05 inference(rewrite,[status(thm)],[])).
% 2.86/3.05 tff(16128,plain,
% 2.86/3.05 (((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.86/3.05 inference(rewrite,[status(thm)],[])).
% 2.86/3.05 tff(16129,plain,
% 2.86/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 2.86/3.05 inference(monotonicity,[status(thm)],[16128])).
% 2.86/3.05 tff(16130,plain,
% 2.86/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.86/3.05 inference(transitivity,[status(thm)],[16129, 16127])).
% 2.86/3.05 tff(16131,plain,
% 2.86/3.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)))),
% 2.86/3.05 inference(quant_inst,[status(thm)],[])).
% 2.86/3.05 tff(16132,plain,
% 2.86/3.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 2.86/3.05 inference(modus_ponens,[status(thm)],[16131, 16130])).
% 2.86/3.05 tff(16133,plain,
% 2.86/3.05 (~b(elem!1, s(s(elem!1)))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[16132, 246, 11962, 16062, 16061, 16069, 15604])).
% 2.86/3.05 tff(16134,plain,
% 2.86/3.05 (~(s(s(elem!1)) = elem!1)),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[2130, 16079, 16062])).
% 2.86/3.05 tff(16135,plain,
% 2.86/3.05 (~(elem!1 = s(s(elem!1)))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[5450, 16134])).
% 2.86/3.05 tff(16136,plain,
% 2.86/3.05 (r(elem!1, s(s(elem!1)))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[1268, 16135, 16133])).
% 2.86/3.05 tff(16137,plain,
% 2.86/3.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.86/3.05 inference(rewrite,[status(thm)],[])).
% 2.86/3.05 tff(16138,plain,
% 2.86/3.05 (((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.86/3.05 inference(rewrite,[status(thm)],[])).
% 2.86/3.05 tff(16139,plain,
% 2.86/3.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1))))),
% 2.86/3.05 inference(monotonicity,[status(thm)],[16138])).
% 2.86/3.05 tff(16140,plain,
% 2.86/3.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.86/3.05 inference(transitivity,[status(thm)],[16139, 16137])).
% 2.86/3.05 tff(16141,plain,
% 2.86/3.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.86/3.05 inference(quant_inst,[status(thm)],[])).
% 2.86/3.05 tff(16142,plain,
% 2.86/3.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1))),
% 2.86/3.05 inference(modus_ponens,[status(thm)],[16141, 16140])).
% 2.86/3.05 tff(16143,plain,
% 2.86/3.05 (~r(s(s(s(s(z)))), elem!1)),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[16142, 183, 16136, 16126, 16123])).
% 2.86/3.05 tff(16144,plain,
% 2.86/3.05 (s(s(s(s(z)))) = elem!1),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[13052, 16143, 16074])).
% 2.86/3.05 tff(16145,plain,
% 2.86/3.05 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 2.86/3.05 inference(monotonicity,[status(thm)],[16144])).
% 2.86/3.05 tff(16146,plain,
% 2.86/3.05 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 2.86/3.05 inference(transitivity,[status(thm)],[16145, 123])).
% 2.86/3.05 tff(16147,plain,
% 2.86/3.05 ((~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(s(elem!1))))) = elem!1))),
% 2.86/3.05 inference(monotonicity,[status(thm)],[16146])).
% 2.86/3.05 tff(16148,plain,
% 2.86/3.05 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 2.86/3.05 inference(modus_ponens,[status(thm)],[1501, 16147])).
% 2.86/3.05 tff(16149,plain,
% 2.86/3.05 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[86, 16148, 16073])).
% 2.86/3.05 tff(16150,plain,
% 2.86/3.05 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[2318, 183, 16064, 16149])).
% 2.86/3.06 tff(16151,plain,
% 2.86/3.06 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[1626, 16150])).
% 2.86/3.06 tff(16152,plain,
% 2.86/3.06 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[6281, 15705])).
% 2.86/3.06 tff(16153,plain,
% 2.86/3.06 (elem!1 = s(s(s(s(z))))),
% 2.86/3.06 inference(modus_ponens,[status(thm)],[16144, 5879])).
% 2.86/3.06 tff(16154,plain,
% 2.86/3.06 (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[11936, 16153, 16152])).
% 2.86/3.06 tff(16155,plain,
% 2.86/3.06 (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[1543, 183, 14545, 16149])).
% 2.86/3.06 tff(16156,plain,
% 2.86/3.06 (b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[1547, 47, 16155, 16154])).
% 2.86/3.06 tff(16157,plain,
% 2.86/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.86/3.06 inference(rewrite,[status(thm)],[])).
% 2.86/3.06 tff(16158,plain,
% 2.86/3.06 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.86/3.06 inference(rewrite,[status(thm)],[])).
% 2.86/3.06 tff(16159,plain,
% 2.86/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 2.86/3.06 inference(monotonicity,[status(thm)],[16158])).
% 2.86/3.06 tff(16160,plain,
% 2.86/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.86/3.06 inference(transitivity,[status(thm)],[16159, 16157])).
% 2.86/3.06 tff(16161,plain,
% 2.86/3.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 2.86/3.06 inference(quant_inst,[status(thm)],[])).
% 2.86/3.06 tff(16162,plain,
% 2.86/3.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 2.86/3.06 inference(modus_ponens,[status(thm)],[16161, 16160])).
% 2.86/3.06 tff(16163,plain,
% 2.86/3.06 ($false),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[16162, 246, 16077, 16069, 15604, 16156, 16151])).
% 2.86/3.06 tff(16164,plain,((~b(elem!1, z)) | (~r(s(s(s(s(s(elem!1))))), s(z))) | b(z, s(z)) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.86/3.06 tff(16165,plain,
% 2.86/3.06 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[16164, 15702, 54, 1])).
% 2.86/3.06 tff(16166,plain,
% 2.86/3.06 (b(s(s(s(s(s(elem!1))))), s(z))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[6447, 16165])).
% 2.86/3.06 tff(16167,plain,
% 2.86/3.06 (r(z, s(s(s(z))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[6165, 15915])).
% 2.86/3.06 tff(16168,plain,
% 2.86/3.06 (~r(s(z), s(s(s(z))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[6607, 16167, 170])).
% 2.86/3.06 tff(16169,plain,
% 2.86/3.06 (b(s(z), s(s(s(z))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[1291, 16168])).
% 2.86/3.06 tff(16170,plain,
% 2.86/3.06 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[642, 15862, 14545])).
% 2.86/3.06 tff(16171,plain,
% 2.86/3.06 (b(s(s(s(z))), s(s(elem!1)))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[689, 16170, 15705])).
% 2.86/3.06 tff(16172,plain,
% 2.86/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.86/3.06 inference(rewrite,[status(thm)],[])).
% 2.86/3.06 tff(16173,plain,
% 2.86/3.06 (((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z)))) <=> ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.86/3.06 inference(rewrite,[status(thm)],[])).
% 2.86/3.06 tff(16174,plain,
% 2.86/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 2.86/3.06 inference(monotonicity,[status(thm)],[16173])).
% 2.86/3.06 tff(16175,plain,
% 2.86/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.86/3.06 inference(transitivity,[status(thm)],[16174, 16172])).
% 2.86/3.06 tff(16176,plain,
% 2.86/3.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 2.86/3.06 inference(quant_inst,[status(thm)],[])).
% 2.86/3.06 tff(16177,plain,
% 2.86/3.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 2.86/3.06 inference(modus_ponens,[status(thm)],[16176, 16175])).
% 2.86/3.06 tff(16178,plain,
% 2.86/3.06 ($false),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[16177, 246, 4327, 2401, 963, 1885, 6875])).
% 2.86/3.06 tff(16179,plain,((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.06 tff(16180,plain,
% 2.86/3.06 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[16179, 16171, 16169, 15907, 16166])).
% 2.86/3.06 tff(16181,plain,
% 2.86/3.06 (r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[1626, 16180])).
% 2.86/3.06 tff(16182,plain,
% 2.86/3.06 (~b(elem!1, s(s(s(z))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[2011, 15860, 15604, 15840])).
% 2.86/3.06 tff(16183,plain,
% 2.86/3.06 (~(elem!1 = s(s(s(z))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[3013, 15861])).
% 2.86/3.06 tff(16184,plain,
% 2.86/3.06 (r(elem!1, s(s(s(z))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[470, 16183, 16182])).
% 2.86/3.06 tff(16185,plain,
% 2.86/3.06 ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z)))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[15817, 246, 15860, 15907, 15604])).
% 2.86/3.06 tff(16186,plain,
% 2.86/3.06 (~b(s(s(elem!1)), s(z))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[16185, 16169])).
% 2.86/3.06 tff(16187,plain,
% 2.86/3.06 (~(s(s(elem!1)) = elem!1)),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[2130, 16186, 15840])).
% 2.86/3.06 tff(16188,plain,
% 2.86/3.06 (~(elem!1 = s(s(elem!1)))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[5450, 16187])).
% 2.86/3.06 tff(16189,plain,
% 2.86/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))),
% 2.86/3.06 inference(rewrite,[status(thm)],[])).
% 2.86/3.06 tff(16190,plain,
% 2.86/3.06 (((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))),
% 2.86/3.06 inference(rewrite,[status(thm)],[])).
% 2.86/3.06 tff(16191,plain,
% 2.86/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z))))),
% 2.86/3.06 inference(monotonicity,[status(thm)],[16190])).
% 2.86/3.06 tff(16192,plain,
% 2.86/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))),
% 2.86/3.06 inference(transitivity,[status(thm)],[16191, 16189])).
% 2.86/3.06 tff(16193,plain,
% 2.86/3.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))),
% 2.86/3.06 inference(quant_inst,[status(thm)],[])).
% 2.86/3.06 tff(16194,plain,
% 2.86/3.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z))),
% 2.86/3.06 inference(modus_ponens,[status(thm)],[16193, 16192])).
% 2.86/3.06 tff(16195,plain,
% 2.86/3.06 (~b(elem!1, s(s(elem!1)))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[16194, 246, 11962, 15702, 15905])).
% 2.86/3.06 tff(16196,plain,
% 2.86/3.06 (r(elem!1, s(s(elem!1)))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[1268, 16195, 16188])).
% 2.86/3.06 tff(16197,plain,
% 2.86/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.86/3.06 inference(rewrite,[status(thm)],[])).
% 2.86/3.06 tff(16198,plain,
% 2.86/3.06 (((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.86/3.06 inference(rewrite,[status(thm)],[])).
% 2.86/3.06 tff(16199,plain,
% 2.86/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), elem!1))))),
% 2.86/3.06 inference(monotonicity,[status(thm)],[16198])).
% 2.86/3.06 tff(16200,plain,
% 2.86/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.86/3.06 inference(transitivity,[status(thm)],[16199, 16197])).
% 2.86/3.06 tff(16201,plain,
% 2.86/3.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.86/3.06 inference(quant_inst,[status(thm)],[])).
% 2.86/3.06 tff(16202,plain,
% 2.86/3.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 2.86/3.06 inference(modus_ponens,[status(thm)],[16201, 16200])).
% 2.86/3.06 tff(16203,plain,
% 2.86/3.06 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[16202, 183, 16196, 16184, 16181])).
% 2.86/3.06 tff(16204,plain,
% 2.86/3.06 (s(s(s(s(s(elem!1))))) = elem!1),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[86, 16203, 16051])).
% 2.86/3.06 tff(16205,plain,
% 2.86/3.06 (s(s(s(s(s(s(elem!1)))))) = s(elem!1)),
% 2.86/3.06 inference(monotonicity,[status(thm)],[16204])).
% 2.86/3.06 tff(16206,plain,
% 2.86/3.06 (s(s(s(s(s(s(s(elem!1))))))) = s(s(elem!1))),
% 2.86/3.06 inference(monotonicity,[status(thm)],[16205])).
% 2.86/3.06 tff(16207,plain,
% 2.86/3.06 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(elem!1)))))))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 2.86/3.06 inference(monotonicity,[status(thm)],[16206])).
% 2.86/3.06 tff(16208,plain,
% 2.86/3.06 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(s(elem!1))))))))),
% 2.86/3.06 inference(symmetry,[status(thm)],[16207])).
% 2.86/3.06 tff(16209,plain,
% 2.86/3.06 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(z)))))),
% 2.86/3.06 inference(transitivity,[status(thm)],[16208, 10601])).
% 2.86/3.06 tff(16210,plain,
% 2.86/3.06 (~b(s(s(s(s(z)))), elem!1)),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[12741, 15860, 15702])).
% 2.86/3.06 tff(16211,plain,
% 2.86/3.06 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(z)))) = elem!1)),
% 2.86/3.06 inference(monotonicity,[status(thm)],[16204])).
% 2.86/3.06 tff(16212,plain,
% 2.86/3.06 ((~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 2.86/3.06 inference(monotonicity,[status(thm)],[16211])).
% 2.86/3.06 tff(16213,plain,
% 2.86/3.06 (~(s(s(s(s(z)))) = elem!1)),
% 2.86/3.06 inference(modus_ponens,[status(thm)],[1501, 16212])).
% 2.86/3.06 tff(16214,plain,
% 2.86/3.06 (r(s(s(s(s(z)))), elem!1)),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[13052, 16213, 16210])).
% 2.86/3.06 tff(16215,plain,
% 2.86/3.06 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[9058, 183, 15862, 16214])).
% 2.86/3.06 tff(16216,plain,
% 2.86/3.06 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[1702, 16215])).
% 2.86/3.06 tff(16217,plain,
% 2.86/3.06 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[16102, 246, 15905, 16171, 15907, 16216])).
% 2.86/3.06 tff(16218,plain,
% 2.86/3.06 (r(s(s(elem!1)), s(z))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[197, 16186])).
% 2.86/3.06 tff(16219,plain,
% 2.86/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.86/3.06 inference(rewrite,[status(thm)],[])).
% 2.86/3.06 tff(16220,plain,
% 2.86/3.06 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.86/3.06 inference(rewrite,[status(thm)],[])).
% 2.86/3.06 tff(16221,plain,
% 2.86/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 2.86/3.06 inference(monotonicity,[status(thm)],[16220])).
% 2.86/3.06 tff(16222,plain,
% 2.86/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.86/3.06 inference(transitivity,[status(thm)],[16221, 16219])).
% 2.86/3.06 tff(16223,plain,
% 2.86/3.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.86/3.06 inference(quant_inst,[status(thm)],[])).
% 2.86/3.06 tff(16224,plain,
% 2.86/3.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 2.86/3.06 inference(modus_ponens,[status(thm)],[16223, 16222])).
% 2.86/3.06 tff(16225,plain,
% 2.86/3.06 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[16224, 183, 16218, 14545, 16214])).
% 2.86/3.06 tff(16226,plain,
% 2.86/3.06 ((s(s(s(s(z)))) = s(s(elem!1))) | b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[6521, 47, 16225])).
% 2.86/3.06 tff(16227,plain,
% 2.86/3.06 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[16226, 16217])).
% 2.86/3.06 tff(16228,plain,
% 2.86/3.06 (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(z))))),
% 2.86/3.06 inference(modus_ponens,[status(thm)],[16227, 16209])).
% 2.86/3.06 tff(16229,plain,
% 2.86/3.06 (~(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(z)))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[7214, 16204])).
% 2.86/3.06 tff(16230,plain,
% 2.86/3.06 ($false),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[16229, 16228])).
% 2.86/3.06 tff(16231,plain,(b(z, s(z)) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.86/3.06 tff(16232,plain,
% 2.86/3.06 (b(z, s(z))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[16231, 1])).
% 2.86/3.06 tff(16233,plain,
% 2.86/3.06 (~r(s(z), elem!1)),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[15837, 15811, 14545, 15705, 15806])).
% 2.86/3.06 tff(16234,plain,
% 2.86/3.06 (b(s(z), elem!1)),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[1034, 16233, 15605])).
% 2.86/3.06 tff(16235,plain,
% 2.86/3.06 (~r(elem!1, z)),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[13724, 15806, 15809, 16232])).
% 2.86/3.06 tff(16236,plain,
% 2.86/3.06 (b(elem!1, z)),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[12008, 16235])).
% 2.86/3.06 tff(16237,plain,
% 2.86/3.06 ($false),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[13451, 16236, 16234, 16232])).
% 2.86/3.06 tff(16238,plain,(b(elem!1, s(z)) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.86/3.06 tff(16239,plain,
% 2.86/3.06 (b(elem!1, s(z))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[16238, 1])).
% 2.86/3.06 tff(16240,plain,
% 2.86/3.06 (~b(s(z), elem!1)),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[13509, 16239, 16232])).
% 2.86/3.06 tff(16241,plain,
% 2.86/3.06 (r(s(z), elem!1)),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[1034, 16240, 15605])).
% 2.86/3.06 tff(16242,plain,
% 2.86/3.06 (~b(elem!1, z)),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[15858, 16241, 1])).
% 2.86/3.06 tff(16243,plain,
% 2.86/3.06 (r(elem!1, z)),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[12008, 16242])).
% 2.86/3.06 tff(16244,plain,
% 2.86/3.06 (~r(s(s(elem!1)), z)),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[14863, 16243, 14545])).
% 2.86/3.06 tff(16245,plain,
% 2.86/3.06 (b(s(s(elem!1)), z)),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[523, 16244])).
% 2.86/3.06 tff(16246,plain,
% 2.86/3.06 (~r(s(z), z)),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[2725, 16243, 16241])).
% 2.86/3.06 tff(16247,plain,
% 2.86/3.06 (b(s(z), z)),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[1069, 16246])).
% 2.86/3.06 tff(16248,plain,
% 2.86/3.06 ($false),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[15696, 16247, 16245, 16239, 16241])).
% 2.86/3.06 tff(16249,plain,(b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.86/3.06 tff(16250,plain,
% 2.86/3.06 (~r(elem!1, s(s(elem!1)))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[13212, 2340, 2246])).
% 2.86/3.06 tff(16251,plain,
% 2.86/3.06 (~r(s(s(elem!1)), s(z))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[11704, 2340, 14545])).
% 2.86/3.06 tff(16252,plain,
% 2.86/3.06 (b(s(s(elem!1)), s(z))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[197, 16251])).
% 2.86/3.06 tff(16253,plain,
% 2.86/3.06 (~r(z, s(z))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[2351, 2340, 2246])).
% 2.86/3.06 tff(16254,plain,
% 2.86/3.06 (b(z, s(z))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[169, 16253])).
% 2.86/3.06 tff(16255,plain,
% 2.86/3.06 (~r(s(z), z)),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[1163, 2340, 2246])).
% 2.86/3.06 tff(16256,plain,
% 2.86/3.06 (b(s(z), z)),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[1069, 16255])).
% 2.86/3.06 tff(16257,plain,
% 2.86/3.06 (~b(z, s(s(elem!1)))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[1154, 16256, 16254, 16252])).
% 2.86/3.06 tff(16258,plain,
% 2.86/3.06 (~(s(s(elem!1)) = elem!1)),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[11980, 16257])).
% 2.86/3.06 tff(16259,plain,
% 2.86/3.06 (~(elem!1 = s(s(elem!1)))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[5450, 16258])).
% 2.86/3.06 tff(16260,plain,
% 2.86/3.06 (b(elem!1, s(s(elem!1)))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[1268, 16259, 16250])).
% 2.86/3.06 tff(16261,plain,
% 2.86/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.86/3.06 inference(rewrite,[status(thm)],[])).
% 2.86/3.06 tff(16262,plain,
% 2.86/3.06 (((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.86/3.06 inference(rewrite,[status(thm)],[])).
% 2.86/3.06 tff(16263,plain,
% 2.86/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))))),
% 2.86/3.06 inference(monotonicity,[status(thm)],[16262])).
% 2.86/3.06 tff(16264,plain,
% 2.86/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.86/3.06 inference(transitivity,[status(thm)],[16263, 16261])).
% 2.86/3.06 tff(16265,plain,
% 2.86/3.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 2.86/3.06 inference(quant_inst,[status(thm)],[])).
% 2.86/3.06 tff(16266,plain,
% 2.86/3.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))),
% 2.86/3.06 inference(modus_ponens,[status(thm)],[16265, 16264])).
% 2.86/3.06 tff(16267,plain,
% 2.86/3.06 ($false),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[16266, 246, 11962, 16252, 16256, 6389, 16254, 16260])).
% 2.86/3.06 tff(16268,plain,((s(z) = elem!1) | (~r(elem!1, z)) | b(elem!1, s(z)) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.86/3.06 tff(16269,plain,
% 2.86/3.06 (s(z) = elem!1),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[16268, 13732, 210, 6388])).
% 2.86/3.06 tff(16270,plain,
% 2.86/3.06 (s(s(s(z))) = s(s(elem!1))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[121, 16269])).
% 2.86/3.06 tff(16271,plain,
% 2.86/3.06 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 2.86/3.06 inference(monotonicity,[status(thm)],[16270])).
% 2.86/3.06 tff(16272,plain,
% 2.86/3.06 (~(elem!1 = s(s(s(z))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[5785, 16249])).
% 2.86/3.06 tff(16273,plain,
% 2.86/3.06 (elem!1 = s(z)),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[9, 16269])).
% 2.86/3.06 tff(16274,plain,
% 2.86/3.06 (~b(s(z), z)),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[13737, 16273, 13731])).
% 2.86/3.06 tff(16275,plain,
% 2.86/3.06 (r(s(z), z)),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[1069, 16274])).
% 2.86/3.06 tff(16276,plain,
% 2.86/3.06 (b(s(s(s(z))), s(z))),
% 2.86/3.06 inference(modus_ponens,[status(thm)],[16249, 2286])).
% 2.86/3.06 tff(16277,plain,
% 2.86/3.06 ($false),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[2, 16276])).
% 2.86/3.06 tff(16278,plain,((~(s(z) = elem!1)) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.06 tff(16279,plain,
% 2.86/3.06 (b(s(s(s(z))), s(z))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[16278, 16269])).
% 2.86/3.06 tff(16280,plain,
% 2.86/3.06 (b(z, s(z))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[11969, 16273])).
% 2.86/3.06 tff(16281,plain,
% 2.86/3.06 (~r(elem!1, s(z))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[1163, 16275, 13732])).
% 2.86/3.06 tff(16282,plain,
% 2.86/3.06 (~(s(s(s(s(z)))) = elem!1)),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[13813, 16281, 16280, 6388])).
% 2.86/3.07 tff(16283,plain,
% 2.86/3.07 (~r(elem!1, s(s(s(z))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[14003, 16282, 16249, 13732, 16279, 16275])).
% 2.86/3.07 tff(16284,plain,
% 2.86/3.07 (b(elem!1, s(s(s(z))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[470, 16283, 16272])).
% 2.86/3.07 tff(16285,plain,
% 2.86/3.07 (b(elem!1, s(s(elem!1)))),
% 2.86/3.07 inference(modus_ponens,[status(thm)],[16284, 16271])).
% 2.86/3.07 tff(16286,plain,
% 2.86/3.07 (b(s(s(elem!1)), s(z))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[5773, 16273, 16249])).
% 2.86/3.07 tff(16287,plain,
% 2.86/3.07 (b(s(s(elem!1)), elem!1)),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[207, 16273, 16286])).
% 2.86/3.07 tff(16288,plain,
% 2.86/3.07 ($false),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[12995, 246, 11962, 16287, 14865, 16285])).
% 2.86/3.07 tff(16289,plain,(b(elem!1, z) | r(s(z), elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.07 tff(16290,plain,
% 2.86/3.07 (b(elem!1, z)),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[16289, 6388, 210])).
% 2.86/3.07 tff(16291,plain,
% 2.86/3.07 (~b(z, s(s(s(z))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[12015, 246, 11962, 1051, 16249])).
% 2.86/3.07 tff(16292,plain,
% 2.86/3.07 (r(z, s(s(s(z))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[6165, 16291])).
% 2.86/3.07 tff(16293,plain,
% 2.86/3.07 (~b(z, s(z))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[13451, 1044, 1051])).
% 2.86/3.07 tff(16294,plain,
% 2.86/3.07 (r(z, s(z))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[169, 16293])).
% 2.86/3.07 tff(16295,plain,
% 2.86/3.07 (~b(s(s(s(z))), s(z))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[12788, 1044, 16249, 1051])).
% 2.86/3.07 tff(16296,plain,
% 2.86/3.07 (r(s(s(s(z))), s(z))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[52, 16295])).
% 2.86/3.07 tff(16297,plain,
% 2.86/3.07 ($false),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[438, 16296, 16294, 16292])).
% 2.86/3.07 tff(16298,plain,((~b(s(z), elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.07 tff(16299,plain,
% 2.86/3.07 (~b(s(z), elem!1)),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[16298, 16290])).
% 2.86/3.07 tff(16300,plain,
% 2.86/3.07 (s(z) = elem!1),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[1034, 16299, 6388])).
% 2.86/3.07 tff(16301,plain,
% 2.86/3.07 (elem!1 = s(z)),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[9, 16300])).
% 2.86/3.07 tff(16302,plain,
% 2.86/3.07 (b(z, s(z))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[11969, 16301])).
% 2.86/3.07 tff(16303,plain,
% 2.86/3.07 (b(s(z), z)),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[14060, 16300, 16290])).
% 2.86/3.07 tff(16304,plain,
% 2.86/3.07 ($false),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[14317, 16303, 16301, 16249, 16302, 16290])).
% 2.86/3.07 tff(16305,plain,(r(s(z), elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.07 tff(16306,plain,
% 2.86/3.07 (r(s(z), elem!1)),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[16305, 210])).
% 2.86/3.07 tff(16307,plain,
% 2.86/3.07 (~r(s(z), s(s(elem!1)))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[223, 183, 16306, 14545])).
% 2.86/3.07 tff(16308,plain,
% 2.86/3.07 (b(s(z), s(s(elem!1)))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[233, 16307])).
% 2.86/3.07 tff(16309,plain,
% 2.86/3.07 (~r(s(z), z)),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[2725, 13732, 16306])).
% 2.86/3.07 tff(16310,plain,
% 2.86/3.07 (b(s(z), z)),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[1069, 16309])).
% 2.86/3.07 tff(16311,plain,
% 2.86/3.07 (~(elem!1 = s(z))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[13737, 16310, 13731])).
% 2.86/3.07 tff(16312,plain,
% 2.86/3.07 (r(elem!1, s(z))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[214, 16311, 210])).
% 2.86/3.07 tff(16313,plain,
% 2.86/3.07 (~r(elem!1, s(s(elem!1)))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[13212, 16312, 13732])).
% 2.86/3.07 tff(16314,plain,
% 2.86/3.07 (~r(s(s(elem!1)), s(z))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[11730, 16306, 14545])).
% 2.86/3.07 tff(16315,plain,
% 2.86/3.07 (b(s(s(elem!1)), s(z))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[197, 16314])).
% 2.86/3.07 tff(16316,plain,
% 2.86/3.07 (~r(z, s(z))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[2351, 16312, 13732])).
% 2.86/3.07 tff(16317,plain,
% 2.86/3.07 (b(z, s(z))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[169, 16316])).
% 2.86/3.07 tff(16318,plain,
% 2.86/3.07 (~b(z, s(s(elem!1)))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[1154, 16317, 16310, 16315])).
% 2.86/3.07 tff(16319,plain,
% 2.86/3.07 (~(s(s(elem!1)) = elem!1)),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[11980, 16318])).
% 2.86/3.07 tff(16320,plain,
% 2.86/3.07 (~(elem!1 = s(s(elem!1)))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[5450, 16319])).
% 2.86/3.07 tff(16321,plain,
% 2.86/3.07 (b(elem!1, s(s(elem!1)))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[1268, 16320, 16313])).
% 2.86/3.07 tff(16322,plain,
% 2.86/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))),
% 2.86/3.07 inference(rewrite,[status(thm)],[])).
% 2.86/3.07 tff(16323,plain,
% 2.86/3.07 (((~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))),
% 2.86/3.07 inference(rewrite,[status(thm)],[])).
% 2.86/3.07 tff(16324,plain,
% 2.86/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1))))))),
% 2.86/3.07 inference(monotonicity,[status(thm)],[16323])).
% 2.86/3.07 tff(16325,plain,
% 2.86/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))),
% 2.86/3.07 inference(transitivity,[status(thm)],[16324, 16322])).
% 2.86/3.07 tff(16326,plain,
% 2.86/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 2.86/3.07 inference(quant_inst,[status(thm)],[])).
% 2.86/3.07 tff(16327,plain,
% 2.86/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1))))),
% 2.86/3.07 inference(modus_ponens,[status(thm)],[16326, 16325])).
% 2.86/3.07 tff(16328,plain,
% 2.86/3.07 ($false),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[16327, 246, 11962, 16315, 16310, 14865, 16321, 16308])).
% 2.86/3.07 tff(16329,plain,(b(elem!1, z) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.07 tff(16330,plain,
% 2.86/3.07 (b(elem!1, z)),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[16329, 210])).
% 2.86/3.07 tff(16331,plain,
% 2.86/3.07 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[13383, 16330, 16249])).
% 2.86/3.07 tff(16332,plain,
% 2.86/3.07 (~b(s(s(s(z))), z)),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[12595, 246, 11962, 16330, 16249])).
% 2.86/3.07 tff(16333,plain,
% 2.86/3.07 (r(s(s(s(z))), z)),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[995, 16332])).
% 2.86/3.07 tff(16334,plain,
% 2.86/3.07 (~r(s(s(s(z))), s(z))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[438, 170, 16292])).
% 2.86/3.07 tff(16335,plain,
% 2.86/3.07 (b(s(s(s(z))), s(z))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[52, 16334])).
% 2.86/3.07 tff(16336,plain,
% 2.86/3.07 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[3488, 246, 15687, 14969, 16335])).
% 2.86/3.07 tff(16337,plain,
% 2.86/3.07 (r(s(s(elem!1)), s(s(s(z))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[454, 16336, 13043])).
% 2.86/3.07 tff(16338,plain,
% 2.86/3.07 (~b(s(s(s(z))), z)),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[12595, 246, 11962, 1051, 16249])).
% 2.86/3.07 tff(16339,plain,
% 2.86/3.07 (r(s(s(s(z))), z)),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[995, 16338])).
% 2.86/3.07 tff(16340,plain,
% 2.86/3.07 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[12070, 246, 15687, 14969, 16335])).
% 2.86/3.07 tff(16341,plain,
% 2.86/3.07 (r(s(s(s(z))), s(s(elem!1)))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[689, 16340, 13042])).
% 2.86/3.07 tff(16342,plain,
% 2.86/3.07 (~r(s(s(elem!1)), z)),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[1005, 16341, 14545, 16339])).
% 2.86/3.07 tff(16343,plain,
% 2.86/3.07 (b(s(s(elem!1)), z)),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[523, 16342])).
% 2.86/3.07 tff(16344,plain,
% 2.86/3.07 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[6281, 13042])).
% 2.86/3.07 tff(16345,plain,
% 2.86/3.07 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[13383, 1051, 16249])).
% 2.86/3.07 tff(16346,plain,
% 2.86/3.07 (~b(s(z), z)),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[12851, 1100, 1051, 15687])).
% 2.86/3.07 tff(16347,plain,
% 2.86/3.07 (r(s(z), z)),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[1069, 16346])).
% 2.86/3.07 tff(16348,plain,
% 2.86/3.07 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(elem!1)))))))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 2.86/3.07 inference(monotonicity,[status(thm)],[7197])).
% 2.86/3.07 tff(16349,plain,
% 2.86/3.07 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(s(elem!1))))))))),
% 2.86/3.07 inference(symmetry,[status(thm)],[16348])).
% 2.86/3.07 tff(16350,plain,
% 2.86/3.07 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(z)))))),
% 2.86/3.07 inference(transitivity,[status(thm)],[16349, 10601])).
% 2.86/3.07 tff(16351,plain,
% 2.86/3.07 (~r(s(z), s(s(s(z))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[6607, 171, 16292])).
% 2.86/3.07 tff(16352,plain,
% 2.86/3.07 (b(s(z), s(s(s(z))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[1291, 16351])).
% 2.86/3.07 tff(16353,plain,
% 2.86/3.07 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[14113, 8046, 217, 1114, 1051, 2002, 16249, 16352])).
% 2.86/3.07 tff(16354,plain,
% 2.86/3.07 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[1702, 16353])).
% 2.86/3.07 tff(16355,plain,
% 2.86/3.07 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[11340, 183, 216, 3886, 2593])).
% 2.86/3.07 tff(16356,assumption,(~(s(s(s(s(z)))) = s(s(elem!1)))), introduced(assumption)).
% 2.86/3.07 tff(16357,plain,
% 2.86/3.07 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[6521, 47, 16356, 16355])).
% 2.86/3.07 tff(16358,plain,
% 2.86/3.07 (b(s(s(s(s(z)))), z)),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[2424, 47, 2421, 12604])).
% 2.86/3.07 tff(16359,plain,
% 2.86/3.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.86/3.07 inference(rewrite,[status(thm)],[])).
% 2.86/3.07 tff(16360,plain,
% 2.86/3.07 (((~r(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.86/3.07 inference(rewrite,[status(thm)],[])).
% 2.86/3.07 tff(16361,plain,
% 2.86/3.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 2.86/3.07 inference(monotonicity,[status(thm)],[16360])).
% 2.86/3.07 tff(16362,plain,
% 2.86/3.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.86/3.07 inference(transitivity,[status(thm)],[16361, 16359])).
% 2.86/3.07 tff(16363,plain,
% 2.86/3.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(s(elem!1)))))),
% 2.86/3.07 inference(quant_inst,[status(thm)],[])).
% 2.86/3.07 tff(16364,plain,
% 2.86/3.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 2.86/3.07 inference(modus_ponens,[status(thm)],[16363, 16362])).
% 2.86/3.07 tff(16365,plain,
% 2.86/3.07 (~r(z, s(s(elem!1)))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[16364, 183, 3886, 429])).
% 2.86/3.07 tff(16366,plain,
% 2.86/3.07 (b(z, s(s(elem!1)))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[264, 16365])).
% 2.86/3.07 tff(16367,plain,
% 2.86/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)))),
% 2.86/3.07 inference(rewrite,[status(thm)],[])).
% 2.86/3.07 tff(16368,plain,
% 2.86/3.07 (((~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)))),
% 2.86/3.07 inference(rewrite,[status(thm)],[])).
% 2.86/3.07 tff(16369,plain,
% 2.86/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), z))))),
% 2.86/3.07 inference(monotonicity,[status(thm)],[16368])).
% 2.86/3.07 tff(16370,plain,
% 2.86/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)))),
% 2.86/3.07 inference(transitivity,[status(thm)],[16369, 16367])).
% 2.86/3.07 tff(16371,plain,
% 2.86/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)))),
% 2.86/3.07 inference(quant_inst,[status(thm)],[])).
% 2.86/3.07 tff(16372,plain,
% 2.86/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), z))),
% 2.86/3.07 inference(modus_ponens,[status(thm)],[16371, 16370])).
% 2.86/3.07 tff(16373,plain,
% 2.86/3.07 ($false),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[16372, 246, 201, 16366, 235, 16358, 16357])).
% 2.86/3.07 tff(16374,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (s(s(s(s(z)))) = s(s(elem!1))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.07 tff(16375,plain,
% 2.86/3.07 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[16374, 16354, 14545, 14969, 16292, 15687, 171, 3886])).
% 2.86/3.07 tff(16376,plain,
% 2.86/3.07 (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(z))))),
% 2.86/3.07 inference(modus_ponens,[status(thm)],[16375, 16350])).
% 2.86/3.07 tff(16377,plain,
% 2.86/3.07 ($false),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[7215, 16376])).
% 2.86/3.07 tff(16378,plain,((~(s(s(s(s(s(elem!1))))) = elem!1)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.07 tff(16379,plain,
% 2.86/3.07 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[16378, 2002, 3886, 217, 16347, 1051, 171])).
% 2.86/3.07 tff(16380,plain,
% 2.86/3.07 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[86, 16379, 16345])).
% 2.86/3.07 tff(16381,plain,
% 2.86/3.07 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[1551, 16380, 14545])).
% 2.86/3.07 tff(16382,plain,
% 2.86/3.07 (~r(z, s(s(elem!1)))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[16364, 183, 3886, 16292])).
% 2.86/3.07 tff(16383,plain,
% 2.86/3.07 (b(z, s(s(elem!1)))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[264, 16382])).
% 2.86/3.07 tff(16384,plain,
% 2.86/3.07 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[14064, 16380, 16347, 217])).
% 2.86/3.07 tff(16385,plain,
% 2.86/3.07 (b(s(s(s(s(s(elem!1))))), s(z))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[6447, 16384])).
% 2.86/3.07 tff(16386,plain,
% 2.86/3.07 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[10981, 16385, 14969, 1100, 16383])).
% 2.86/3.07 tff(16387,plain,
% 2.86/3.07 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[1557, 16386, 16381])).
% 2.86/3.07 tff(16388,plain,
% 2.86/3.07 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 2.86/3.07 inference(monotonicity,[status(thm)],[16387])).
% 2.86/3.07 tff(16389,plain,
% 2.86/3.07 ((~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(z)))) = s(s(elem!1))))),
% 2.86/3.07 inference(monotonicity,[status(thm)],[16388])).
% 2.86/3.07 tff(16390,plain,
% 2.86/3.07 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 2.86/3.07 inference(modus_ponens,[status(thm)],[1501, 16389])).
% 2.86/3.07 tff(16391,plain,
% 2.86/3.07 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[16374, 16390, 14545, 14969, 16292, 15687, 171, 3886])).
% 2.86/3.07 tff(16392,plain,
% 2.86/3.07 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(elem!1)))),
% 2.86/3.07 inference(monotonicity,[status(thm)],[16387])).
% 2.86/3.07 tff(16393,plain,
% 2.86/3.07 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(elem!1))))))),
% 2.86/3.07 inference(symmetry,[status(thm)],[16392])).
% 2.86/3.07 tff(16394,plain,
% 2.86/3.07 (s(elem!1) = s(s(s(s(elem!1))))),
% 2.86/3.07 inference(transitivity,[status(thm)],[108, 16393, 325])).
% 2.86/3.07 tff(16395,plain,
% 2.86/3.07 (inj_0(s(elem!1)) = inj_0(s(s(s(s(elem!1)))))),
% 2.86/3.07 inference(monotonicity,[status(thm)],[16394])).
% 2.86/3.07 tff(16396,plain,
% 2.86/3.07 (elem!1 = s(s(s(elem!1)))),
% 2.86/3.07 inference(transitivity,[status(thm)],[3154, 16395, 351])).
% 2.86/3.07 tff(16397,plain,
% 2.86/3.07 ((s(s(s(s(z)))) = elem!1) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 2.86/3.07 inference(monotonicity,[status(thm)],[16396])).
% 2.86/3.07 tff(16398,plain,
% 2.86/3.07 ((s(s(s(s(z)))) = elem!1) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 2.86/3.07 inference(transitivity,[status(thm)],[16397, 12214])).
% 2.86/3.07 tff(16399,plain,
% 2.86/3.07 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 2.86/3.07 inference(symmetry,[status(thm)],[16398])).
% 2.86/3.07 tff(16400,plain,
% 2.86/3.07 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 2.86/3.07 inference(monotonicity,[status(thm)],[16399])).
% 2.86/3.07 tff(16401,plain,
% 2.86/3.07 (~(s(s(s(s(z)))) = elem!1)),
% 2.86/3.07 inference(modus_ponens,[status(thm)],[6330, 16400])).
% 2.86/3.07 tff(16402,plain,
% 2.86/3.07 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[14113, 16401, 217, 16347, 1051, 2002, 16249, 16352])).
% 2.86/3.07 tff(16403,plain,
% 2.86/3.07 ($false),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[1702, 16402, 16391])).
% 2.86/3.07 tff(16404,plain,((~b(elem!1, s(s(s(z))))) | (~r(s(z), elem!1)) | (~b(elem!1, z)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(s(s(z))))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.07 tff(16405,plain,
% 2.86/3.07 (~b(elem!1, s(s(s(z))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[16404, 170, 1051, 217, 16337, 16344, 16343])).
% 2.86/3.07 tff(16406,plain,
% 2.86/3.07 (r(elem!1, s(s(s(z))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[470, 16405, 16272])).
% 2.86/3.07 tff(16407,plain,
% 2.86/3.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 2.86/3.07 inference(rewrite,[status(thm)],[])).
% 2.86/3.07 tff(16408,plain,
% 2.86/3.07 (((~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 2.86/3.07 inference(rewrite,[status(thm)],[])).
% 2.86/3.07 tff(16409,plain,
% 2.86/3.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))))),
% 2.86/3.07 inference(monotonicity,[status(thm)],[16408])).
% 2.86/3.07 tff(16410,plain,
% 2.86/3.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 2.86/3.07 inference(transitivity,[status(thm)],[16409, 16407])).
% 2.86/3.07 tff(16411,plain,
% 2.86/3.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)))),
% 2.86/3.07 inference(quant_inst,[status(thm)],[])).
% 2.86/3.07 tff(16412,plain,
% 2.86/3.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 2.86/3.07 inference(modus_ponens,[status(thm)],[16411, 16410])).
% 2.86/3.07 tff(16413,plain,
% 2.86/3.07 ($false),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[16412, 183, 14545, 16406, 16337])).
% 2.86/3.07 tff(16414,plain,(b(z, s(z)) | (~b(elem!1, z)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.07 tff(16415,plain,
% 2.86/3.07 (b(z, s(z))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[16414, 16330, 16306])).
% 2.86/3.07 tff(16416,plain,
% 2.86/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))),
% 2.86/3.07 inference(rewrite,[status(thm)],[])).
% 2.86/3.07 tff(16417,plain,
% 2.86/3.07 (((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z))) <=> ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))),
% 2.86/3.07 inference(rewrite,[status(thm)],[])).
% 2.86/3.07 tff(16418,plain,
% 2.86/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1))))))),
% 2.86/3.07 inference(monotonicity,[status(thm)],[16417])).
% 2.86/3.07 tff(16419,plain,
% 2.86/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))),
% 2.86/3.07 inference(transitivity,[status(thm)],[16418, 16416])).
% 2.86/3.07 tff(16420,plain,
% 2.86/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))),
% 2.86/3.07 inference(quant_inst,[status(thm)],[])).
% 2.86/3.07 tff(16421,plain,
% 2.86/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1))))),
% 2.86/3.07 inference(modus_ponens,[status(thm)],[16420, 16419])).
% 2.86/3.07 tff(16422,plain,
% 2.86/3.07 (~b(s(s(elem!1)), z)),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[16421, 246, 16315, 16415, 16308])).
% 2.86/3.07 tff(16423,plain,
% 2.86/3.07 (r(s(s(elem!1)), z)),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[523, 16422])).
% 2.86/3.08 tff(16424,plain,
% 2.86/3.08 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[1005, 16423, 14545, 16333])).
% 2.86/3.08 tff(16425,plain,
% 2.86/3.08 (b(s(s(s(z))), s(s(elem!1)))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[689, 7736, 16424])).
% 2.86/3.08 tff(16426,plain,
% 2.86/3.08 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))))),
% 2.86/3.08 inference(rewrite,[status(thm)],[])).
% 2.86/3.08 tff(16427,plain,
% 2.86/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z)))))),
% 2.86/3.08 inference(monotonicity,[status(thm)],[16426])).
% 2.86/3.08 tff(16428,plain,
% 2.86/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))))),
% 2.86/3.08 inference(transitivity,[status(thm)],[16427, 12065])).
% 2.86/3.08 tff(16429,plain,
% 2.86/3.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))))),
% 2.86/3.08 inference(quant_inst,[status(thm)],[])).
% 2.86/3.08 tff(16430,plain,
% 2.86/3.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z)))),
% 2.86/3.08 inference(modus_ponens,[status(thm)],[16429, 16428])).
% 2.86/3.08 tff(16431,plain,
% 2.86/3.08 (~b(s(s(s(z))), s(z))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[16430, 246, 16315, 16308, 16425])).
% 2.86/3.08 tff(16432,plain,
% 2.86/3.08 (r(s(s(s(z))), s(z))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[52, 16431])).
% 2.86/3.08 tff(16433,plain,
% 2.86/3.08 (~b(z, s(s(s(z))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[12015, 246, 11962, 16330, 16249])).
% 2.86/3.08 tff(16434,plain,
% 2.86/3.08 (r(z, s(s(s(z))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[6165, 16433])).
% 2.86/3.08 tff(16435,plain,
% 2.86/3.08 (~r(s(z), z)),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[13521, 16432, 16249, 16306])).
% 2.86/3.08 tff(16436,plain,
% 2.86/3.08 (b(s(z), z)),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[1069, 16435])).
% 2.86/3.08 tff(16437,plain,
% 2.86/3.08 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[13233, 16436, 16434, 16415, 16432])).
% 2.86/3.08 tff(16438,plain,
% 2.86/3.08 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[1702, 16437])).
% 2.86/3.08 tff(16439,plain,
% 2.86/3.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.86/3.08 inference(rewrite,[status(thm)],[])).
% 2.86/3.08 tff(16440,plain,
% 2.86/3.08 (((~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z)))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.86/3.08 inference(rewrite,[status(thm)],[])).
% 2.86/3.08 tff(16441,plain,
% 2.86/3.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 2.86/3.08 inference(monotonicity,[status(thm)],[16440])).
% 2.86/3.08 tff(16442,plain,
% 2.86/3.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.86/3.08 inference(transitivity,[status(thm)],[16441, 16439])).
% 2.86/3.08 tff(16443,plain,
% 2.86/3.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.86/3.08 inference(quant_inst,[status(thm)],[])).
% 2.86/3.08 tff(16444,plain,
% 2.86/3.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 2.86/3.08 inference(modus_ponens,[status(thm)],[16443, 16442])).
% 2.86/3.08 tff(16445,plain,
% 2.86/3.08 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[16444, 183, 16423, 16333])).
% 2.86/3.08 tff(16446,plain,
% 2.86/3.08 (b(s(s(elem!1)), s(s(s(z))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[454, 12305, 16445])).
% 2.86/3.08 tff(16447,plain,
% 2.86/3.08 (r(elem!1, s(z))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[214, 3, 210])).
% 2.86/3.08 tff(16448,plain,
% 2.86/3.08 (~r(elem!1, s(s(s(z))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[5796, 183, 16447, 16432])).
% 2.86/3.08 tff(16449,plain,
% 2.86/3.08 (b(elem!1, s(s(s(z))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[470, 16448, 16272])).
% 2.86/3.08 tff(16450,plain,
% 2.86/3.08 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[11859, 16449, 14545, 16249, 16446, 16438])).
% 2.86/3.08 tff(16451,plain,
% 2.86/3.08 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[86, 16450, 16331])).
% 2.86/3.08 tff(16452,plain,
% 2.86/3.08 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[1551, 16451, 14545])).
% 2.86/3.08 tff(16453,plain,
% 2.86/3.08 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[2307, 183, 16306, 16451])).
% 2.86/3.08 tff(16454,plain,
% 2.86/3.08 (b(s(s(s(s(s(elem!1))))), s(z))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[6447, 16453])).
% 2.86/3.08 tff(16455,plain,
% 2.86/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(elem!1))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 2.86/3.08 inference(rewrite,[status(thm)],[])).
% 2.86/3.08 tff(16456,plain,
% 2.86/3.08 (((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(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(elem!1))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 2.86/3.08 inference(rewrite,[status(thm)],[])).
% 2.86/3.08 tff(16457,plain,
% 2.86/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(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(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z)))))),
% 2.86/3.08 inference(monotonicity,[status(thm)],[16456])).
% 2.86/3.08 tff(16458,plain,
% 2.86/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(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(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 2.86/3.08 inference(transitivity,[status(thm)],[16457, 16455])).
% 2.86/3.08 tff(16459,plain,
% 2.86/3.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(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(elem!1)))))),
% 2.86/3.08 inference(quant_inst,[status(thm)],[])).
% 2.86/3.08 tff(16460,plain,
% 2.86/3.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z)))),
% 2.86/3.08 inference(modus_ponens,[status(thm)],[16459, 16458])).
% 2.86/3.08 tff(16461,plain,
% 2.86/3.08 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[16460, 246, 16315, 16436, 16415, 16454])).
% 2.86/3.08 tff(16462,plain,
% 2.86/3.08 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[1557, 16461, 16452])).
% 2.86/3.08 tff(16463,plain,
% 2.86/3.08 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(elem!1)))),
% 2.86/3.08 inference(monotonicity,[status(thm)],[16462])).
% 2.86/3.08 tff(16464,plain,
% 2.86/3.08 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(elem!1))))))),
% 2.86/3.08 inference(symmetry,[status(thm)],[16463])).
% 2.86/3.08 tff(16465,plain,
% 2.86/3.08 (s(elem!1) = s(s(s(s(elem!1))))),
% 2.86/3.08 inference(transitivity,[status(thm)],[108, 16464, 325])).
% 2.86/3.08 tff(16466,plain,
% 2.86/3.08 (inj_0(s(elem!1)) = inj_0(s(s(s(s(elem!1)))))),
% 2.86/3.08 inference(monotonicity,[status(thm)],[16465])).
% 2.86/3.08 tff(16467,plain,
% 2.86/3.08 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(elem!1))),
% 2.86/3.08 inference(symmetry,[status(thm)],[16466])).
% 2.86/3.08 tff(16468,plain,
% 2.86/3.08 (s(s(s(elem!1))) = elem!1),
% 2.86/3.08 inference(transitivity,[status(thm)],[352, 16467, 343])).
% 2.86/3.08 tff(16469,plain,
% 2.86/3.08 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 2.86/3.08 inference(monotonicity,[status(thm)],[16468])).
% 2.86/3.08 tff(16470,plain,
% 2.86/3.08 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.86/3.08 inference(symmetry,[status(thm)],[16469])).
% 2.86/3.08 tff(16471,plain,
% 2.86/3.08 (~b(elem!1, s(s(s(s(z)))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[13760, 16449, 16249, 16434])).
% 2.86/3.08 tff(16472,plain,
% 2.86/3.08 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[6281, 7736])).
% 2.86/3.08 tff(16473,plain,
% 2.86/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 2.86/3.08 inference(rewrite,[status(thm)],[])).
% 2.86/3.08 tff(16474,plain,
% 2.86/3.08 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 2.86/3.08 inference(rewrite,[status(thm)],[])).
% 2.86/3.08 tff(16475,plain,
% 2.86/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z)))))),
% 2.86/3.08 inference(monotonicity,[status(thm)],[16474])).
% 2.86/3.08 tff(16476,plain,
% 2.86/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 2.86/3.08 inference(transitivity,[status(thm)],[16475, 16473])).
% 2.86/3.08 tff(16477,plain,
% 2.86/3.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 2.86/3.08 inference(quant_inst,[status(thm)],[])).
% 2.86/3.08 tff(16478,plain,
% 2.86/3.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z)))),
% 2.86/3.08 inference(modus_ponens,[status(thm)],[16477, 16476])).
% 2.86/3.08 tff(16479,plain,
% 2.86/3.08 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[16478, 246, 16315, 16308, 16454])).
% 2.86/3.08 tff(16480,plain,
% 2.86/3.08 (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[1543, 183, 14545, 16451])).
% 2.86/3.08 tff(16481,plain,
% 2.86/3.08 ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[1547, 47, 16480])).
% 2.86/3.08 tff(16482,plain,
% 2.86/3.08 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[16481, 16479])).
% 2.86/3.08 tff(16483,plain,
% 2.86/3.08 (~(elem!1 = s(s(s(s(z)))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[11936, 16482, 16472])).
% 2.86/3.08 tff(16484,plain,
% 2.86/3.08 (r(elem!1, s(s(s(s(z)))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[13769, 16483, 16471])).
% 2.86/3.08 tff(16485,plain,
% 2.86/3.08 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.86/3.08 inference(modus_ponens,[status(thm)],[16484, 16470])).
% 2.86/3.08 tff(16486,plain,
% 2.86/3.08 (~(s(elem!1) = s(s(s(z))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[11452, 16462])).
% 2.86/3.08 tff(16487,plain,
% 2.86/3.08 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[16086, 16486])).
% 2.86/3.08 tff(16488,plain,
% 2.86/3.08 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[15127, 246, 16425, 16446, 16438])).
% 2.86/3.08 tff(16489,plain,
% 2.86/3.08 ((s(s(elem!1)) = s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[15060, 47, 16488])).
% 2.86/3.08 tff(16490,plain,
% 2.86/3.08 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[16489, 16487])).
% 2.86/3.08 tff(16491,plain,
% 2.86/3.08 (elem!1 = s(s(s(elem!1)))),
% 2.86/3.08 inference(transitivity,[status(thm)],[3154, 16466, 351])).
% 2.86/3.08 tff(16492,plain,
% 2.86/3.08 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.86/3.08 inference(monotonicity,[status(thm)],[16491])).
% 2.86/3.08 tff(16493,plain,
% 2.86/3.08 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.86/3.08 inference(modus_ponens,[status(thm)],[14545, 16492])).
% 2.86/3.08 tff(16494,plain,
% 2.86/3.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.86/3.08 inference(rewrite,[status(thm)],[])).
% 2.86/3.08 tff(16495,plain,
% 2.86/3.08 (((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.86/3.08 inference(rewrite,[status(thm)],[])).
% 2.86/3.08 tff(16496,plain,
% 2.86/3.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 2.86/3.08 inference(monotonicity,[status(thm)],[16495])).
% 2.86/3.08 tff(16497,plain,
% 2.86/3.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.86/3.08 inference(transitivity,[status(thm)],[16496, 16494])).
% 2.86/3.08 tff(16498,plain,
% 2.86/3.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.86/3.08 inference(quant_inst,[status(thm)],[])).
% 2.86/3.08 tff(16499,plain,
% 2.86/3.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 2.86/3.08 inference(modus_ponens,[status(thm)],[16498, 16497])).
% 2.86/3.08 tff(16500,plain,
% 2.86/3.08 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[16499, 183, 16493, 16490])).
% 2.86/3.08 tff(16501,plain,
% 2.86/3.08 ($false),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[16500, 16485])).
% 2.86/3.08 tff(16502,plain,((elem!1 = s(z)) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.08 tff(16503,plain,
% 2.86/3.08 (elem!1 = s(z)),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[16502, 210])).
% 2.86/3.08 tff(16504,plain,
% 2.86/3.08 (s(z) = elem!1),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[2279, 16503])).
% 2.86/3.08 tff(16505,plain,
% 2.86/3.08 (~b(s(z), z)),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[14317, 16503, 16249, 16415, 16330])).
% 2.86/3.08 tff(16506,plain,
% 2.86/3.08 ($false),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[14060, 16505, 16504, 16330])).
% 2.86/3.08 tff(16507,plain,(b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.08 tff(16508,plain,
% 2.86/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 2.86/3.08 inference(rewrite,[status(thm)],[])).
% 2.86/3.08 tff(16509,plain,
% 2.86/3.08 (((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z))) <=> ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 2.86/3.08 inference(rewrite,[status(thm)],[])).
% 2.86/3.08 tff(16510,plain,
% 2.86/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z))))),
% 2.86/3.08 inference(monotonicity,[status(thm)],[16509])).
% 2.86/3.08 tff(16511,plain,
% 2.86/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 2.86/3.08 inference(transitivity,[status(thm)],[16510, 16508])).
% 2.86/3.08 tff(16512,plain,
% 2.86/3.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 2.86/3.08 inference(quant_inst,[status(thm)],[])).
% 2.86/3.08 tff(16513,plain,
% 2.86/3.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z))),
% 2.86/3.09 inference(modus_ponens,[status(thm)],[16512, 16511])).
% 2.86/3.09 tff(16514,plain,
% 2.86/3.09 (~b(s(s(s(z))), z)),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[16513, 246, 11962, 1044, 16507, 16249])).
% 2.86/3.09 tff(16515,plain,
% 2.86/3.09 (r(s(s(s(z))), z)),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[995, 16514])).
% 2.86/3.09 tff(16516,plain,
% 2.86/3.09 (~b(s(z), z)),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[12312, 246, 11962, 1044, 16507])).
% 2.86/3.09 tff(16517,plain,
% 2.86/3.09 (r(s(z), z)),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[1069, 16516])).
% 2.86/3.09 tff(16518,plain,
% 2.86/3.09 (~b(s(s(s(z))), s(z))),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[7339, 246, 1044, 16507, 16249])).
% 2.86/3.09 tff(16519,plain,
% 2.86/3.09 (r(s(s(s(z))), s(z))),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[52, 16518])).
% 2.86/3.09 tff(16520,plain,
% 2.86/3.09 ($false),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[13364, 16519, 16517, 16515])).
% 2.86/3.09 tff(16521,plain,(~b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.86/3.09 tff(16522,plain,
% 2.86/3.09 (b(elem!1, s(z)) <=> b(elem!1, elem!1)),
% 2.86/3.09 inference(monotonicity,[status(thm)],[6])).
% 2.86/3.09 tff(16523,plain,
% 2.86/3.09 (b(elem!1, elem!1) <=> b(elem!1, s(z))),
% 2.86/3.09 inference(symmetry,[status(thm)],[16522])).
% 2.86/3.09 tff(16524,plain,
% 2.86/3.09 ((~b(elem!1, elem!1)) <=> (~b(elem!1, s(z)))),
% 2.86/3.09 inference(monotonicity,[status(thm)],[16523])).
% 2.86/3.09 tff(16525,plain,
% 2.86/3.09 (~b(elem!1, s(z))),
% 2.86/3.09 inference(modus_ponens,[status(thm)],[5691, 16524])).
% 2.86/3.09 tff(16526,plain,
% 2.86/3.09 ($false),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[16507, 16525])).
% 2.86/3.09 tff(16527,plain,(~(s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.86/3.09 tff(16528,plain,
% 2.86/3.09 (r(s(z), elem!1)),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[1034, 16527, 16521])).
% 2.86/3.09 tff(16529,plain,
% 2.86/3.09 (~r(s(z), z)),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[2725, 2246, 16528])).
% 2.86/3.09 tff(16530,plain,
% 2.86/3.09 (b(s(z), z)),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[1069, 16529])).
% 2.86/3.09 tff(16531,plain,
% 2.86/3.09 ($false),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[15696, 16530, 15293, 16507, 16528])).
% 2.86/3.09 tff(16532,plain,(~r(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 2.86/3.09 tff(16533,plain,
% 2.86/3.09 (b(elem!1, z)),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[12008, 16532])).
% 2.86/3.09 tff(16534,plain,
% 2.86/3.09 (b(z, s(z))),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[16414, 16533, 16528])).
% 2.86/3.09 tff(16535,plain,
% 2.86/3.09 (~b(s(z), z)),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[15718, 16533, 16507])).
% 2.86/3.09 tff(16536,plain,
% 2.86/3.09 (~b(s(s(s(z))), s(z))),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[14135, 16535, 16249, 16533, 16534])).
% 2.86/3.09 tff(16537,plain,
% 2.86/3.09 (r(s(z), z)),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[1069, 16535])).
% 2.86/3.09 tff(16538,plain,
% 2.86/3.09 (~r(s(s(s(z))), s(z))),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[13521, 16537, 16249, 16528])).
% 2.86/3.09 tff(16539,plain,
% 2.86/3.09 ($false),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[52, 16538, 16536])).
% 2.86/3.09 % SZS output end Proof
% 2.86/3.09 % E exiting
%------------------------------------------------------------------------------