%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRA166-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 06:34:21 PM UTC 2026
% Result : Unsatisfiable 0.97s 1.13s
% Output : Proof 1.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRA166-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.14/0.32 % Computer : n006.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 : Tue May 5 00:43:02 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.97/1.13 % SZS status Unsatisfiable
% 0.97/1.13 % SZS output start Proof
% 0.97/1.13 tff(r_type, type, (
% 0.97/1.13 r: ( $i * $i ) > $o)).
% 0.97/1.13 tff(s_type, type, (
% 0.97/1.13 s: $i > $i)).
% 0.97/1.13 tff(z_type, type, (
% 0.97/1.13 z: $i)).
% 0.97/1.13 tff(elem_1_type, type, (
% 0.97/1.13 elem_1: $i)).
% 0.97/1.13 tff(b_type, type, (
% 0.97/1.13 b: ( $i * $i ) > $o)).
% 0.97/1.13 tff(inj_0_type, type, (
% 0.97/1.13 inj_0: $i > $i)).
% 0.97/1.13 tff(1,assumption,(b(s(s(elem!1)), s(z))), introduced(assumption)).
% 0.97/1.13 tff(2,assumption,(s(z) = s(s(s(z)))), introduced(assumption)).
% 0.97/1.13 tff(3,plain,
% 0.97/1.13 (s(s(s(z))) = s(z)),
% 0.97/1.13 inference(symmetry,[status(thm)],[2])).
% 0.97/1.13 tff(4,plain,
% 0.97/1.13 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.97/1.13 inference(rewrite,[status(thm)],[])).
% 0.97/1.13 tff(5,plain,
% 0.97/1.13 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.97/1.13 inference(rewrite,[status(thm)],[])).
% 0.97/1.13 tff(6,plain,
% 0.97/1.13 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 0.97/1.13 inference(rewrite,[status(thm)],[])).
% 0.97/1.13 tff(7,axiom,(![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sinj')).
% 0.97/1.14 tff(8,plain,
% 0.97/1.14 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.97/1.14 tff(9,plain,(
% 0.97/1.14 ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 0.97/1.14 inference(skolemize,[status(sab)],[8])).
% 0.97/1.14 tff(10,plain,
% 0.97/1.14 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.97/1.14 tff(11,plain,
% 0.97/1.14 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[10, 4])).
% 0.97/1.14 tff(12,plain,
% 0.97/1.14 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(z)) = z)),
% 0.97/1.14 inference(quant_inst,[status(thm)],[])).
% 0.97/1.14 tff(13,plain,
% 0.97/1.14 (inj_0(s(z)) = z),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.97/1.14 tff(14,assumption,(s(s(s(z))) = s(z)), introduced(assumption)).
% 0.97/1.14 tff(15,plain,
% 0.97/1.14 (inj_0(s(s(s(z)))) = inj_0(s(z))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[14])).
% 0.97/1.14 tff(16,plain,
% 0.97/1.14 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(z)))) = s(s(z)))),
% 0.97/1.14 inference(quant_inst,[status(thm)],[])).
% 0.97/1.14 tff(17,plain,
% 0.97/1.14 (inj_0(s(s(s(z)))) = s(s(z))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[16, 11])).
% 0.97/1.14 tff(18,plain,
% 0.97/1.14 (s(s(z)) = inj_0(s(s(s(z))))),
% 0.97/1.14 inference(symmetry,[status(thm)],[17])).
% 0.97/1.14 tff(19,plain,
% 0.97/1.14 (s(s(z)) = z),
% 0.97/1.14 inference(transitivity,[status(thm)],[18, 15, 13])).
% 0.97/1.14 tff(20,plain,
% 0.97/1.14 (^[X: $i] : refl((~(s(X) = z)) <=> (~(s(X) = z)))),
% 0.97/1.14 inference(bind,[status(th)],[])).
% 0.97/1.14 tff(21,plain,
% 0.97/1.14 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 0.97/1.14 inference(quant_intro,[status(thm)],[20])).
% 0.97/1.14 tff(22,plain,
% 0.97/1.14 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 0.97/1.14 inference(rewrite,[status(thm)],[])).
% 0.97/1.14 tff(23,axiom,(![X: $i] : (~(s(X) = z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','snz')).
% 0.97/1.14 tff(24,plain,
% 0.97/1.14 (![X: $i] : (~(s(X) = z))),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.97/1.14 tff(25,plain,(
% 0.97/1.14 ![X: $i] : (~(s(X) = z))),
% 0.97/1.14 inference(skolemize,[status(sab)],[24])).
% 0.97/1.14 tff(26,plain,
% 0.97/1.14 (![X: $i] : (~(s(X) = z))),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.97/1.14 tff(27,plain,
% 0.97/1.14 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(z)) = z))),
% 0.97/1.14 inference(quant_inst,[status(thm)],[])).
% 0.97/1.14 tff(28,plain,
% 0.97/1.14 (~(s(s(z)) = z)),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.97/1.14 tff(29,plain,
% 0.97/1.14 ($false),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[28, 19])).
% 0.97/1.14 tff(30,plain,(~(s(s(s(z))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.14 tff(31,plain,
% 0.97/1.14 ($false),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[30, 3])).
% 0.97/1.14 tff(32,plain,(~(s(z) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.14 tff(33,assumption,(~b(s(s(z)), s(s(elem!1)))), introduced(assumption)).
% 0.97/1.14 tff(34,assumption,(~b(z, s(s(z)))), introduced(assumption)).
% 0.97/1.14 tff(35,assumption,(~b(z, s(s(elem!1)))), introduced(assumption)).
% 0.97/1.14 tff(36,plain,
% 0.97/1.14 ((z = s(s(elem!1))) <=> (s(s(elem!1)) = z)),
% 0.97/1.14 inference(commutativity,[status(thm)],[])).
% 0.97/1.14 tff(37,plain,
% 0.97/1.14 ((s(s(elem!1)) = z) <=> (z = s(s(elem!1)))),
% 0.97/1.14 inference(symmetry,[status(thm)],[36])).
% 0.97/1.14 tff(38,plain,
% 0.97/1.14 ((~(s(s(elem!1)) = z)) <=> (~(z = s(s(elem!1))))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[37])).
% 0.97/1.14 tff(39,plain,
% 0.97/1.14 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(elem!1)) = z))),
% 0.97/1.14 inference(quant_inst,[status(thm)],[])).
% 0.97/1.14 tff(40,plain,
% 0.97/1.14 (~(s(s(elem!1)) = z)),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[39, 26])).
% 0.97/1.14 tff(41,plain,
% 0.97/1.14 (~(z = s(s(elem!1)))),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[40, 38])).
% 0.97/1.14 tff(42,plain,
% 0.97/1.14 (^[Y: $i, X: $i] : refl(((X = Y) | b(X, Y) | r(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 0.97/1.14 inference(bind,[status(th)],[])).
% 0.97/1.14 tff(43,plain,
% 0.97/1.14 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.97/1.14 inference(quant_intro,[status(thm)],[42])).
% 0.97/1.14 tff(44,plain,
% 0.97/1.14 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.97/1.14 inference(rewrite,[status(thm)],[])).
% 0.97/1.14 tff(45,plain,
% 0.97/1.14 (^[Y: $i, X: $i] : rewrite((((X = Y) | r(X, Y)) | b(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 0.97/1.14 inference(bind,[status(th)],[])).
% 0.97/1.14 tff(46,plain,
% 0.97/1.14 (![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.97/1.14 inference(quant_intro,[status(thm)],[45])).
% 0.97/1.14 tff(47,axiom,(![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rb')).
% 0.97/1.14 tff(48,plain,
% 0.97/1.14 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.97/1.14 tff(49,plain,
% 0.97/1.14 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.97/1.14 tff(50,plain,(
% 0.97/1.14 ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.97/1.14 inference(skolemize,[status(sab)],[49])).
% 0.97/1.14 tff(51,plain,
% 0.97/1.14 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.97/1.14 tff(52,plain,
% 0.97/1.14 (((~![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))))),
% 0.97/1.14 inference(rewrite,[status(thm)],[])).
% 0.97/1.14 tff(53,plain,
% 0.97/1.14 ((~![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))))),
% 0.97/1.14 inference(quant_inst,[status(thm)],[])).
% 0.97/1.14 tff(54,plain,
% 0.97/1.14 ((~![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)))),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.97/1.14 tff(55,plain,
% 0.97/1.14 ((z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1)))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[54, 51])).
% 0.97/1.14 tff(56,plain,
% 0.97/1.14 (b(z, s(s(elem!1))) | r(z, s(s(elem!1)))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[55, 41])).
% 0.97/1.14 tff(57,plain,
% 0.97/1.14 (r(z, s(s(elem!1)))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[56, 35])).
% 0.97/1.14 tff(58,assumption,(~(s(s(s(elem!1))) = s(s(elem!1)))), introduced(assumption)).
% 0.97/1.14 tff(59,assumption,(~r(s(z), z)), introduced(assumption)).
% 0.97/1.14 tff(60,assumption,(~b(s(z), z)), introduced(assumption)).
% 0.97/1.14 tff(61,plain,
% 0.97/1.14 ((~![X: $i] : (~(s(X) = z))) | (~(s(z) = z))),
% 0.97/1.14 inference(quant_inst,[status(thm)],[])).
% 0.97/1.14 tff(62,plain,
% 0.97/1.14 (~(s(z) = z)),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[61, 26])).
% 0.97/1.14 tff(63,plain,
% 0.97/1.14 (((~![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))),
% 0.97/1.14 inference(rewrite,[status(thm)],[])).
% 0.97/1.14 tff(64,plain,
% 0.97/1.14 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = z) | b(s(z), z) | r(s(z), z))),
% 0.97/1.14 inference(quant_inst,[status(thm)],[])).
% 0.97/1.14 tff(65,plain,
% 0.97/1.14 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = z) | b(s(z), z) | r(s(z), z)),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.97/1.14 tff(66,plain,
% 0.97/1.14 ($false),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[65, 51, 62, 59, 60])).
% 0.97/1.14 tff(67,plain,(r(s(z), z) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 0.97/1.14 tff(68,plain,
% 0.97/1.14 (b(s(z), z)),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[67, 59])).
% 0.97/1.14 tff(69,assumption,(~r(s(s(z)), s(s(elem!1)))), introduced(assumption)).
% 0.97/1.14 tff(70,assumption,(r(z, s(s(elem!1)))), introduced(assumption)).
% 0.97/1.14 tff(71,assumption,(~b(s(s(elem!1)), z)), introduced(assumption)).
% 0.97/1.14 tff(72,plain,
% 0.97/1.14 (((~![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))),
% 0.97/1.14 inference(rewrite,[status(thm)],[])).
% 0.97/1.14 tff(73,plain,
% 0.97/1.14 ((~![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))),
% 0.97/1.14 inference(quant_inst,[status(thm)],[])).
% 0.97/1.14 tff(74,plain,
% 0.97/1.14 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = z) | b(s(s(elem!1)), z) | r(s(s(elem!1)), z)),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.97/1.14 tff(75,plain,
% 0.97/1.14 (b(s(s(elem!1)), z) | r(s(s(elem!1)), z)),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[74, 51, 40])).
% 0.97/1.14 tff(76,plain,
% 0.97/1.14 (r(s(s(elem!1)), z)),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[75, 71])).
% 0.97/1.14 tff(77,assumption,(s(s(elem!1)) = s(s(s(elem!1)))), introduced(assumption)).
% 0.97/1.14 tff(78,plain,
% 0.97/1.14 (s(s(s(elem!1))) = s(s(elem!1))),
% 0.97/1.14 inference(symmetry,[status(thm)],[77])).
% 0.97/1.14 tff(79,plain,
% 0.97/1.14 ($false),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[58, 78])).
% 0.97/1.14 tff(80,plain,((~(s(s(elem!1)) = s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.14 tff(81,plain,
% 0.97/1.14 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[80, 58])).
% 0.97/1.14 tff(82,plain,
% 0.97/1.14 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(elem!1)))) = s(s(elem!1)))),
% 0.97/1.14 inference(quant_inst,[status(thm)],[])).
% 0.97/1.14 tff(83,plain,
% 0.97/1.14 (inj_0(s(s(s(elem!1)))) = s(s(elem!1))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[82, 11])).
% 0.97/1.14 tff(84,assumption,(s(s(s(elem!1))) = s(s(s(s(elem!1))))), introduced(assumption)).
% 0.97/1.14 tff(85,plain,
% 0.97/1.14 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(elem!1)))))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[84])).
% 0.97/1.14 tff(86,plain,
% 0.97/1.14 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(elem!1))))),
% 0.97/1.14 inference(symmetry,[status(thm)],[85])).
% 0.97/1.14 tff(87,plain,
% 0.97/1.14 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 0.97/1.14 inference(quant_inst,[status(thm)],[])).
% 0.97/1.14 tff(88,plain,
% 0.97/1.14 (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[87, 11])).
% 0.97/1.14 tff(89,plain,
% 0.97/1.14 (s(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 0.97/1.14 inference(symmetry,[status(thm)],[88])).
% 0.97/1.14 tff(90,plain,
% 0.97/1.14 (s(s(s(elem!1))) = s(s(elem!1))),
% 0.97/1.14 inference(transitivity,[status(thm)],[89, 86, 83])).
% 0.97/1.14 tff(91,plain,
% 0.97/1.14 ($false),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[58, 90])).
% 0.97/1.14 tff(92,plain,((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.14 tff(93,plain,
% 0.97/1.14 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[92, 58])).
% 0.97/1.14 tff(94,plain,
% 0.97/1.14 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1)))))),
% 0.97/1.14 inference(quant_inst,[status(thm)],[])).
% 0.97/1.14 tff(95,plain,
% 0.97/1.14 (inj_0(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[94, 11])).
% 0.97/1.14 tff(96,assumption,(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))), introduced(assumption)).
% 0.97/1.14 tff(97,plain,
% 0.97/1.14 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(s(elem!1))))))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[96])).
% 0.97/1.14 tff(98,plain,
% 0.97/1.14 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 0.97/1.14 inference(transitivity,[status(thm)],[89, 97, 95])).
% 0.97/1.14 tff(99,assumption,(~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))), introduced(assumption)).
% 0.97/1.14 tff(100,plain,
% 0.97/1.14 ($false),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.97/1.14 tff(101,plain,((~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.14 tff(102,plain,
% 0.97/1.14 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[101, 93])).
% 0.97/1.14 tff(103,assumption,(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))), introduced(assumption)).
% 0.97/1.14 tff(104,plain,
% 0.97/1.14 (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))),
% 0.97/1.14 inference(symmetry,[status(thm)],[103])).
% 0.97/1.14 tff(105,assumption,(~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 0.97/1.14 tff(106,plain,
% 0.97/1.14 ($false),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.97/1.14 tff(107,plain,((~(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.14 tff(108,plain,
% 0.97/1.14 (~(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[107, 102])).
% 0.97/1.14 tff(109,assumption,(s(elem!1) = s(s(elem!1))), introduced(assumption)).
% 0.97/1.14 tff(110,plain,
% 0.97/1.14 (s(s(elem!1)) = s(elem!1)),
% 0.97/1.14 inference(symmetry,[status(thm)],[109])).
% 0.97/1.14 tff(111,plain,
% 0.97/1.14 (s(s(s(elem!1))) = s(s(elem!1))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[110])).
% 0.97/1.14 tff(112,plain,
% 0.97/1.14 ($false),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[58, 111])).
% 0.97/1.14 tff(113,plain,((~(s(elem!1) = s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.14 tff(114,plain,
% 0.97/1.14 (~(s(elem!1) = s(s(elem!1)))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[113, 58])).
% 0.97/1.14 tff(115,assumption,(r(s(s(elem!1)), z)), introduced(assumption)).
% 0.97/1.14 tff(116,assumption,(b(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 0.97/1.14 tff(117,plain,
% 0.97/1.14 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(elem!1))) = s(elem!1))),
% 0.97/1.14 inference(quant_inst,[status(thm)],[])).
% 0.97/1.14 tff(118,plain,
% 0.97/1.14 (inj_0(s(s(elem!1))) = s(elem!1)),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[117, 11])).
% 0.97/1.14 tff(119,plain,
% 0.97/1.14 (((~![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))))),
% 0.97/1.14 inference(rewrite,[status(thm)],[])).
% 0.97/1.14 tff(120,plain,
% 0.97/1.14 ((~![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))))),
% 0.97/1.14 inference(quant_inst,[status(thm)],[])).
% 0.97/1.14 tff(121,plain,
% 0.97/1.14 ((~![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)))),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.97/1.14 tff(122,plain,
% 0.97/1.14 ((s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1)))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[121, 51])).
% 0.97/1.14 tff(123,plain,
% 0.97/1.14 (s(s(z)) = s(s(elem!1))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[122, 33, 69])).
% 0.97/1.14 tff(124,plain,
% 0.97/1.14 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[123])).
% 0.97/1.14 tff(125,plain,
% 0.97/1.14 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(z))) = s(z))),
% 0.97/1.14 inference(quant_inst,[status(thm)],[])).
% 0.97/1.14 tff(126,plain,
% 0.97/1.14 (inj_0(s(s(z))) = s(z)),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[125, 11])).
% 0.97/1.14 tff(127,plain,
% 0.97/1.14 (s(z) = inj_0(s(s(z)))),
% 0.97/1.14 inference(symmetry,[status(thm)],[126])).
% 0.97/1.14 tff(128,plain,
% 0.97/1.14 (s(z) = s(elem!1)),
% 0.97/1.14 inference(transitivity,[status(thm)],[127, 124, 118])).
% 0.97/1.14 tff(129,plain,
% 0.97/1.14 (s(s(s(z))) = s(s(s(elem!1)))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[123])).
% 0.97/1.14 tff(130,plain,
% 0.97/1.14 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[129])).
% 0.97/1.14 tff(131,plain,
% 0.97/1.14 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[130, 128])).
% 0.97/1.14 tff(132,plain,
% 0.97/1.14 (s(s(z)) = s(s(elem!1))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[122, 69, 33])).
% 0.97/1.14 tff(133,assumption,(s(s(z)) = s(s(elem!1))), introduced(assumption)).
% 0.97/1.14 tff(134,plain,
% 0.97/1.14 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[133])).
% 0.97/1.14 tff(135,plain,
% 0.97/1.14 (s(z) = s(elem!1)),
% 0.97/1.14 inference(transitivity,[status(thm)],[127, 134, 118])).
% 0.97/1.14 tff(136,assumption,(~(s(z) = s(elem!1))), introduced(assumption)).
% 0.97/1.14 tff(137,plain,
% 0.97/1.14 ($false),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.97/1.14 tff(138,plain,((~(s(s(z)) = s(s(elem!1)))) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.14 tff(139,plain,
% 0.97/1.14 (s(z) = s(elem!1)),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[138, 132])).
% 0.97/1.14 tff(140,plain,
% 0.97/1.14 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(elem!1)) = elem!1)),
% 0.97/1.14 inference(quant_inst,[status(thm)],[])).
% 0.97/1.14 tff(141,plain,
% 0.97/1.14 (inj_0(s(elem!1)) = elem!1),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[140, 11])).
% 0.97/1.14 tff(142,assumption,(s(z) = s(elem!1)), introduced(assumption)).
% 0.97/1.14 tff(143,plain,
% 0.97/1.14 (inj_0(s(z)) = inj_0(s(elem!1))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[142])).
% 0.97/1.14 tff(144,plain,
% 0.97/1.14 (z = inj_0(s(z))),
% 0.97/1.14 inference(symmetry,[status(thm)],[13])).
% 0.97/1.14 tff(145,plain,
% 0.97/1.14 (z = elem!1),
% 0.97/1.14 inference(transitivity,[status(thm)],[144, 143, 141])).
% 0.97/1.14 tff(146,assumption,(~(z = elem!1)), introduced(assumption)).
% 0.97/1.14 tff(147,plain,
% 0.97/1.14 ($false),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.97/1.14 tff(148,plain,((~(s(z) = s(elem!1))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.97/1.14 tff(149,plain,
% 0.97/1.14 (z = elem!1),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[148, 139])).
% 0.97/1.14 tff(150,plain,
% 0.97/1.14 ((s(s(s(s(s(elem!1))))) = z) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 0.97/1.14 inference(monotonicity,[status(thm)],[149])).
% 0.97/1.14 tff(151,plain,
% 0.97/1.14 ((~(s(s(s(s(s(elem!1))))) = z)) <=> (~(s(s(s(s(s(elem!1))))) = elem!1))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[150])).
% 0.97/1.14 tff(152,plain,
% 0.97/1.14 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(elem!1))))) = z))),
% 0.97/1.14 inference(quant_inst,[status(thm)],[])).
% 0.97/1.14 tff(153,plain,
% 0.97/1.14 (~(s(s(s(s(s(elem!1))))) = z)),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[152, 26])).
% 0.97/1.14 tff(154,plain,
% 0.97/1.14 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[153, 151])).
% 0.97/1.14 tff(155,plain,
% 0.97/1.14 (elem!1 = z),
% 0.97/1.14 inference(symmetry,[status(thm)],[149])).
% 0.97/1.14 tff(156,plain,
% 0.97/1.14 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(elem!1))) = z)),
% 0.97/1.14 inference(monotonicity,[status(thm)],[155])).
% 0.97/1.14 tff(157,plain,
% 0.97/1.14 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 0.97/1.14 inference(symmetry,[status(thm)],[156])).
% 0.97/1.14 tff(158,plain,
% 0.97/1.14 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[157])).
% 0.97/1.14 tff(159,plain,
% 0.97/1.14 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(elem!1))) = z))),
% 0.97/1.14 inference(quant_inst,[status(thm)],[])).
% 0.97/1.14 tff(160,plain,
% 0.97/1.14 (~(s(s(s(elem!1))) = z)),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[159, 26])).
% 0.97/1.14 tff(161,plain,
% 0.97/1.14 (~(s(s(s(elem!1))) = elem!1)),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[160, 158])).
% 0.97/1.14 tff(162,plain,
% 0.97/1.14 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[132])).
% 0.97/1.14 tff(163,plain,
% 0.97/1.14 (s(z) = s(elem!1)),
% 0.97/1.14 inference(transitivity,[status(thm)],[127, 162, 118])).
% 0.97/1.14 tff(164,plain,
% 0.97/1.14 ((s(s(s(elem!1))) = s(z)) <=> (s(s(s(elem!1))) = s(elem!1))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[163])).
% 0.97/1.14 tff(165,plain,
% 0.97/1.14 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[164])).
% 0.97/1.14 tff(166,assumption,(s(s(s(elem!1))) = s(z)), introduced(assumption)).
% 0.97/1.14 tff(167,plain,
% 0.97/1.14 (inj_0(s(s(s(elem!1)))) = inj_0(s(z))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[166])).
% 0.97/1.14 tff(168,plain,
% 0.97/1.14 (s(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 0.97/1.14 inference(symmetry,[status(thm)],[83])).
% 0.97/1.14 tff(169,plain,
% 0.97/1.14 (s(s(elem!1)) = z),
% 0.97/1.14 inference(transitivity,[status(thm)],[168, 167, 13])).
% 0.97/1.14 tff(170,plain,
% 0.97/1.14 ($false),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[40, 169])).
% 0.97/1.14 tff(171,plain,(~(s(s(s(elem!1))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.14 tff(172,plain,
% 0.97/1.14 (~(s(s(s(elem!1))) = s(elem!1))),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[171, 165])).
% 0.97/1.14 tff(173,assumption,(s(s(s(s(elem!1)))) = s(s(elem!1))), introduced(assumption)).
% 0.97/1.14 tff(174,plain,
% 0.97/1.14 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(elem!1)))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[173])).
% 0.97/1.14 tff(175,plain,
% 0.97/1.14 (s(s(s(elem!1))) = s(elem!1)),
% 0.97/1.14 inference(transitivity,[status(thm)],[89, 174, 118])).
% 0.97/1.14 tff(176,assumption,(~(s(s(s(elem!1))) = s(elem!1))), introduced(assumption)).
% 0.97/1.14 tff(177,plain,
% 0.97/1.14 ($false),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[176, 175])).
% 0.97/1.14 tff(178,plain,((~(s(s(s(s(elem!1)))) = s(s(elem!1)))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.14 tff(179,plain,
% 0.97/1.14 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[178, 172])).
% 0.97/1.14 tff(180,assumption,(~r(s(s(elem!1)), s(z))), introduced(assumption)).
% 0.97/1.14 tff(181,plain,
% 0.97/1.14 ((s(s(s(elem!1))) = s(z)) <=> (s(s(s(elem!1))) = s(elem!1))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[135])).
% 0.97/1.14 tff(182,plain,
% 0.97/1.14 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[181])).
% 0.97/1.14 tff(183,plain,
% 0.97/1.14 (~(s(s(s(elem!1))) = s(elem!1))),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[171, 182])).
% 0.97/1.14 tff(184,plain,
% 0.97/1.14 ((s(elem!1) = elem!1) <=> (elem!1 = s(elem!1))),
% 0.97/1.14 inference(commutativity,[status(thm)],[])).
% 0.97/1.14 tff(185,plain,
% 0.97/1.14 ((elem!1 = s(elem!1)) <=> (s(elem!1) = elem!1)),
% 0.97/1.14 inference(symmetry,[status(thm)],[184])).
% 0.97/1.14 tff(186,plain,
% 0.97/1.14 (s(z) = s(elem!1)),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[138, 133])).
% 0.97/1.14 tff(187,plain,
% 0.97/1.14 (z = elem!1),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[148, 186])).
% 0.97/1.14 tff(188,plain,
% 0.97/1.14 ((s(elem!1) = z) <=> (s(elem!1) = elem!1)),
% 0.97/1.14 inference(monotonicity,[status(thm)],[187])).
% 0.97/1.14 tff(189,plain,
% 0.97/1.14 ((s(elem!1) = z) <=> (elem!1 = s(elem!1))),
% 0.97/1.14 inference(transitivity,[status(thm)],[188, 184])).
% 0.97/1.14 tff(190,plain,
% 0.97/1.14 ((s(elem!1) = z) <=> (s(elem!1) = elem!1)),
% 0.97/1.14 inference(transitivity,[status(thm)],[189, 185])).
% 0.97/1.14 tff(191,plain,
% 0.97/1.14 ((~(s(elem!1) = z)) <=> (~(s(elem!1) = elem!1))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[190])).
% 0.97/1.14 tff(192,plain,
% 0.97/1.14 ((~![X: $i] : (~(s(X) = z))) | (~(s(elem!1) = z))),
% 0.97/1.14 inference(quant_inst,[status(thm)],[])).
% 0.97/1.14 tff(193,plain,
% 0.97/1.14 (~(s(elem!1) = z)),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[192, 26])).
% 0.97/1.14 tff(194,plain,
% 0.97/1.14 (~(s(elem!1) = elem!1)),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[193, 191])).
% 0.97/1.14 tff(195,plain,
% 0.97/1.14 (r(s(z), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[135])).
% 0.97/1.14 tff(196,plain,
% 0.97/1.14 (r(s(elem!1), s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 0.97/1.14 inference(symmetry,[status(thm)],[195])).
% 0.97/1.14 tff(197,assumption,(r(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 0.97/1.14 tff(198,plain,
% 0.97/1.14 (r(s(z), s(s(elem!1)))),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.97/1.14 tff(199,plain,
% 0.97/1.14 (r(s(elem!1), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[133])).
% 0.97/1.14 tff(200,plain,
% 0.97/1.14 (r(s(elem!1), s(s(elem!1))) <=> r(s(elem!1), s(s(z)))),
% 0.97/1.14 inference(symmetry,[status(thm)],[199])).
% 0.97/1.14 tff(201,plain,
% 0.97/1.14 (r(s(elem!1), s(s(z)))),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[197, 200])).
% 0.97/1.14 tff(202,assumption,(b(z, s(s(elem!1)))), introduced(assumption)).
% 0.97/1.14 tff(203,assumption,(r(s(elem!1), s(s(z)))), introduced(assumption)).
% 0.97/1.14 tff(204,assumption,(s(s(elem!1)) = s(z)), introduced(assumption)).
% 0.97/1.14 tff(205,plain,
% 0.97/1.14 (inj_0(s(s(elem!1))) = inj_0(s(z))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[204])).
% 0.97/1.14 tff(206,plain,
% 0.97/1.14 (s(elem!1) = inj_0(s(s(elem!1)))),
% 0.97/1.14 inference(symmetry,[status(thm)],[118])).
% 0.97/1.14 tff(207,plain,
% 0.97/1.14 (s(elem!1) = z),
% 0.97/1.14 inference(transitivity,[status(thm)],[206, 205, 13])).
% 0.97/1.14 tff(208,plain,
% 0.97/1.14 ($false),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[193, 207])).
% 0.97/1.14 tff(209,plain,(~(s(s(elem!1)) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.14 tff(210,plain,
% 0.97/1.14 (((~![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)))),
% 0.97/1.14 inference(rewrite,[status(thm)],[])).
% 0.97/1.14 tff(211,plain,
% 0.97/1.14 ((~![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)))),
% 0.97/1.14 inference(quant_inst,[status(thm)],[])).
% 0.97/1.14 tff(212,plain,
% 0.97/1.14 ((~![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))),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.97/1.14 tff(213,plain,
% 0.97/1.14 ((s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[212, 51])).
% 0.97/1.14 tff(214,plain,
% 0.97/1.14 (b(s(s(elem!1)), s(z))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[213, 180, 209])).
% 0.97/1.14 tff(215,plain,
% 0.97/1.14 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 0.97/1.14 inference(symmetry,[status(thm)],[134])).
% 0.97/1.14 tff(216,plain,
% 0.97/1.14 (s(elem!1) = s(z)),
% 0.97/1.14 inference(transitivity,[status(thm)],[206, 215, 126])).
% 0.97/1.14 tff(217,plain,
% 0.97/1.14 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(z))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[216])).
% 0.97/1.14 tff(218,plain,
% 0.97/1.14 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 0.97/1.14 inference(symmetry,[status(thm)],[217])).
% 0.97/1.14 tff(219,plain,
% 0.97/1.14 (b(s(s(elem!1)), s(elem!1))),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[1, 218])).
% 0.97/1.14 tff(220,plain,
% 0.97/1.14 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 0.97/1.14 inference(commutativity,[status(thm)],[])).
% 0.97/1.14 tff(221,plain,
% 0.97/1.14 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[133])).
% 0.97/1.14 tff(222,plain,
% 0.97/1.14 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 0.97/1.14 inference(transitivity,[status(thm)],[221, 220])).
% 0.97/1.14 tff(223,plain,
% 0.97/1.14 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[222])).
% 0.97/1.14 tff(224,assumption,(s(s(z)) = s(s(s(elem!1)))), introduced(assumption)).
% 0.97/1.14 tff(225,plain,
% 0.97/1.14 (inj_0(s(s(z))) = inj_0(s(s(s(elem!1))))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[224])).
% 0.97/1.14 tff(226,plain,
% 0.97/1.14 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(z)))),
% 0.97/1.14 inference(symmetry,[status(thm)],[225])).
% 0.97/1.14 tff(227,plain,
% 0.97/1.14 (s(s(elem!1)) = s(z)),
% 0.97/1.14 inference(transitivity,[status(thm)],[168, 226, 126])).
% 0.97/1.14 tff(228,assumption,(~(s(s(elem!1)) = s(z))), introduced(assumption)).
% 0.97/1.14 tff(229,plain,
% 0.97/1.14 ($false),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[228, 227])).
% 0.97/1.14 tff(230,plain,((~(s(s(z)) = s(s(s(elem!1))))) | (s(s(elem!1)) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.14 tff(231,plain,
% 0.97/1.14 (~(s(s(z)) = s(s(s(elem!1))))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[230, 209])).
% 0.97/1.14 tff(232,plain,
% 0.97/1.14 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[231, 223])).
% 0.97/1.14 tff(233,plain,
% 0.97/1.14 (elem!1 = z),
% 0.97/1.14 inference(symmetry,[status(thm)],[187])).
% 0.97/1.14 tff(234,plain,
% 0.97/1.14 (b(elem!1, s(s(z))) <=> b(z, s(s(elem!1)))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[233, 133])).
% 0.97/1.14 tff(235,plain,
% 0.97/1.14 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(z)))),
% 0.97/1.14 inference(symmetry,[status(thm)],[234])).
% 0.97/1.14 tff(236,plain,
% 0.97/1.14 (b(elem!1, s(s(z)))),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[202, 235])).
% 0.97/1.14 tff(237,plain,
% 0.97/1.14 (s(s(elem!1)) = s(s(z))),
% 0.97/1.14 inference(symmetry,[status(thm)],[133])).
% 0.97/1.14 tff(238,plain,
% 0.97/1.14 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(z)))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[237])).
% 0.97/1.14 tff(239,plain,
% 0.97/1.14 (b(elem!1, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 0.97/1.14 inference(symmetry,[status(thm)],[238])).
% 0.97/1.14 tff(240,assumption,(b(elem!1, s(s(z)))), introduced(assumption)).
% 0.97/1.14 tff(241,plain,
% 0.97/1.14 (b(elem!1, s(s(elem!1)))),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[240, 239])).
% 0.97/1.14 tff(242,assumption,(~b(elem!1, s(s(elem!1)))), introduced(assumption)).
% 0.97/1.14 tff(243,plain,
% 0.97/1.14 ($false),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[242, 241])).
% 0.97/1.14 tff(244,plain,(b(elem!1, s(s(elem!1))) | (~b(elem!1, s(s(z)))) | (~(s(s(z)) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.14 tff(245,plain,
% 0.97/1.14 (b(elem!1, s(s(elem!1)))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[244, 236, 133])).
% 0.97/1.14 tff(246,plain,
% 0.97/1.14 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(elem!1))) = z)),
% 0.97/1.14 inference(monotonicity,[status(thm)],[233])).
% 0.97/1.14 tff(247,plain,
% 0.97/1.14 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 0.97/1.14 inference(symmetry,[status(thm)],[246])).
% 0.97/1.14 tff(248,plain,
% 0.97/1.14 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[247])).
% 0.97/1.14 tff(249,plain,
% 0.97/1.14 (~(s(s(s(elem!1))) = elem!1)),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[160, 248])).
% 0.97/1.14 tff(250,plain,
% 0.97/1.14 ((elem!1 = s(s(elem!1))) <=> (z = s(s(elem!1)))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[233])).
% 0.97/1.14 tff(251,plain,
% 0.97/1.14 ((elem!1 = s(s(elem!1))) <=> (s(s(elem!1)) = z)),
% 0.97/1.14 inference(transitivity,[status(thm)],[250, 36])).
% 0.97/1.14 tff(252,plain,
% 0.97/1.14 ((s(s(elem!1)) = z) <=> (elem!1 = s(s(elem!1)))),
% 0.97/1.14 inference(symmetry,[status(thm)],[251])).
% 0.97/1.14 tff(253,plain,
% 0.97/1.14 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = s(s(elem!1))))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[252])).
% 0.97/1.14 tff(254,plain,
% 0.97/1.14 (~(elem!1 = s(s(elem!1)))),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[40, 253])).
% 0.97/1.14 tff(255,assumption,(s(s(s(elem!1))) = s(elem!1)), introduced(assumption)).
% 0.97/1.14 tff(256,plain,
% 0.97/1.14 (inj_0(s(s(s(elem!1)))) = inj_0(s(elem!1))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[255])).
% 0.97/1.14 tff(257,plain,
% 0.97/1.14 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 0.97/1.14 inference(symmetry,[status(thm)],[256])).
% 0.97/1.14 tff(258,plain,
% 0.97/1.14 (elem!1 = inj_0(s(elem!1))),
% 0.97/1.14 inference(symmetry,[status(thm)],[141])).
% 0.97/1.14 tff(259,plain,
% 0.97/1.14 (elem!1 = s(s(elem!1))),
% 0.97/1.14 inference(transitivity,[status(thm)],[258, 257, 83])).
% 0.97/1.14 tff(260,assumption,(~(elem!1 = s(s(elem!1)))), introduced(assumption)).
% 0.97/1.14 tff(261,plain,
% 0.97/1.14 ($false),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[260, 259])).
% 0.97/1.14 tff(262,plain,((~(s(s(s(elem!1))) = s(elem!1))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.14 tff(263,plain,
% 0.97/1.14 (~(s(s(s(elem!1))) = s(elem!1))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[262, 254])).
% 0.97/1.14 tff(264,plain,
% 0.97/1.14 (r(s(elem!1), s(s(elem!1)))),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[203, 199])).
% 0.97/1.14 tff(265,plain,
% 0.97/1.14 (r(s(z), s(s(elem!1)))),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[264, 196])).
% 0.97/1.14 tff(266,assumption,(s(elem!1) = s(s(s(elem!1)))), introduced(assumption)).
% 0.97/1.14 tff(267,plain,
% 0.97/1.14 (s(s(s(elem!1))) = s(elem!1)),
% 0.97/1.14 inference(symmetry,[status(thm)],[266])).
% 0.97/1.14 tff(268,plain,
% 0.97/1.14 ($false),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[176, 267])).
% 0.97/1.14 tff(269,plain,((~(s(elem!1) = s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.14 tff(270,plain,
% 0.97/1.14 (~(s(elem!1) = s(s(s(elem!1))))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[269, 263])).
% 0.97/1.14 tff(271,plain,
% 0.97/1.14 ((~(s(elem!1) = z)) <=> (~(elem!1 = s(elem!1)))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[189])).
% 0.97/1.14 tff(272,plain,
% 0.97/1.14 (~(elem!1 = s(elem!1))),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[193, 271])).
% 0.97/1.14 tff(273,plain,
% 0.97/1.14 (b(elem!1, s(s(elem!1)))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[244, 240, 133])).
% 0.97/1.14 tff(274,assumption,(b(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 0.97/1.14 tff(275,assumption,(b(elem!1, s(elem!1))), introduced(assumption)).
% 0.97/1.14 tff(276,plain,
% 0.97/1.14 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 0.97/1.14 inference(commutativity,[status(thm)],[])).
% 0.97/1.14 tff(277,plain,
% 0.97/1.14 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(elem!1))))),
% 0.97/1.14 inference(symmetry,[status(thm)],[276])).
% 0.97/1.14 tff(278,plain,
% 0.97/1.14 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[277])).
% 0.97/1.14 tff(279,plain,
% 0.97/1.14 (~(s(elem!1) = s(s(s(elem!1))))),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[263, 278])).
% 0.97/1.14 tff(280,plain,
% 0.97/1.14 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 0.97/1.14 inference(monotonicity,[status(thm)],[187])).
% 0.97/1.14 tff(281,plain,
% 0.97/1.14 (r(s(z), z) <=> r(s(z), elem!1)),
% 0.97/1.14 inference(monotonicity,[status(thm)],[187])).
% 0.97/1.14 tff(282,plain,
% 0.97/1.14 (r(s(z), elem!1) <=> r(s(z), z)),
% 0.97/1.14 inference(symmetry,[status(thm)],[281])).
% 0.97/1.14 tff(283,plain,
% 0.97/1.14 (r(s(z), elem!1) <=> r(s(elem!1), elem!1)),
% 0.97/1.14 inference(monotonicity,[status(thm)],[135])).
% 0.97/1.14 tff(284,plain,
% 0.97/1.14 (r(s(elem!1), elem!1) <=> r(s(z), elem!1)),
% 0.97/1.14 inference(symmetry,[status(thm)],[283])).
% 0.97/1.14 tff(285,plain,
% 0.97/1.14 (r(s(elem!1), elem!1) <=> r(s(z), z)),
% 0.97/1.14 inference(transitivity,[status(thm)],[284, 282])).
% 0.97/1.14 tff(286,assumption,(r(s(elem!1), elem!1)), introduced(assumption)).
% 0.97/1.14 tff(287,plain,
% 0.97/1.14 (r(s(z), z)),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[286, 285])).
% 0.97/1.14 tff(288,plain,
% 0.97/1.14 (^[X0: $i, X2: $i, X1: $i] : refl(((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))))),
% 0.97/1.14 inference(bind,[status(th)],[])).
% 0.97/1.14 tff(289,plain,
% 0.97/1.14 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.97/1.14 inference(quant_intro,[status(thm)],[288])).
% 0.97/1.14 tff(290,plain,
% 0.97/1.14 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.97/1.14 inference(rewrite,[status(thm)],[])).
% 0.97/1.14 tff(291,plain,
% 0.97/1.14 (^[X0: $i, X2: $i, X1: $i] : rewrite((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) <=> ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))))),
% 0.97/1.14 inference(bind,[status(th)],[])).
% 0.97/1.14 tff(292,plain,
% 0.97/1.14 (![X0: $i, X2: $i, X1: $i] : (((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) <=> ![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.97/1.14 inference(quant_intro,[status(thm)],[291])).
% 0.97/1.14 tff(293,axiom,(![X0: $i, X2: $i, X1: $i] : (((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axr')).
% 0.97/1.14 tff(294,plain,
% 0.97/1.14 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[293, 292])).
% 0.97/1.14 tff(295,plain,
% 0.97/1.15 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[294, 290])).
% 0.97/1.15 tff(296,plain,(
% 0.97/1.15 ![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.97/1.15 inference(skolemize,[status(sab)],[295])).
% 0.97/1.15 tff(297,plain,
% 0.97/1.15 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[296, 289])).
% 0.97/1.15 tff(298,plain,
% 0.97/1.15 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(299,plain,
% 0.97/1.15 (((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(300,plain,
% 0.97/1.15 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z))))),
% 0.97/1.15 inference(monotonicity,[status(thm)],[299])).
% 0.97/1.15 tff(301,plain,
% 0.97/1.15 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)))),
% 0.97/1.15 inference(transitivity,[status(thm)],[300, 298])).
% 0.97/1.15 tff(302,plain,
% 0.97/1.15 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))),
% 0.97/1.15 inference(quant_inst,[status(thm)],[])).
% 0.97/1.15 tff(303,plain,
% 0.97/1.15 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[302, 301])).
% 0.97/1.15 tff(304,plain,
% 0.97/1.15 ((~r(s(z), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z))),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[303, 297])).
% 0.97/1.15 tff(305,plain,
% 0.97/1.15 (~r(s(s(elem!1)), z)),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[304, 287, 198])).
% 0.97/1.15 tff(306,plain,
% 0.97/1.15 (b(s(s(elem!1)), z)),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[75, 305])).
% 0.97/1.15 tff(307,plain,
% 0.97/1.15 (b(s(s(elem!1)), elem!1)),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[306, 280])).
% 0.97/1.15 tff(308,assumption,(b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 0.97/1.15 tff(309,assumption,(b(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 0.97/1.15 tff(310,plain,
% 0.97/1.15 (^[X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) <=> ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))))),
% 0.97/1.15 inference(bind,[status(th)],[])).
% 0.97/1.15 tff(311,plain,
% 0.97/1.15 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 0.97/1.15 inference(quant_intro,[status(thm)],[310])).
% 0.97/1.15 tff(312,plain,
% 0.97/1.15 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(313,plain,
% 0.97/1.15 (^[X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~b(X0, X1)) | (~b(X1, X2))) <=> ((~b(X1, X2)) | (~b(X0, X1)))), ((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) <=> (((~b(X1, X2)) | (~b(X0, X1))) | (~b(X0, X3))))), rewrite((((~b(X1, X2)) | (~b(X0, X1))) | (~b(X0, X3))) <=> ((~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))), ((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) <=> ((~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))))), (((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) <=> (((~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X1, X3))))), rewrite((((~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X1, X3))) <=> ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))), (((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) <=> ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))))), ((((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) | (~b(X2, X4))) <=> (((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X2, X4))))), rewrite((((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X2, X4))) <=> ((~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))), ((((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) | (~b(X2, X4))) <=> ((~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))))), (((((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) | (~b(X2, X4))) | (~b(X3, X4))) <=> (((~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X3, X4))))), rewrite((((~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X3, X4))) <=> ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))), (((((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) | (~b(X2, X4))) | (~b(X3, X4))) <=> ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))))),
% 0.97/1.15 inference(bind,[status(th)],[])).
% 0.97/1.15 tff(314,plain,
% 0.97/1.15 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) | (~b(X2, X4))) | (~b(X3, X4))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 0.97/1.15 inference(quant_intro,[status(thm)],[313])).
% 0.97/1.15 tff(315,axiom,(![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) | (~b(X2, X4))) | (~b(X3, X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axb')).
% 0.97/1.15 tff(316,plain,
% 0.97/1.15 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[315, 314])).
% 0.97/1.15 tff(317,plain,
% 0.97/1.15 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[316, 312])).
% 0.97/1.15 tff(318,plain,(
% 0.97/1.15 ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 0.97/1.15 inference(skolemize,[status(sab)],[317])).
% 0.97/1.15 tff(319,plain,
% 0.97/1.15 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[318, 311])).
% 0.97/1.15 tff(320,plain,
% 0.97/1.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(321,plain,
% 0.97/1.15 (((~b(s(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(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(322,plain,
% 0.97/1.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))))),
% 0.97/1.15 inference(monotonicity,[status(thm)],[321])).
% 0.97/1.15 tff(323,plain,
% 0.97/1.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 0.97/1.15 inference(transitivity,[status(thm)],[322, 320])).
% 0.97/1.15 tff(324,plain,
% 0.97/1.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 0.97/1.15 inference(quant_inst,[status(thm)],[])).
% 0.97/1.15 tff(325,plain,
% 0.97/1.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[324, 323])).
% 0.97/1.15 tff(326,plain,
% 0.97/1.15 ($false),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[325, 319, 275, 309, 274, 308])).
% 0.97/1.15 tff(327,plain,((~b(s(elem!1), 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))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.15 tff(328,plain,
% 0.97/1.15 (~b(s(elem!1), s(s(s(elem!1))))),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[327, 307, 274, 275])).
% 0.97/1.15 tff(329,plain,
% 0.97/1.15 (((~![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)))))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(330,plain,
% 0.97/1.15 ((~![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)))))),
% 0.97/1.15 inference(quant_inst,[status(thm)],[])).
% 0.97/1.15 tff(331,plain,
% 0.97/1.15 ((~![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))))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[330, 329])).
% 0.97/1.15 tff(332,plain,
% 0.97/1.15 ((s(elem!1) = s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1))))),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[331, 51, 328])).
% 0.97/1.15 tff(333,plain,
% 0.97/1.15 (r(s(elem!1), s(s(s(elem!1))))),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[332, 279])).
% 0.97/1.15 tff(334,assumption,(r(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 0.97/1.15 tff(335,assumption,(r(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 0.97/1.15 tff(336,plain,
% 0.97/1.15 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(337,plain,
% 0.97/1.15 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1)))))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(338,plain,
% 0.97/1.15 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1))))))),
% 0.97/1.15 inference(monotonicity,[status(thm)],[337])).
% 0.97/1.15 tff(339,plain,
% 0.97/1.15 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 0.97/1.15 inference(transitivity,[status(thm)],[338, 336])).
% 0.97/1.15 tff(340,plain,
% 0.97/1.15 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 0.97/1.15 inference(quant_inst,[status(thm)],[])).
% 0.97/1.15 tff(341,plain,
% 0.97/1.15 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1))))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[340, 339])).
% 0.97/1.15 tff(342,plain,
% 0.97/1.15 ($false),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[341, 297, 197, 335, 334])).
% 0.97/1.15 tff(343,plain,((~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)))))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.15 tff(344,plain,
% 0.97/1.15 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[343, 333, 197])).
% 0.97/1.15 tff(345,plain,
% 0.97/1.15 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1))))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(346,plain,
% 0.97/1.15 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1))))),
% 0.97/1.15 inference(quant_inst,[status(thm)],[])).
% 0.97/1.15 tff(347,plain,
% 0.97/1.15 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[346, 345])).
% 0.97/1.15 tff(348,plain,
% 0.97/1.15 ((s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[347, 51])).
% 0.97/1.15 tff(349,plain,
% 0.97/1.15 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[348, 344, 232])).
% 0.97/1.15 tff(350,plain,
% 0.97/1.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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))), elem!1)))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(351,plain,
% 0.97/1.15 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(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))), elem!1)))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(352,plain,
% 0.97/1.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))), elem!1))))),
% 0.97/1.15 inference(monotonicity,[status(thm)],[351])).
% 0.97/1.15 tff(353,plain,
% 0.97/1.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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))), elem!1)))),
% 0.97/1.15 inference(transitivity,[status(thm)],[352, 350])).
% 0.97/1.15 tff(354,plain,
% 0.97/1.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))),
% 0.97/1.15 inference(quant_inst,[status(thm)],[])).
% 0.97/1.15 tff(355,plain,
% 0.97/1.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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))), elem!1))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[354, 353])).
% 0.97/1.15 tff(356,plain,
% 0.97/1.15 ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1))),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[355, 319, 274, 349])).
% 0.97/1.15 tff(357,plain,
% 0.97/1.15 (~b(s(s(s(elem!1))), elem!1)),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[356, 241])).
% 0.97/1.15 tff(358,plain,
% 0.97/1.15 (((~![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))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(359,plain,
% 0.97/1.15 ((~![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))),
% 0.97/1.15 inference(quant_inst,[status(thm)],[])).
% 0.97/1.15 tff(360,plain,
% 0.97/1.15 ((~![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)),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[359, 358])).
% 0.97/1.15 tff(361,plain,
% 0.97/1.15 ((s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1)),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[360, 51])).
% 0.97/1.15 tff(362,plain,
% 0.97/1.15 (r(s(s(s(elem!1))), elem!1)),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[361, 357, 249])).
% 0.97/1.15 tff(363,plain,
% 0.97/1.15 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(364,plain,
% 0.97/1.15 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1)))))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(365,plain,
% 0.97/1.15 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1))))),
% 0.97/1.15 inference(monotonicity,[status(thm)],[364])).
% 0.97/1.15 tff(366,plain,
% 0.97/1.15 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)))),
% 0.97/1.15 inference(transitivity,[status(thm)],[365, 363])).
% 0.97/1.15 tff(367,plain,
% 0.97/1.15 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 0.97/1.15 inference(quant_inst,[status(thm)],[])).
% 0.97/1.15 tff(368,plain,
% 0.97/1.15 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[367, 366])).
% 0.97/1.15 tff(369,plain,
% 0.97/1.15 ($false),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[368, 297, 286, 362, 333])).
% 0.97/1.15 tff(370,plain,((~r(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(z)))) | (~(s(s(z)) = s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.15 tff(371,plain,
% 0.97/1.15 (~r(s(elem!1), elem!1)),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[370, 275, 240, 133, 197, 274])).
% 0.97/1.15 tff(372,plain,
% 0.97/1.15 (((~![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))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(373,plain,
% 0.97/1.15 ((~![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))),
% 0.97/1.15 inference(quant_inst,[status(thm)],[])).
% 0.97/1.15 tff(374,plain,
% 0.97/1.15 ((~![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)),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[373, 372])).
% 0.97/1.15 tff(375,plain,
% 0.97/1.15 ((s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1)),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[374, 51])).
% 0.97/1.15 tff(376,plain,
% 0.97/1.15 (b(s(elem!1), elem!1)),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[375, 371, 194])).
% 0.97/1.15 tff(377,plain,
% 0.97/1.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(378,plain,
% 0.97/1.15 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(379,plain,
% 0.97/1.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 0.97/1.15 inference(monotonicity,[status(thm)],[378])).
% 0.97/1.15 tff(380,plain,
% 0.97/1.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 0.97/1.15 inference(transitivity,[status(thm)],[379, 377])).
% 0.97/1.15 tff(381,plain,
% 0.97/1.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 0.97/1.15 inference(quant_inst,[status(thm)],[])).
% 0.97/1.15 tff(382,plain,
% 0.97/1.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[381, 380])).
% 0.97/1.15 tff(383,plain,
% 0.97/1.15 ($false),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[382, 319, 275, 376, 274, 273])).
% 0.97/1.15 tff(384,plain,((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(z)))) | (~(s(s(z)) = s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.15 tff(385,plain,
% 0.97/1.15 (~b(elem!1, s(elem!1))),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[384, 219, 236, 133, 264])).
% 0.97/1.15 tff(386,plain,
% 0.97/1.15 (((~![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)))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(387,plain,
% 0.97/1.15 ((~![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)))),
% 0.97/1.15 inference(quant_inst,[status(thm)],[])).
% 0.97/1.15 tff(388,plain,
% 0.97/1.15 ((~![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))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[387, 386])).
% 0.97/1.15 tff(389,plain,
% 0.97/1.15 ((elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1))),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[388, 51])).
% 0.97/1.15 tff(390,plain,
% 0.97/1.15 (r(elem!1, s(elem!1))),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[389, 385, 272])).
% 0.97/1.15 tff(391,assumption,(z = elem!1), introduced(assumption)).
% 0.97/1.15 tff(392,plain,
% 0.97/1.16 (elem!1 = z),
% 0.97/1.16 inference(symmetry,[status(thm)],[391])).
% 0.97/1.16 tff(393,plain,
% 0.97/1.16 (r(elem!1, s(s(s(elem!1)))) <=> r(z, s(s(s(elem!1))))),
% 0.97/1.16 inference(monotonicity,[status(thm)],[392])).
% 0.97/1.16 tff(394,plain,
% 0.97/1.16 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 0.97/1.16 inference(symmetry,[status(thm)],[393])).
% 0.97/1.16 tff(395,plain,
% 0.97/1.16 (b(elem!1, s(s(s(elem!1)))) <=> b(z, s(s(s(elem!1))))),
% 0.97/1.16 inference(monotonicity,[status(thm)],[392])).
% 0.97/1.16 tff(396,plain,
% 0.97/1.16 ((~b(elem!1, s(s(s(elem!1))))) <=> (~b(z, s(s(s(elem!1)))))),
% 0.97/1.16 inference(monotonicity,[status(thm)],[395])).
% 0.97/1.16 tff(397,assumption,(b(elem!1, s(s(elem!1)))), introduced(assumption)).
% 0.97/1.16 tff(398,plain,
% 0.97/1.16 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[343, 334, 197])).
% 0.97/1.16 tff(399,plain,
% 0.97/1.16 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[348, 398, 58])).
% 0.97/1.16 tff(400,plain,
% 0.97/1.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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(elem!1, s(s(s(elem!1))))))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(401,plain,
% 0.97/1.16 (((~b(s(s(elem!1)), s(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(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(402,plain,
% 0.97/1.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(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(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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(elem!1, s(s(s(elem!1)))))))),
% 0.97/1.16 inference(monotonicity,[status(thm)],[401])).
% 0.97/1.16 tff(403,plain,
% 0.97/1.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(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(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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(elem!1, s(s(s(elem!1))))))),
% 0.97/1.16 inference(transitivity,[status(thm)],[402, 400])).
% 0.97/1.16 tff(404,plain,
% 0.97/1.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(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(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))),
% 0.97/1.16 inference(quant_inst,[status(thm)],[])).
% 0.97/1.16 tff(405,plain,
% 0.97/1.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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(elem!1, s(s(s(elem!1)))))),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[404, 403])).
% 0.97/1.16 tff(406,plain,
% 0.97/1.16 (~b(elem!1, s(s(s(elem!1))))),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[405, 319, 274, 399, 397])).
% 0.97/1.16 tff(407,plain,
% 0.97/1.16 (~b(z, s(s(s(elem!1))))),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[406, 396])).
% 0.97/1.16 tff(408,plain,
% 0.97/1.16 ((z = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = z)),
% 0.97/1.16 inference(commutativity,[status(thm)],[])).
% 0.97/1.16 tff(409,plain,
% 0.97/1.16 ((s(s(s(elem!1))) = z) <=> (z = s(s(s(elem!1))))),
% 0.97/1.16 inference(symmetry,[status(thm)],[408])).
% 0.97/1.16 tff(410,plain,
% 0.97/1.16 ((~(s(s(s(elem!1))) = z)) <=> (~(z = s(s(s(elem!1)))))),
% 0.97/1.16 inference(monotonicity,[status(thm)],[409])).
% 0.97/1.16 tff(411,plain,
% 0.97/1.16 (~(z = s(s(s(elem!1))))),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[160, 410])).
% 0.97/1.16 tff(412,plain,
% 0.97/1.16 (((~![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)))))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(413,plain,
% 0.97/1.16 ((~![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)))))),
% 0.97/1.16 inference(quant_inst,[status(thm)],[])).
% 0.97/1.16 tff(414,plain,
% 0.97/1.16 ((~![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))))),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[413, 412])).
% 0.97/1.16 tff(415,plain,
% 0.97/1.16 ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[414, 51])).
% 0.97/1.16 tff(416,plain,
% 0.97/1.16 (b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[415, 411])).
% 0.97/1.16 tff(417,plain,
% 0.97/1.16 (r(z, s(s(s(elem!1))))),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[416, 407])).
% 0.97/1.16 tff(418,plain,
% 0.97/1.16 (r(elem!1, s(s(s(elem!1))))),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[417, 394])).
% 0.97/1.16 tff(419,assumption,(r(elem!1, s(elem!1))), introduced(assumption)).
% 0.97/1.16 tff(420,plain,
% 0.97/1.16 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(421,plain,
% 0.97/1.16 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(422,plain,
% 0.97/1.16 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1)))))))),
% 0.97/1.16 inference(monotonicity,[status(thm)],[421])).
% 0.97/1.16 tff(423,plain,
% 0.97/1.16 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))),
% 0.97/1.16 inference(transitivity,[status(thm)],[422, 420])).
% 0.97/1.16 tff(424,plain,
% 0.97/1.16 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))))),
% 0.97/1.16 inference(quant_inst,[status(thm)],[])).
% 0.97/1.16 tff(425,plain,
% 0.97/1.16 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1)))))),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[424, 423])).
% 0.97/1.16 tff(426,plain,
% 0.97/1.16 (~r(elem!1, s(s(s(elem!1))))),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[425, 297, 419, 334])).
% 0.97/1.16 tff(427,plain,
% 0.97/1.16 ($false),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[426, 418])).
% 0.97/1.16 tff(428,plain,((~r(s(elem!1), s(s(s(elem!1))))) | (~(z = elem!1)) | (~r(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.16 tff(429,plain,
% 0.97/1.16 (~r(s(elem!1), s(s(s(elem!1))))),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[428, 187, 390, 219, 245, 232, 264])).
% 0.97/1.16 tff(430,assumption,(~(s(elem!1) = s(s(s(elem!1))))), introduced(assumption)).
% 0.97/1.16 tff(431,assumption,(~r(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 0.97/1.16 tff(432,assumption,(~b(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 0.97/1.16 tff(433,plain,
% 0.97/1.16 ($false),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[331, 51, 432, 431, 430])).
% 0.97/1.16 tff(434,plain,(r(s(elem!1), s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1)))) | (s(elem!1) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.16 tff(435,plain,
% 0.97/1.16 (b(s(elem!1), s(s(s(elem!1))))),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[434, 429, 270])).
% 0.97/1.16 tff(436,plain,
% 0.97/1.16 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 0.97/1.16 inference(monotonicity,[status(thm)],[237])).
% 0.97/1.16 tff(437,plain,
% 0.97/1.16 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.97/1.16 inference(symmetry,[status(thm)],[436])).
% 0.97/1.16 tff(438,plain,
% 0.97/1.16 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 0.97/1.16 inference(monotonicity,[status(thm)],[237])).
% 0.97/1.16 tff(439,plain,
% 0.97/1.16 ((~r(s(s(elem!1)), s(s(s(elem!1))))) <=> (~r(s(s(z)), s(s(s(elem!1)))))),
% 0.97/1.16 inference(monotonicity,[status(thm)],[438])).
% 0.97/1.16 tff(440,plain,
% 0.97/1.16 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 0.97/1.16 inference(monotonicity,[status(thm)],[187])).
% 0.97/1.16 tff(441,plain,
% 0.97/1.16 (r(s(s(elem!1)), elem!1)),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[115, 440])).
% 0.97/1.16 tff(442,plain,
% 0.97/1.16 (r(s(z), z) <=> r(s(elem!1), elem!1)),
% 0.97/1.16 inference(transitivity,[status(thm)],[281, 283])).
% 0.97/1.16 tff(443,plain,
% 0.97/1.16 ((~r(s(z), z)) <=> (~r(s(elem!1), elem!1))),
% 0.97/1.16 inference(monotonicity,[status(thm)],[442])).
% 0.97/1.16 tff(444,assumption,(r(s(z), s(s(elem!1)))), introduced(assumption)).
% 0.97/1.16 tff(445,plain,
% 0.97/1.16 (~r(s(z), z)),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[304, 115, 444])).
% 0.97/1.16 tff(446,plain,
% 0.97/1.16 (~r(s(elem!1), elem!1)),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[445, 443])).
% 0.97/1.16 tff(447,plain,
% 0.97/1.16 (b(s(elem!1), elem!1)),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[375, 446, 194])).
% 0.97/1.16 tff(448,assumption,(b(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 0.97/1.16 tff(449,assumption,(b(s(elem!1), elem!1)), introduced(assumption)).
% 0.97/1.16 tff(450,plain,
% 0.97/1.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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)))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(451,plain,
% 0.97/1.16 (((~b(elem!1, s(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(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(452,plain,
% 0.97/1.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(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(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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))))),
% 0.97/1.16 inference(monotonicity,[status(thm)],[451])).
% 0.97/1.16 tff(453,plain,
% 0.97/1.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(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(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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)))),
% 0.97/1.16 inference(transitivity,[status(thm)],[452, 450])).
% 0.97/1.16 tff(454,plain,
% 0.97/1.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(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(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 0.97/1.16 inference(quant_inst,[status(thm)],[])).
% 0.97/1.16 tff(455,plain,
% 0.97/1.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1))),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[454, 453])).
% 0.97/1.16 tff(456,plain,
% 0.97/1.16 ($false),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[455, 319, 449, 309, 448, 397])).
% 0.97/1.16 tff(457,plain,((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.16 tff(458,plain,
% 0.97/1.16 (~b(s(s(s(elem!1))), elem!1)),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[457, 447, 309, 397])).
% 0.97/1.16 tff(459,plain,
% 0.97/1.16 (r(s(s(s(elem!1))), elem!1)),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[361, 458, 249])).
% 0.97/1.16 tff(460,assumption,(r(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 0.97/1.16 tff(461,assumption,(r(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 0.97/1.16 tff(462,assumption,(r(s(s(elem!1)), elem!1)), introduced(assumption)).
% 0.97/1.16 tff(463,plain,
% 0.97/1.16 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(464,plain,
% 0.97/1.16 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(465,plain,
% 0.97/1.16 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))))),
% 0.97/1.16 inference(monotonicity,[status(thm)],[464])).
% 0.97/1.16 tff(466,plain,
% 0.97/1.16 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 0.97/1.16 inference(transitivity,[status(thm)],[465, 463])).
% 0.97/1.16 tff(467,plain,
% 0.97/1.16 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.97/1.16 inference(quant_inst,[status(thm)],[])).
% 0.97/1.16 tff(468,plain,
% 0.97/1.16 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[467, 466])).
% 0.97/1.16 tff(469,plain,
% 0.97/1.16 ($false),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[468, 297, 462, 461, 460])).
% 0.97/1.16 tff(470,plain,((~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)))))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.16 tff(471,plain,
% 0.97/1.16 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[470, 459, 441])).
% 0.97/1.16 tff(472,plain,
% 0.97/1.16 (~r(s(s(z)), s(s(s(elem!1))))),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[471, 439])).
% 0.97/1.16 tff(473,plain,
% 0.97/1.16 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(elem!1)))) | b(s(s(z)), s(s(s(elem!1)))) | r(s(s(z)), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(elem!1)))) | b(s(s(z)), s(s(s(elem!1)))) | r(s(s(z)), s(s(s(elem!1)))))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(474,plain,
% 0.97/1.16 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(elem!1)))) | b(s(s(z)), s(s(s(elem!1)))) | r(s(s(z)), s(s(s(elem!1)))))),
% 0.97/1.16 inference(quant_inst,[status(thm)],[])).
% 0.97/1.16 tff(475,plain,
% 0.97/1.16 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(elem!1)))) | b(s(s(z)), s(s(s(elem!1)))) | r(s(s(z)), s(s(s(elem!1))))),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[474, 473])).
% 0.97/1.16 tff(476,plain,
% 0.97/1.16 ((s(s(z)) = s(s(s(elem!1)))) | b(s(s(z)), s(s(s(elem!1)))) | r(s(s(z)), s(s(s(elem!1))))),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[475, 51])).
% 0.97/1.16 tff(477,plain,
% 0.97/1.16 (b(s(s(z)), s(s(s(elem!1))))),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[476, 472, 231])).
% 0.97/1.16 tff(478,plain,
% 0.97/1.16 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[477, 437])).
% 0.97/1.16 tff(479,plain,
% 0.97/1.16 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(480,plain,
% 0.97/1.16 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.97/1.16 inference(quant_inst,[status(thm)],[])).
% 0.97/1.16 tff(481,plain,
% 0.97/1.16 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[480, 479])).
% 0.97/1.16 tff(482,plain,
% 0.97/1.16 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[481, 297, 441, 459])).
% 0.97/1.16 tff(483,plain,
% 0.97/1.16 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[348, 482, 232])).
% 0.97/1.16 tff(484,plain,
% 0.97/1.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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(elem!1)), s(s(s(elem!1))))))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(485,plain,
% 0.97/1.16 (((~b(s(s(s(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(s(s(elem!1)), s(s(s(elem!1))))) | (~b(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(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(486,plain,
% 0.97/1.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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(elem!1)), s(s(s(elem!1)))))))),
% 0.97/1.16 inference(monotonicity,[status(thm)],[485])).
% 0.97/1.16 tff(487,plain,
% 0.97/1.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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(elem!1)), s(s(s(elem!1))))))),
% 0.97/1.16 inference(transitivity,[status(thm)],[486, 484])).
% 0.97/1.16 tff(488,plain,
% 0.97/1.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(elem!1)), s(elem!1))))),
% 0.97/1.16 inference(quant_inst,[status(thm)],[])).
% 0.97/1.16 tff(489,plain,
% 0.97/1.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[488, 487])).
% 0.97/1.16 tff(490,plain,
% 0.97/1.16 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[489, 319, 309, 274, 483])).
% 0.97/1.16 tff(491,plain,
% 0.97/1.16 ($false),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[490, 478])).
% 0.97/1.16 tff(492,plain,((~r(s(s(elem!1)), z)) | (~(s(s(z)) = s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.16 tff(493,plain,
% 0.97/1.16 (~r(s(s(elem!1)), z)),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[492, 133, 435, 219, 245, 265])).
% 0.97/1.16 tff(494,plain,
% 0.97/1.16 (b(s(s(elem!1)), z)),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[75, 493])).
% 0.97/1.16 tff(495,plain,
% 0.97/1.16 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 0.97/1.16 inference(monotonicity,[status(thm)],[391])).
% 0.97/1.16 tff(496,assumption,(b(s(s(elem!1)), z)), introduced(assumption)).
% 0.97/1.16 tff(497,plain,
% 0.97/1.16 (b(s(s(elem!1)), elem!1)),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[496, 495])).
% 0.97/1.16 tff(498,assumption,(~b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 0.97/1.16 tff(499,plain,
% 0.97/1.16 ($false),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[498, 497])).
% 0.97/1.16 tff(500,plain,((~b(s(s(elem!1)), z)) | b(s(s(elem!1)), elem!1) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.16 tff(501,plain,
% 0.97/1.16 (b(s(s(elem!1)), elem!1)),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[500, 494, 187])).
% 0.97/1.16 tff(502,plain,
% 0.97/1.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(503,plain,
% 0.97/1.16 (((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 0.97/1.17 inference(rewrite,[status(thm)],[])).
% 0.97/1.17 tff(504,plain,
% 0.97/1.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))))),
% 0.97/1.17 inference(monotonicity,[status(thm)],[503])).
% 0.97/1.17 tff(505,plain,
% 0.97/1.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 0.97/1.17 inference(transitivity,[status(thm)],[504, 502])).
% 0.97/1.17 tff(506,plain,
% 0.97/1.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 0.97/1.17 inference(quant_inst,[status(thm)],[])).
% 0.97/1.17 tff(507,plain,
% 0.97/1.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))),
% 0.97/1.17 inference(modus_ponens,[status(thm)],[506, 505])).
% 0.97/1.17 tff(508,plain,
% 0.97/1.17 ($false),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[507, 319, 449, 274, 308, 397])).
% 0.97/1.17 tff(509,plain,((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.17 tff(510,plain,
% 0.97/1.17 (~b(s(elem!1), elem!1)),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[509, 501, 219, 245])).
% 0.97/1.17 tff(511,plain,
% 0.97/1.17 (r(s(elem!1), elem!1)),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[375, 510, 194])).
% 0.97/1.17 tff(512,assumption,(~(s(s(s(elem!1))) = elem!1)), introduced(assumption)).
% 0.97/1.17 tff(513,plain,
% 0.97/1.17 (~b(s(s(s(elem!1))), elem!1)),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[355, 319, 274, 116, 397])).
% 0.97/1.17 tff(514,plain,
% 0.97/1.17 (r(s(s(s(elem!1))), elem!1)),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[361, 513, 512])).
% 0.97/1.17 tff(515,plain,
% 0.97/1.17 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 0.97/1.17 inference(rewrite,[status(thm)],[])).
% 0.97/1.17 tff(516,plain,
% 0.97/1.17 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 0.97/1.17 inference(quant_inst,[status(thm)],[])).
% 0.97/1.17 tff(517,plain,
% 0.97/1.17 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 0.97/1.17 inference(modus_ponens,[status(thm)],[516, 515])).
% 0.97/1.17 tff(518,plain,
% 0.97/1.17 (~r(s(s(s(elem!1))), s(elem!1))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[517, 297, 286, 514])).
% 0.97/1.17 tff(519,plain,
% 0.97/1.17 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(elem!1)))),
% 0.97/1.17 inference(rewrite,[status(thm)],[])).
% 0.97/1.17 tff(520,plain,
% 0.97/1.17 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(elem!1)))),
% 0.97/1.17 inference(quant_inst,[status(thm)],[])).
% 0.97/1.17 tff(521,plain,
% 0.97/1.17 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(elem!1))),
% 0.97/1.17 inference(modus_ponens,[status(thm)],[520, 519])).
% 0.97/1.17 tff(522,plain,
% 0.97/1.17 (b(s(s(s(elem!1))), s(elem!1))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[521, 51, 176, 518])).
% 0.97/1.17 tff(523,plain,
% 0.97/1.17 (~(s(elem!1) = s(s(s(elem!1))))),
% 0.97/1.17 inference(modus_ponens,[status(thm)],[176, 278])).
% 0.97/1.17 tff(524,plain,
% 0.97/1.17 (~r(s(elem!1), s(s(s(elem!1))))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[368, 297, 286, 514])).
% 0.97/1.17 tff(525,plain,
% 0.97/1.17 ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1))))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[331, 51, 524])).
% 0.97/1.17 tff(526,plain,
% 0.97/1.17 (b(s(elem!1), s(s(s(elem!1))))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[525, 523])).
% 0.97/1.17 tff(527,plain,
% 0.97/1.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.97/1.17 inference(rewrite,[status(thm)],[])).
% 0.97/1.17 tff(528,plain,
% 0.97/1.17 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), 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(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.97/1.17 inference(rewrite,[status(thm)],[])).
% 0.97/1.17 tff(529,plain,
% 0.97/1.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 0.97/1.17 inference(monotonicity,[status(thm)],[528])).
% 0.97/1.17 tff(530,plain,
% 0.97/1.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.97/1.17 inference(transitivity,[status(thm)],[529, 527])).
% 0.97/1.17 tff(531,plain,
% 0.97/1.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.97/1.17 inference(quant_inst,[status(thm)],[])).
% 0.97/1.17 tff(532,plain,
% 0.97/1.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 0.97/1.17 inference(modus_ponens,[status(thm)],[531, 530])).
% 0.97/1.17 tff(533,plain,
% 0.97/1.17 ($false),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[532, 319, 526, 522, 274, 116])).
% 0.97/1.17 tff(534,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(elem!1), elem!1)) | (s(s(s(elem!1))) = elem!1) | (~b(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.17 tff(535,plain,
% 0.97/1.17 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[534, 511, 263, 219, 249, 245])).
% 0.97/1.17 tff(536,plain,
% 0.97/1.17 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[348, 535, 232])).
% 0.97/1.17 tff(537,plain,
% 0.97/1.17 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[178, 263])).
% 0.97/1.17 tff(538,plain,
% 0.97/1.17 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[92, 232])).
% 0.97/1.17 tff(539,plain,
% 0.97/1.17 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 0.97/1.17 inference(rewrite,[status(thm)],[])).
% 0.97/1.17 tff(540,plain,
% 0.97/1.17 (((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 0.97/1.17 inference(rewrite,[status(thm)],[])).
% 0.97/1.17 tff(541,plain,
% 0.97/1.17 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1))))))),
% 0.97/1.17 inference(monotonicity,[status(thm)],[540])).
% 0.97/1.17 tff(542,plain,
% 0.97/1.17 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 0.97/1.17 inference(transitivity,[status(thm)],[541, 539])).
% 0.97/1.17 tff(543,plain,
% 0.97/1.17 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 0.97/1.17 inference(quant_inst,[status(thm)],[])).
% 0.97/1.17 tff(544,plain,
% 0.97/1.17 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1))))),
% 0.97/1.17 inference(modus_ponens,[status(thm)],[543, 542])).
% 0.97/1.17 tff(545,plain,
% 0.97/1.17 (~r(s(s(s(elem!1))), s(elem!1))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[544, 297, 264, 536])).
% 0.97/1.17 tff(546,plain,
% 0.97/1.17 (b(s(s(s(elem!1))), s(elem!1))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[521, 51, 263, 545])).
% 0.97/1.17 tff(547,assumption,(b(s(s(s(s(elem!1)))), s(elem!1))), introduced(assumption)).
% 0.97/1.17 tff(548,assumption,(b(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 0.97/1.17 tff(549,plain,
% 0.97/1.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 0.97/1.17 inference(rewrite,[status(thm)],[])).
% 0.97/1.17 tff(550,plain,
% 0.97/1.17 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 0.97/1.17 inference(rewrite,[status(thm)],[])).
% 0.97/1.17 tff(551,plain,
% 0.97/1.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 0.97/1.17 inference(monotonicity,[status(thm)],[550])).
% 0.97/1.17 tff(552,plain,
% 0.97/1.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 0.97/1.17 inference(transitivity,[status(thm)],[551, 549])).
% 0.97/1.17 tff(553,plain,
% 0.97/1.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 0.97/1.17 inference(quant_inst,[status(thm)],[])).
% 0.97/1.17 tff(554,plain,
% 0.97/1.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 0.97/1.17 inference(modus_ponens,[status(thm)],[553, 552])).
% 0.97/1.17 tff(555,plain,
% 0.97/1.17 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[554, 319, 309, 548, 547])).
% 0.97/1.17 tff(556,plain,
% 0.97/1.17 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 0.97/1.17 inference(rewrite,[status(thm)],[])).
% 0.97/1.17 tff(557,plain,
% 0.97/1.17 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 0.97/1.17 inference(quant_inst,[status(thm)],[])).
% 0.97/1.17 tff(558,plain,
% 0.97/1.17 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 0.97/1.17 inference(modus_ponens,[status(thm)],[557, 556])).
% 0.97/1.17 tff(559,plain,
% 0.97/1.17 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[558, 51, 99, 555])).
% 0.97/1.17 tff(560,assumption,(~(s(s(s(s(elem!1)))) = s(s(elem!1)))), introduced(assumption)).
% 0.97/1.17 tff(561,plain,
% 0.97/1.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 0.97/1.17 inference(rewrite,[status(thm)],[])).
% 0.97/1.17 tff(562,plain,
% 0.97/1.17 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 0.97/1.17 inference(rewrite,[status(thm)],[])).
% 0.97/1.17 tff(563,plain,
% 0.97/1.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 0.97/1.17 inference(monotonicity,[status(thm)],[562])).
% 0.97/1.17 tff(564,plain,
% 0.97/1.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 0.97/1.17 inference(transitivity,[status(thm)],[563, 561])).
% 0.97/1.17 tff(565,plain,
% 0.97/1.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 0.97/1.17 inference(quant_inst,[status(thm)],[])).
% 0.97/1.17 tff(566,plain,
% 0.97/1.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 0.97/1.17 inference(modus_ponens,[status(thm)],[565, 564])).
% 0.97/1.17 tff(567,plain,
% 0.97/1.17 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[566, 319, 309, 274, 547])).
% 0.97/1.17 tff(568,plain,
% 0.97/1.17 (((~![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))))),
% 0.97/1.17 inference(rewrite,[status(thm)],[])).
% 0.97/1.17 tff(569,plain,
% 0.97/1.17 ((~![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))))),
% 0.97/1.17 inference(quant_inst,[status(thm)],[])).
% 0.97/1.17 tff(570,plain,
% 0.97/1.17 ((~![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)))),
% 0.97/1.17 inference(modus_ponens,[status(thm)],[569, 568])).
% 0.97/1.17 tff(571,plain,
% 0.97/1.17 ((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)))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[570, 51])).
% 0.97/1.17 tff(572,plain,
% 0.97/1.17 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[571, 567, 560])).
% 0.97/1.17 tff(573,plain,
% 0.97/1.17 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 0.97/1.17 inference(rewrite,[status(thm)],[])).
% 0.97/1.17 tff(574,plain,
% 0.97/1.17 (((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 0.97/1.17 inference(rewrite,[status(thm)],[])).
% 0.97/1.17 tff(575,plain,
% 0.97/1.17 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 0.97/1.17 inference(monotonicity,[status(thm)],[574])).
% 0.97/1.17 tff(576,plain,
% 0.97/1.17 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 0.97/1.17 inference(transitivity,[status(thm)],[575, 573])).
% 0.97/1.17 tff(577,plain,
% 0.97/1.17 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 0.97/1.17 inference(quant_inst,[status(thm)],[])).
% 0.97/1.17 tff(578,plain,
% 0.97/1.17 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 0.97/1.17 inference(modus_ponens,[status(thm)],[577, 576])).
% 0.97/1.17 tff(579,plain,
% 0.97/1.17 ($false),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[578, 297, 335, 572, 559])).
% 0.97/1.17 tff(580,plain,((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = 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(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.17 tff(581,plain,
% 0.97/1.17 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[580, 546, 538, 537, 435, 536, 219])).
% 0.97/1.17 tff(582,assumption,(s(s(s(s(elem!1)))) = s(elem!1)), introduced(assumption)).
% 0.97/1.17 tff(583,plain,
% 0.97/1.17 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(elem!1))),
% 0.97/1.17 inference(monotonicity,[status(thm)],[582])).
% 0.97/1.17 tff(584,plain,
% 0.97/1.17 (s(s(s(elem!1))) = elem!1),
% 0.97/1.17 inference(transitivity,[status(thm)],[89, 583, 141])).
% 0.97/1.17 tff(585,plain,
% 0.97/1.17 ($false),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[512, 584])).
% 0.97/1.17 tff(586,plain,((~(s(s(s(s(elem!1)))) = s(elem!1))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.97/1.17 tff(587,plain,
% 0.97/1.17 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[586, 249])).
% 0.97/1.17 tff(588,assumption,(~r(s(s(s(s(elem!1)))), s(elem!1))), introduced(assumption)).
% 0.97/1.17 tff(589,assumption,(~b(s(s(s(s(elem!1)))), s(elem!1))), introduced(assumption)).
% 0.97/1.17 tff(590,assumption,(~(s(s(s(s(elem!1)))) = s(elem!1))), introduced(assumption)).
% 0.97/1.17 tff(591,plain,
% 0.97/1.17 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1)) | r(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1)) | r(s(s(s(s(elem!1)))), s(elem!1)))),
% 0.97/1.17 inference(rewrite,[status(thm)],[])).
% 0.97/1.17 tff(592,plain,
% 0.97/1.17 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1)) | r(s(s(s(s(elem!1)))), s(elem!1)))),
% 0.97/1.17 inference(quant_inst,[status(thm)],[])).
% 0.97/1.17 tff(593,plain,
% 0.97/1.17 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1)) | r(s(s(s(s(elem!1)))), s(elem!1))),
% 0.97/1.17 inference(modus_ponens,[status(thm)],[592, 591])).
% 0.97/1.17 tff(594,plain,
% 0.97/1.17 ($false),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[593, 51, 590, 589, 588])).
% 0.97/1.17 tff(595,plain,(r(s(s(s(s(elem!1)))), s(elem!1)) | (s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.17 tff(596,plain,
% 0.97/1.17 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[595, 587, 581])).
% 0.97/1.17 tff(597,plain,
% 0.97/1.17 ((s(s(s(s(elem!1)))) = elem!1) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 0.97/1.17 inference(commutativity,[status(thm)],[])).
% 0.97/1.17 tff(598,plain,
% 0.97/1.17 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 0.97/1.17 inference(symmetry,[status(thm)],[597])).
% 0.97/1.17 tff(599,plain,
% 0.97/1.17 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 0.97/1.17 inference(monotonicity,[status(thm)],[187])).
% 0.97/1.17 tff(600,plain,
% 0.97/1.17 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 0.97/1.17 inference(transitivity,[status(thm)],[599, 597])).
% 0.97/1.17 tff(601,plain,
% 0.97/1.17 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 0.97/1.17 inference(transitivity,[status(thm)],[600, 598])).
% 0.97/1.17 tff(602,plain,
% 0.97/1.17 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 0.97/1.17 inference(monotonicity,[status(thm)],[601])).
% 0.97/1.17 tff(603,plain,
% 0.97/1.17 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(elem!1)))) = z))),
% 0.97/1.17 inference(quant_inst,[status(thm)],[])).
% 0.97/1.17 tff(604,plain,
% 0.97/1.17 (~(s(s(s(s(elem!1)))) = z)),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[603, 26])).
% 0.97/1.17 tff(605,plain,
% 0.97/1.17 (~(s(s(s(s(elem!1)))) = elem!1)),
% 0.97/1.17 inference(modus_ponens,[status(thm)],[604, 602])).
% 0.97/1.17 tff(606,plain,
% 0.97/1.17 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 0.97/1.17 inference(rewrite,[status(thm)],[])).
% 0.97/1.17 tff(607,plain,
% 0.97/1.17 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 0.97/1.17 inference(rewrite,[status(thm)],[])).
% 0.97/1.17 tff(608,plain,
% 0.97/1.17 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 0.97/1.17 inference(monotonicity,[status(thm)],[607])).
% 0.97/1.17 tff(609,plain,
% 0.97/1.17 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 0.97/1.18 inference(transitivity,[status(thm)],[608, 606])).
% 0.97/1.18 tff(610,plain,
% 0.97/1.18 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 0.97/1.18 inference(quant_inst,[status(thm)],[])).
% 0.97/1.18 tff(611,plain,
% 0.97/1.18 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 0.97/1.18 inference(modus_ponens,[status(thm)],[610, 609])).
% 0.97/1.18 tff(612,plain,
% 0.97/1.18 (~r(s(s(s(s(elem!1)))), elem!1)),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[611, 297, 390, 596])).
% 0.97/1.18 tff(613,plain,
% 0.97/1.18 (((~![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))),
% 0.97/1.18 inference(rewrite,[status(thm)],[])).
% 0.97/1.18 tff(614,plain,
% 0.97/1.18 ((~![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))),
% 0.97/1.18 inference(quant_inst,[status(thm)],[])).
% 0.97/1.18 tff(615,plain,
% 0.97/1.18 ((~![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)),
% 0.97/1.18 inference(modus_ponens,[status(thm)],[614, 613])).
% 0.97/1.18 tff(616,plain,
% 0.97/1.18 ((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)),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[615, 51])).
% 0.97/1.18 tff(617,plain,
% 0.97/1.18 (b(s(s(s(s(elem!1)))), elem!1)),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[616, 612, 605])).
% 0.97/1.18 tff(618,plain,
% 0.97/1.18 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 0.97/1.18 inference(monotonicity,[status(thm)],[600])).
% 0.97/1.18 tff(619,plain,
% 0.97/1.18 (~(elem!1 = s(s(s(s(elem!1)))))),
% 0.97/1.18 inference(modus_ponens,[status(thm)],[604, 618])).
% 0.97/1.18 tff(620,assumption,(r(s(s(s(s(elem!1)))), s(elem!1))), introduced(assumption)).
% 0.97/1.18 tff(621,assumption,(r(elem!1, s(s(s(s(elem!1)))))), introduced(assumption)).
% 0.97/1.18 tff(622,plain,
% 0.97/1.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 0.97/1.18 inference(rewrite,[status(thm)],[])).
% 0.97/1.18 tff(623,plain,
% 0.97/1.18 (((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1))))))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 0.97/1.18 inference(rewrite,[status(thm)],[])).
% 0.97/1.18 tff(624,plain,
% 0.97/1.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 0.97/1.18 inference(monotonicity,[status(thm)],[623])).
% 0.97/1.18 tff(625,plain,
% 0.97/1.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 0.97/1.18 inference(transitivity,[status(thm)],[624, 622])).
% 0.97/1.18 tff(626,plain,
% 0.97/1.18 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 0.97/1.18 inference(quant_inst,[status(thm)],[])).
% 0.97/1.18 tff(627,plain,
% 0.97/1.18 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 0.97/1.18 inference(modus_ponens,[status(thm)],[626, 625])).
% 0.97/1.18 tff(628,plain,
% 0.97/1.18 ($false),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[627, 297, 419, 621, 620])).
% 0.97/1.18 tff(629,plain,((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.18 tff(630,plain,
% 0.97/1.18 (~r(elem!1, s(s(s(s(elem!1)))))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[629, 596, 390])).
% 0.97/1.18 tff(631,plain,
% 0.97/1.18 (((~![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))))))),
% 0.97/1.18 inference(rewrite,[status(thm)],[])).
% 0.97/1.18 tff(632,plain,
% 0.97/1.18 ((~![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))))))),
% 0.97/1.18 inference(quant_inst,[status(thm)],[])).
% 0.97/1.18 tff(633,plain,
% 0.97/1.18 ((~![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)))))),
% 0.97/1.18 inference(modus_ponens,[status(thm)],[632, 631])).
% 0.97/1.18 tff(634,plain,
% 0.97/1.18 ((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)))))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[633, 51])).
% 0.97/1.18 tff(635,plain,
% 0.97/1.18 (b(elem!1, s(s(s(s(elem!1)))))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[634, 630, 619])).
% 0.97/1.18 tff(636,plain,
% 0.97/1.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 0.97/1.18 inference(rewrite,[status(thm)],[])).
% 0.97/1.18 tff(637,plain,
% 0.97/1.18 (((~b(elem!1, s(s(s(s(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(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 0.97/1.18 inference(rewrite,[status(thm)],[])).
% 0.97/1.18 tff(638,plain,
% 0.97/1.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 0.97/1.18 inference(monotonicity,[status(thm)],[637])).
% 0.97/1.18 tff(639,plain,
% 0.97/1.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 0.97/1.18 inference(transitivity,[status(thm)],[638, 636])).
% 0.97/1.18 tff(640,plain,
% 0.97/1.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 0.97/1.18 inference(quant_inst,[status(thm)],[])).
% 0.97/1.18 tff(641,plain,
% 0.97/1.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 0.97/1.18 inference(modus_ponens,[status(thm)],[640, 639])).
% 0.97/1.18 tff(642,plain,
% 0.97/1.18 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[641, 319, 635, 501, 617])).
% 0.97/1.18 tff(643,plain,
% 0.97/1.18 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[571, 642, 537])).
% 0.97/1.18 tff(644,plain,
% 0.97/1.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 0.97/1.18 inference(rewrite,[status(thm)],[])).
% 0.97/1.18 tff(645,plain,
% 0.97/1.18 (((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 0.97/1.18 inference(rewrite,[status(thm)],[])).
% 0.97/1.18 tff(646,plain,
% 0.97/1.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 0.97/1.18 inference(monotonicity,[status(thm)],[645])).
% 0.97/1.18 tff(647,plain,
% 0.97/1.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 0.97/1.18 inference(transitivity,[status(thm)],[646, 644])).
% 0.97/1.18 tff(648,plain,
% 0.97/1.18 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 0.97/1.18 inference(quant_inst,[status(thm)],[])).
% 0.97/1.18 tff(649,plain,
% 0.97/1.18 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 0.97/1.18 inference(modus_ponens,[status(thm)],[648, 647])).
% 0.97/1.18 tff(650,plain,
% 0.97/1.18 ($false),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[649, 297, 264, 643, 596])).
% 0.97/1.18 tff(651,plain,((~(s(s(z)) = s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.18 tff(652,plain,
% 0.97/1.18 (~(s(s(z)) = s(s(elem!1)))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[651, 202, 214, 203])).
% 0.97/1.18 tff(653,plain,
% 0.97/1.18 (b(s(s(z)), s(s(elem!1)))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[122, 652, 69])).
% 0.97/1.18 tff(654,plain,
% 0.97/1.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(z))))),
% 0.97/1.18 inference(rewrite,[status(thm)],[])).
% 0.97/1.18 tff(655,plain,
% 0.97/1.18 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(z))))),
% 0.97/1.18 inference(rewrite,[status(thm)],[])).
% 0.97/1.18 tff(656,plain,
% 0.97/1.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(z)))))),
% 0.97/1.18 inference(monotonicity,[status(thm)],[655])).
% 0.97/1.18 tff(657,plain,
% 0.97/1.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(z))))),
% 0.97/1.18 inference(transitivity,[status(thm)],[656, 654])).
% 0.97/1.18 tff(658,plain,
% 0.97/1.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)))),
% 0.97/1.18 inference(quant_inst,[status(thm)],[])).
% 0.97/1.18 tff(659,plain,
% 0.97/1.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(z)))),
% 0.97/1.18 inference(modus_ponens,[status(thm)],[658, 657])).
% 0.97/1.18 tff(660,plain,
% 0.97/1.18 (~b(s(s(z)), z)),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[659, 319, 214, 653, 202])).
% 0.97/1.18 tff(661,plain,
% 0.97/1.18 (((~![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))),
% 0.97/1.18 inference(rewrite,[status(thm)],[])).
% 0.97/1.18 tff(662,plain,
% 0.97/1.18 ((~![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))),
% 0.97/1.18 inference(quant_inst,[status(thm)],[])).
% 0.97/1.18 tff(663,plain,
% 0.97/1.18 ((~![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)),
% 0.97/1.18 inference(modus_ponens,[status(thm)],[662, 661])).
% 0.97/1.18 tff(664,plain,
% 0.97/1.18 (r(s(s(z)), z)),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[663, 51, 28, 660])).
% 0.97/1.18 tff(665,assumption,(r(s(s(z)), z)), introduced(assumption)).
% 0.97/1.18 tff(666,assumption,(r(s(z), z)), introduced(assumption)).
% 0.97/1.18 tff(667,plain,
% 0.97/1.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), z)))),
% 0.97/1.18 inference(rewrite,[status(thm)],[])).
% 0.97/1.18 tff(668,plain,
% 0.97/1.18 (((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), z)))),
% 0.97/1.18 inference(rewrite,[status(thm)],[])).
% 0.97/1.18 tff(669,plain,
% 0.97/1.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), z))))),
% 0.97/1.18 inference(monotonicity,[status(thm)],[668])).
% 0.97/1.18 tff(670,plain,
% 0.97/1.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), z)))),
% 0.97/1.18 inference(transitivity,[status(thm)],[669, 667])).
% 0.97/1.18 tff(671,plain,
% 0.97/1.18 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))),
% 0.97/1.18 inference(quant_inst,[status(thm)],[])).
% 0.97/1.18 tff(672,plain,
% 0.97/1.18 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), z))),
% 0.97/1.18 inference(modus_ponens,[status(thm)],[671, 670])).
% 0.97/1.18 tff(673,plain,
% 0.97/1.18 (~r(s(z), s(s(z)))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[672, 297, 666, 665])).
% 0.97/1.18 tff(674,assumption,(s(z) = s(s(z))), introduced(assumption)).
% 0.97/1.18 tff(675,plain,
% 0.97/1.18 (inj_0(s(z)) = inj_0(s(s(z)))),
% 0.97/1.18 inference(monotonicity,[status(thm)],[674])).
% 0.97/1.18 tff(676,plain,
% 0.97/1.18 (inj_0(s(s(z))) = inj_0(s(z))),
% 0.97/1.18 inference(symmetry,[status(thm)],[675])).
% 0.97/1.18 tff(677,plain,
% 0.97/1.18 (s(s(z)) = s(z)),
% 0.97/1.18 inference(symmetry,[status(thm)],[674])).
% 0.97/1.18 tff(678,plain,
% 0.97/1.18 (s(s(z)) = z),
% 0.97/1.18 inference(transitivity,[status(thm)],[677, 127, 676, 13])).
% 0.97/1.18 tff(679,plain,
% 0.97/1.18 ($false),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[28, 678])).
% 0.97/1.18 tff(680,plain,(~(s(z) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.18 tff(681,plain,
% 0.97/1.18 (((~![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))))),
% 0.97/1.18 inference(rewrite,[status(thm)],[])).
% 0.97/1.18 tff(682,plain,
% 0.97/1.18 ((~![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))))),
% 0.97/1.18 inference(quant_inst,[status(thm)],[])).
% 0.97/1.18 tff(683,plain,
% 0.97/1.18 ((~![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)))),
% 0.97/1.18 inference(modus_ponens,[status(thm)],[682, 681])).
% 0.97/1.18 tff(684,plain,
% 0.97/1.18 ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[683, 51])).
% 0.97/1.18 tff(685,plain,
% 0.97/1.18 (b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[684, 680])).
% 0.97/1.18 tff(686,plain,
% 0.97/1.18 (b(s(z), s(s(z)))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[685, 673])).
% 0.97/1.18 tff(687,assumption,(b(s(s(z)), s(s(elem!1)))), introduced(assumption)).
% 0.97/1.18 tff(688,plain,
% 0.97/1.18 ((s(s(z)) = s(z)) <=> (s(z) = s(s(z)))),
% 0.97/1.18 inference(commutativity,[status(thm)],[])).
% 0.97/1.18 tff(689,plain,
% 0.97/1.18 ((s(z) = s(s(z))) <=> (s(s(z)) = s(z))),
% 0.97/1.18 inference(symmetry,[status(thm)],[688])).
% 0.97/1.18 tff(690,plain,
% 0.97/1.18 ((~(s(z) = s(s(z)))) <=> (~(s(s(z)) = s(z)))),
% 0.97/1.18 inference(monotonicity,[status(thm)],[689])).
% 0.97/1.18 tff(691,plain,
% 0.97/1.18 (~(s(s(z)) = s(z))),
% 0.97/1.18 inference(modus_ponens,[status(thm)],[680, 690])).
% 0.97/1.18 tff(692,plain,
% 0.97/1.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 0.97/1.18 inference(rewrite,[status(thm)],[])).
% 0.97/1.18 tff(693,plain,
% 0.97/1.18 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 0.97/1.18 inference(quant_inst,[status(thm)],[])).
% 0.97/1.18 tff(694,plain,
% 0.97/1.18 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))),
% 0.97/1.18 inference(modus_ponens,[status(thm)],[693, 692])).
% 0.97/1.18 tff(695,plain,
% 0.97/1.18 (~r(s(s(z)), s(z))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[694, 297, 666, 665])).
% 0.97/1.18 tff(696,plain,
% 0.97/1.19 (((~![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)))),
% 0.97/1.19 inference(rewrite,[status(thm)],[])).
% 0.97/1.19 tff(697,plain,
% 0.97/1.19 ((~![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)))),
% 0.97/1.19 inference(quant_inst,[status(thm)],[])).
% 0.97/1.19 tff(698,plain,
% 0.97/1.19 ((~![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))),
% 0.97/1.19 inference(modus_ponens,[status(thm)],[697, 696])).
% 0.97/1.19 tff(699,plain,
% 0.97/1.19 ((s(s(z)) = s(z)) | b(s(s(z)), s(z))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[698, 51, 695])).
% 0.97/1.19 tff(700,plain,
% 0.97/1.19 (b(s(s(z)), s(z))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[699, 691])).
% 0.97/1.19 tff(701,plain,
% 0.97/1.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))))),
% 0.97/1.19 inference(rewrite,[status(thm)],[])).
% 0.97/1.19 tff(702,plain,
% 0.97/1.19 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))))),
% 0.97/1.19 inference(rewrite,[status(thm)],[])).
% 0.97/1.19 tff(703,plain,
% 0.97/1.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z)))))),
% 0.97/1.19 inference(monotonicity,[status(thm)],[702])).
% 0.97/1.19 tff(704,plain,
% 0.97/1.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))))),
% 0.97/1.19 inference(transitivity,[status(thm)],[703, 701])).
% 0.97/1.19 tff(705,plain,
% 0.97/1.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 0.97/1.19 inference(quant_inst,[status(thm)],[])).
% 0.97/1.19 tff(706,plain,
% 0.97/1.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z)))),
% 0.97/1.19 inference(modus_ponens,[status(thm)],[705, 704])).
% 0.97/1.19 tff(707,plain,
% 0.97/1.19 ($false),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[706, 319, 1, 700, 687, 686])).
% 0.97/1.19 tff(708,plain,((~r(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.19 tff(709,plain,
% 0.97/1.19 (~r(s(z), z)),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[708, 653, 214, 664])).
% 0.97/1.19 tff(710,plain,
% 0.97/1.19 (b(s(z), z)),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[65, 51, 62, 709])).
% 0.97/1.19 tff(711,assumption,(b(z, s(s(z)))), introduced(assumption)).
% 0.97/1.19 tff(712,plain,
% 0.97/1.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(z))))),
% 0.97/1.19 inference(rewrite,[status(thm)],[])).
% 0.97/1.19 tff(713,plain,
% 0.97/1.19 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(z))))),
% 0.97/1.19 inference(rewrite,[status(thm)],[])).
% 0.97/1.19 tff(714,plain,
% 0.97/1.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(z)))))),
% 0.97/1.19 inference(monotonicity,[status(thm)],[713])).
% 0.97/1.19 tff(715,plain,
% 0.97/1.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(z))))),
% 0.97/1.19 inference(transitivity,[status(thm)],[714, 712])).
% 0.97/1.19 tff(716,plain,
% 0.97/1.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))))),
% 0.97/1.19 inference(quant_inst,[status(thm)],[])).
% 0.97/1.19 tff(717,plain,
% 0.97/1.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(z)))),
% 0.97/1.19 inference(modus_ponens,[status(thm)],[716, 715])).
% 0.97/1.19 tff(718,plain,
% 0.97/1.19 ($false),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[717, 319, 1, 711, 687, 202])).
% 0.97/1.19 tff(719,plain,((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.19 tff(720,plain,
% 0.97/1.19 (~b(z, s(s(z)))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[719, 653, 214, 202])).
% 0.97/1.19 tff(721,plain,
% 0.97/1.19 ((z = s(s(z))) <=> (s(s(z)) = z)),
% 0.97/1.19 inference(commutativity,[status(thm)],[])).
% 0.97/1.19 tff(722,plain,
% 0.97/1.19 ((s(s(z)) = z) <=> (z = s(s(z)))),
% 0.97/1.19 inference(symmetry,[status(thm)],[721])).
% 0.97/1.19 tff(723,plain,
% 0.97/1.19 ((~(s(s(z)) = z)) <=> (~(z = s(s(z))))),
% 0.97/1.19 inference(monotonicity,[status(thm)],[722])).
% 0.97/1.19 tff(724,plain,
% 0.97/1.19 (~(z = s(s(z)))),
% 0.97/1.19 inference(modus_ponens,[status(thm)],[28, 723])).
% 0.97/1.19 tff(725,plain,
% 0.97/1.19 (((~![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))))),
% 0.97/1.19 inference(rewrite,[status(thm)],[])).
% 0.97/1.19 tff(726,plain,
% 0.97/1.19 ((~![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))))),
% 0.97/1.19 inference(quant_inst,[status(thm)],[])).
% 0.97/1.19 tff(727,plain,
% 0.97/1.19 ((~![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)))),
% 0.97/1.19 inference(modus_ponens,[status(thm)],[726, 725])).
% 0.97/1.19 tff(728,plain,
% 0.97/1.19 ((z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z)))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[727, 51])).
% 0.97/1.19 tff(729,plain,
% 0.97/1.19 (b(z, s(s(z))) | r(z, s(s(z)))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[728, 724])).
% 0.97/1.19 tff(730,plain,
% 0.97/1.19 (r(z, s(s(z)))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[729, 720])).
% 0.97/1.19 tff(731,assumption,(r(s(elem!1), z)), introduced(assumption)).
% 0.97/1.19 tff(732,assumption,(r(z, s(s(z)))), introduced(assumption)).
% 0.97/1.19 tff(733,plain,
% 0.97/1.19 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z)))))),
% 0.97/1.19 inference(rewrite,[status(thm)],[])).
% 0.97/1.19 tff(734,plain,
% 0.97/1.19 (((~r(z, s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z)))))),
% 0.97/1.19 inference(rewrite,[status(thm)],[])).
% 0.97/1.19 tff(735,plain,
% 0.97/1.19 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z))))))),
% 0.97/1.19 inference(monotonicity,[status(thm)],[734])).
% 0.97/1.19 tff(736,plain,
% 0.97/1.19 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z)))))),
% 0.97/1.19 inference(transitivity,[status(thm)],[735, 733])).
% 0.97/1.19 tff(737,plain,
% 0.97/1.19 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), z)))),
% 0.97/1.19 inference(quant_inst,[status(thm)],[])).
% 0.97/1.19 tff(738,plain,
% 0.97/1.19 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z))))),
% 0.97/1.19 inference(modus_ponens,[status(thm)],[737, 736])).
% 0.97/1.19 tff(739,plain,
% 0.97/1.19 ($false),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[738, 297, 732, 203, 731])).
% 0.97/1.19 tff(740,plain,((~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.19 tff(741,plain,
% 0.97/1.19 (~r(s(elem!1), z)),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[740, 730, 203])).
% 0.97/1.19 tff(742,plain,
% 0.97/1.19 (((~![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))),
% 0.97/1.19 inference(rewrite,[status(thm)],[])).
% 0.97/1.19 tff(743,plain,
% 0.97/1.19 ((~![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))),
% 0.97/1.19 inference(quant_inst,[status(thm)],[])).
% 0.97/1.19 tff(744,plain,
% 0.97/1.19 ((~![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)),
% 0.97/1.19 inference(modus_ponens,[status(thm)],[743, 742])).
% 0.97/1.19 tff(745,plain,
% 0.97/1.19 (b(s(elem!1), z)),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[744, 51, 193, 741])).
% 0.97/1.19 tff(746,plain,
% 0.97/1.19 ((z = s(elem!1)) <=> (s(elem!1) = z)),
% 0.97/1.19 inference(commutativity,[status(thm)],[])).
% 0.97/1.19 tff(747,plain,
% 0.97/1.19 ((s(elem!1) = z) <=> (z = s(elem!1))),
% 0.97/1.19 inference(symmetry,[status(thm)],[746])).
% 0.97/1.19 tff(748,plain,
% 0.97/1.19 ((~(s(elem!1) = z)) <=> (~(z = s(elem!1)))),
% 0.97/1.19 inference(monotonicity,[status(thm)],[747])).
% 0.97/1.19 tff(749,plain,
% 0.97/1.19 (~(z = s(elem!1))),
% 0.97/1.19 inference(modus_ponens,[status(thm)],[193, 748])).
% 0.97/1.19 tff(750,plain,
% 0.97/1.19 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z)))))),
% 0.97/1.19 inference(rewrite,[status(thm)],[])).
% 0.97/1.19 tff(751,plain,
% 0.97/1.19 (((~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z)))))),
% 0.97/1.19 inference(rewrite,[status(thm)],[])).
% 0.97/1.19 tff(752,plain,
% 0.97/1.19 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z))))))),
% 0.97/1.19 inference(monotonicity,[status(thm)],[751])).
% 0.97/1.19 tff(753,plain,
% 0.97/1.19 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z)))))),
% 0.97/1.19 inference(transitivity,[status(thm)],[752, 750])).
% 0.97/1.19 tff(754,plain,
% 0.97/1.19 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(elem!1))))),
% 0.97/1.19 inference(quant_inst,[status(thm)],[])).
% 0.97/1.19 tff(755,plain,
% 0.97/1.19 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z))))),
% 0.97/1.19 inference(modus_ponens,[status(thm)],[754, 753])).
% 0.97/1.19 tff(756,plain,
% 0.97/1.19 (~r(z, s(elem!1))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[755, 297, 730, 203])).
% 0.97/1.19 tff(757,plain,
% 0.97/1.19 (((~![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)))),
% 0.97/1.19 inference(rewrite,[status(thm)],[])).
% 0.97/1.19 tff(758,plain,
% 0.97/1.19 ((~![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)))),
% 0.97/1.19 inference(quant_inst,[status(thm)],[])).
% 0.97/1.19 tff(759,plain,
% 0.97/1.19 ((~![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))),
% 0.97/1.19 inference(modus_ponens,[status(thm)],[758, 757])).
% 0.97/1.19 tff(760,plain,
% 0.97/1.19 ((z = s(elem!1)) | b(z, s(elem!1))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[759, 51, 756])).
% 0.97/1.19 tff(761,plain,
% 0.97/1.19 (b(z, s(elem!1))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[760, 749])).
% 0.97/1.19 tff(762,plain,
% 0.97/1.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))),
% 0.97/1.19 inference(rewrite,[status(thm)],[])).
% 0.97/1.19 tff(763,plain,
% 0.97/1.19 (((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))),
% 0.97/1.19 inference(rewrite,[status(thm)],[])).
% 0.97/1.19 tff(764,plain,
% 0.97/1.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z))))),
% 0.97/1.19 inference(monotonicity,[status(thm)],[763])).
% 0.97/1.19 tff(765,plain,
% 0.97/1.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))),
% 0.97/1.19 inference(transitivity,[status(thm)],[764, 762])).
% 0.97/1.19 tff(766,plain,
% 0.97/1.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 0.97/1.19 inference(quant_inst,[status(thm)],[])).
% 0.97/1.19 tff(767,plain,
% 0.97/1.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z))),
% 0.97/1.19 inference(modus_ponens,[status(thm)],[766, 765])).
% 0.97/1.19 tff(768,plain,
% 0.97/1.19 (~b(s(elem!1), s(z))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[767, 319, 761, 745, 710])).
% 0.97/1.19 tff(769,assumption,(s(elem!1) = s(z)), introduced(assumption)).
% 0.97/1.19 tff(770,plain,
% 0.97/1.19 (s(s(elem!1)) = s(s(z))),
% 0.97/1.19 inference(monotonicity,[status(thm)],[769])).
% 0.97/1.19 tff(771,plain,
% 0.97/1.19 (s(s(z)) = s(s(elem!1))),
% 0.97/1.19 inference(symmetry,[status(thm)],[770])).
% 0.97/1.19 tff(772,assumption,(~(s(s(z)) = s(s(elem!1)))), introduced(assumption)).
% 0.97/1.19 tff(773,plain,
% 0.97/1.19 ($false),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[772, 771])).
% 0.97/1.19 tff(774,plain,((~(s(elem!1) = s(z))) | (s(s(z)) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.19 tff(775,plain,
% 0.97/1.19 (~(s(elem!1) = s(z))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[774, 652])).
% 0.97/1.19 tff(776,assumption,(~(s(elem!1) = s(z))), introduced(assumption)).
% 0.97/1.19 tff(777,assumption,(~r(s(elem!1), s(z))), introduced(assumption)).
% 0.97/1.19 tff(778,assumption,(~b(s(elem!1), s(z))), introduced(assumption)).
% 0.97/1.19 tff(779,plain,
% 0.97/1.19 (((~![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)))),
% 0.97/1.19 inference(rewrite,[status(thm)],[])).
% 0.97/1.19 tff(780,plain,
% 0.97/1.19 ((~![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)))),
% 0.97/1.19 inference(quant_inst,[status(thm)],[])).
% 0.97/1.19 tff(781,plain,
% 0.97/1.19 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z))),
% 0.97/1.19 inference(modus_ponens,[status(thm)],[780, 779])).
% 0.97/1.19 tff(782,plain,
% 0.97/1.19 ($false),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[781, 51, 778, 777, 776])).
% 0.97/1.19 tff(783,plain,(b(s(elem!1), s(z)) | r(s(elem!1), s(z)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.19 tff(784,plain,
% 0.97/1.19 (r(s(elem!1), s(z))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[783, 775, 768])).
% 0.97/1.19 tff(785,assumption,(b(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 0.97/1.19 tff(786,assumption,(b(s(elem!1), z)), introduced(assumption)).
% 0.97/1.19 tff(787,plain,
% 0.97/1.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))),
% 0.97/1.19 inference(rewrite,[status(thm)],[])).
% 0.97/1.19 tff(788,plain,
% 0.97/1.19 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))),
% 0.97/1.19 inference(rewrite,[status(thm)],[])).
% 0.97/1.19 tff(789,plain,
% 0.97/1.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1), s(s(elem!1)))) | (~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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z))))),
% 0.97/1.19 inference(monotonicity,[status(thm)],[788])).
% 0.97/1.19 tff(790,plain,
% 0.97/1.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1), s(s(elem!1)))) | (~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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))),
% 0.97/1.19 inference(transitivity,[status(thm)],[789, 787])).
% 0.97/1.19 tff(791,plain,
% 0.97/1.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)))),
% 0.97/1.19 inference(quant_inst,[status(thm)],[])).
% 0.97/1.19 tff(792,plain,
% 0.97/1.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z))),
% 0.97/1.19 inference(modus_ponens,[status(thm)],[791, 790])).
% 0.97/1.19 tff(793,plain,
% 0.97/1.19 ($false),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[792, 319, 1, 786, 785, 202])).
% 0.97/1.19 tff(794,plain,((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.19 tff(795,plain,
% 0.97/1.19 (~b(s(elem!1), s(s(elem!1)))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[794, 745, 214, 202])).
% 0.97/1.19 tff(796,plain,
% 0.97/1.19 (r(s(elem!1), s(z)) <=> r(s(s(elem!1)), s(z))),
% 0.97/1.19 inference(monotonicity,[status(thm)],[109])).
% 0.97/1.19 tff(797,plain,
% 0.97/1.19 (r(s(s(elem!1)), s(z)) <=> r(s(elem!1), s(z))),
% 0.97/1.19 inference(symmetry,[status(thm)],[796])).
% 0.97/1.19 tff(798,plain,
% 0.97/1.19 ((~r(s(s(elem!1)), s(z))) <=> (~r(s(elem!1), s(z)))),
% 0.97/1.19 inference(monotonicity,[status(thm)],[797])).
% 0.97/1.19 tff(799,plain,
% 0.97/1.19 (~r(s(elem!1), s(z))),
% 0.97/1.19 inference(modus_ponens,[status(thm)],[180, 798])).
% 0.97/1.19 tff(800,assumption,(r(s(elem!1), s(z))), introduced(assumption)).
% 0.97/1.19 tff(801,plain,
% 0.97/1.19 ($false),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[800, 799])).
% 0.97/1.19 tff(802,plain,((~(s(elem!1) = s(s(elem!1)))) | (~r(s(elem!1), s(z))) | r(s(s(elem!1)), s(z))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.19 tff(803,plain,
% 0.97/1.19 (~(s(elem!1) = s(s(elem!1)))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[802, 784, 180])).
% 0.97/1.19 tff(804,plain,
% 0.97/1.19 (((~![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))))),
% 0.97/1.19 inference(rewrite,[status(thm)],[])).
% 0.97/1.19 tff(805,plain,
% 0.97/1.19 ((~![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))))),
% 0.97/1.19 inference(quant_inst,[status(thm)],[])).
% 0.97/1.19 tff(806,plain,
% 0.97/1.19 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1)))),
% 0.97/1.19 inference(modus_ponens,[status(thm)],[805, 804])).
% 0.97/1.19 tff(807,plain,
% 0.97/1.19 ((s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1)))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[806, 51])).
% 0.97/1.19 tff(808,plain,
% 0.97/1.19 (r(s(elem!1), s(s(elem!1)))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[807, 803, 795])).
% 0.97/1.19 tff(809,plain,
% 0.97/1.19 ((s(z) = s(s(elem!1))) <=> (s(s(elem!1)) = s(z))),
% 0.97/1.19 inference(commutativity,[status(thm)],[])).
% 0.97/1.19 tff(810,assumption,(s(z) = s(s(elem!1))), introduced(assumption)).
% 0.97/1.19 tff(811,plain,
% 0.97/1.19 (s(s(elem!1)) = s(z)),
% 0.97/1.20 inference(modus_ponens,[status(thm)],[810, 809])).
% 0.97/1.20 tff(812,plain,
% 0.97/1.20 ($false),
% 0.97/1.20 inference(unit_resolution,[status(thm)],[228, 811])).
% 0.97/1.20 tff(813,plain,((~(s(z) = s(s(elem!1)))) | (s(s(elem!1)) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.20 tff(814,plain,
% 0.97/1.20 (~(s(z) = s(s(elem!1)))),
% 0.97/1.20 inference(unit_resolution,[status(thm)],[813, 209])).
% 0.97/1.20 tff(815,plain,
% 0.97/1.20 (~b(z, s(s(z)))),
% 0.97/1.20 inference(unit_resolution,[status(thm)],[719, 687, 1, 202])).
% 0.97/1.20 tff(816,plain,
% 0.97/1.20 (r(z, s(s(z)))),
% 0.97/1.20 inference(unit_resolution,[status(thm)],[729, 815])).
% 0.97/1.20 tff(817,assumption,(b(s(z), s(s(elem!1)))), introduced(assumption)).
% 0.97/1.20 tff(818,plain,
% 0.97/1.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))))),
% 0.97/1.20 inference(rewrite,[status(thm)],[])).
% 0.97/1.20 tff(819,plain,
% 0.97/1.20 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))))),
% 0.97/1.20 inference(rewrite,[status(thm)],[])).
% 0.97/1.20 tff(820,plain,
% 0.97/1.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z)))))),
% 0.97/1.20 inference(monotonicity,[status(thm)],[819])).
% 0.97/1.20 tff(821,plain,
% 0.97/1.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))))),
% 0.97/1.20 inference(transitivity,[status(thm)],[820, 818])).
% 0.97/1.20 tff(822,plain,
% 0.97/1.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(z)))))),
% 0.97/1.20 inference(quant_inst,[status(thm)],[])).
% 0.97/1.20 tff(823,plain,
% 0.97/1.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z)))),
% 0.97/1.20 inference(modus_ponens,[status(thm)],[822, 821])).
% 0.97/1.20 tff(824,plain,
% 0.97/1.20 (~b(s(z), s(s(z)))),
% 0.97/1.20 inference(unit_resolution,[status(thm)],[823, 319, 1, 687, 817])).
% 0.97/1.20 tff(825,plain,
% 0.97/1.20 (r(s(z), s(s(z)))),
% 0.97/1.20 inference(unit_resolution,[status(thm)],[685, 824])).
% 0.97/1.20 tff(826,plain,
% 0.97/1.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(827,plain,
% 1.04/1.20 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(828,plain,
% 1.04/1.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))))),
% 1.04/1.20 inference(monotonicity,[status(thm)],[827])).
% 1.04/1.20 tff(829,plain,
% 1.04/1.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.04/1.20 inference(transitivity,[status(thm)],[828, 826])).
% 1.04/1.20 tff(830,plain,
% 1.04/1.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)))),
% 1.04/1.20 inference(quant_inst,[status(thm)],[])).
% 1.04/1.20 tff(831,plain,
% 1.04/1.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))),
% 1.04/1.20 inference(modus_ponens,[status(thm)],[830, 829])).
% 1.04/1.20 tff(832,plain,
% 1.04/1.20 (~b(s(z), z)),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[831, 319, 1, 817, 202])).
% 1.04/1.20 tff(833,plain,
% 1.04/1.20 (r(s(z), z)),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[65, 51, 62, 832])).
% 1.04/1.20 tff(834,plain,
% 1.04/1.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(z, s(s(z)))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(835,plain,
% 1.04/1.20 (((~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z))) <=> ((~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(z, s(s(z)))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(836,plain,
% 1.04/1.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(z, s(s(z))))))),
% 1.04/1.20 inference(monotonicity,[status(thm)],[835])).
% 1.04/1.20 tff(837,plain,
% 1.04/1.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(z, s(s(z)))))),
% 1.04/1.20 inference(transitivity,[status(thm)],[836, 834])).
% 1.04/1.20 tff(838,plain,
% 1.04/1.20 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))),
% 1.04/1.20 inference(quant_inst,[status(thm)],[])).
% 1.04/1.20 tff(839,plain,
% 1.04/1.20 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(z, s(s(z))))),
% 1.04/1.20 inference(modus_ponens,[status(thm)],[838, 837])).
% 1.04/1.20 tff(840,plain,
% 1.04/1.20 ($false),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[839, 297, 833, 825, 816])).
% 1.04/1.20 tff(841,plain,((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.20 tff(842,plain,
% 1.04/1.20 (~b(s(z), s(s(elem!1)))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[841, 202, 214, 653])).
% 1.04/1.20 tff(843,plain,
% 1.04/1.20 (((~![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))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(844,plain,
% 1.04/1.20 ((~![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))))),
% 1.04/1.20 inference(quant_inst,[status(thm)],[])).
% 1.04/1.20 tff(845,plain,
% 1.04/1.20 ((~![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)))),
% 1.04/1.20 inference(modus_ponens,[status(thm)],[844, 843])).
% 1.04/1.20 tff(846,plain,
% 1.04/1.20 ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[845, 51])).
% 1.04/1.20 tff(847,plain,
% 1.04/1.20 (r(s(z), s(s(elem!1)))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[846, 842, 814])).
% 1.04/1.20 tff(848,plain,
% 1.04/1.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(849,plain,
% 1.04/1.20 (((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z)))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(850,plain,
% 1.04/1.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.04/1.20 inference(monotonicity,[status(thm)],[849])).
% 1.04/1.20 tff(851,plain,
% 1.04/1.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.04/1.20 inference(transitivity,[status(thm)],[850, 848])).
% 1.04/1.20 tff(852,plain,
% 1.04/1.20 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))))),
% 1.04/1.20 inference(quant_inst,[status(thm)],[])).
% 1.04/1.20 tff(853,plain,
% 1.04/1.20 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1))))),
% 1.04/1.20 inference(modus_ponens,[status(thm)],[852, 851])).
% 1.04/1.20 tff(854,plain,
% 1.04/1.20 ($false),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[853, 297, 847, 808, 784])).
% 1.04/1.20 tff(855,plain,((~b(z, s(s(elem!1)))) | r(s(s(elem!1)), s(z)) | (~r(s(elem!1), s(s(z)))) | r(s(s(z)), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.20 tff(856,plain,
% 1.04/1.20 (~b(z, s(s(elem!1)))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[855, 201, 69, 180])).
% 1.04/1.20 tff(857,plain,
% 1.04/1.20 (r(z, s(s(elem!1)))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[56, 856])).
% 1.04/1.20 tff(858,plain,
% 1.04/1.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(859,plain,
% 1.04/1.20 (((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(860,plain,
% 1.04/1.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), z)) | (~r(z, s(s(elem!1))))))),
% 1.04/1.20 inference(monotonicity,[status(thm)],[859])).
% 1.04/1.20 tff(861,plain,
% 1.04/1.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))))),
% 1.04/1.20 inference(transitivity,[status(thm)],[860, 858])).
% 1.04/1.20 tff(862,plain,
% 1.04/1.20 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z)))),
% 1.04/1.20 inference(quant_inst,[status(thm)],[])).
% 1.04/1.20 tff(863,plain,
% 1.04/1.20 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z)) | (~r(z, s(s(elem!1))))),
% 1.04/1.20 inference(modus_ponens,[status(thm)],[862, 861])).
% 1.04/1.20 tff(864,plain,
% 1.04/1.20 ($false),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[863, 297, 444, 666, 70])).
% 1.04/1.20 tff(865,plain,((~r(s(z), s(s(elem!1)))) | (~r(s(z), z)) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.20 tff(866,plain,
% 1.04/1.20 (~r(s(z), z)),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[865, 857, 198])).
% 1.04/1.20 tff(867,plain,
% 1.04/1.20 ($false),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[59, 287])).
% 1.04/1.20 tff(868,plain,((~r(s(elem!1), elem!1)) | r(s(z), z) | (~(s(s(z)) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.20 tff(869,plain,
% 1.04/1.20 (~r(s(elem!1), elem!1)),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[868, 866, 133])).
% 1.04/1.20 tff(870,plain,
% 1.04/1.20 (b(s(elem!1), elem!1)),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[375, 869, 194])).
% 1.04/1.20 tff(871,plain,
% 1.04/1.20 (b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[213, 209])).
% 1.04/1.20 tff(872,plain,
% 1.04/1.20 (b(s(s(elem!1)), s(z))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[871, 180])).
% 1.04/1.20 tff(873,plain,
% 1.04/1.20 (b(s(s(elem!1)), s(elem!1))),
% 1.04/1.20 inference(modus_ponens,[status(thm)],[872, 218])).
% 1.04/1.20 tff(874,plain,
% 1.04/1.20 (b(z, s(s(z))) <=> b(z, s(s(elem!1)))),
% 1.04/1.20 inference(monotonicity,[status(thm)],[133])).
% 1.04/1.20 tff(875,plain,
% 1.04/1.20 (b(z, s(s(elem!1))) <=> b(z, s(s(z)))),
% 1.04/1.20 inference(symmetry,[status(thm)],[874])).
% 1.04/1.20 tff(876,plain,
% 1.04/1.20 ((~b(z, s(s(elem!1)))) <=> (~b(z, s(s(z))))),
% 1.04/1.20 inference(monotonicity,[status(thm)],[875])).
% 1.04/1.20 tff(877,plain,
% 1.04/1.20 (~b(z, s(s(z)))),
% 1.04/1.20 inference(modus_ponens,[status(thm)],[35, 876])).
% 1.04/1.20 tff(878,plain,
% 1.04/1.20 ($false),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[711, 877])).
% 1.04/1.20 tff(879,plain,((~(s(s(z)) = s(s(elem!1)))) | (~b(z, s(s(z)))) | b(z, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.20 tff(880,plain,
% 1.04/1.20 (~b(z, s(s(z)))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[879, 856, 133])).
% 1.04/1.20 tff(881,plain,
% 1.04/1.20 (r(z, s(s(z)))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[729, 880])).
% 1.04/1.20 tff(882,plain,
% 1.04/1.20 (r(s(z), s(s(z))) <=> r(s(z), s(s(elem!1)))),
% 1.04/1.20 inference(monotonicity,[status(thm)],[133])).
% 1.04/1.20 tff(883,plain,
% 1.04/1.20 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(z)))),
% 1.04/1.20 inference(symmetry,[status(thm)],[882])).
% 1.04/1.20 tff(884,plain,
% 1.04/1.20 (r(s(elem!1), s(s(elem!1))) <=> r(s(z), s(s(z)))),
% 1.04/1.20 inference(transitivity,[status(thm)],[196, 883])).
% 1.04/1.20 tff(885,plain,
% 1.04/1.20 (r(s(z), s(s(z)))),
% 1.04/1.20 inference(modus_ponens,[status(thm)],[197, 884])).
% 1.04/1.20 tff(886,plain,
% 1.04/1.20 (b(s(z), elem!1) <=> b(s(elem!1), elem!1)),
% 1.04/1.20 inference(monotonicity,[status(thm)],[135])).
% 1.04/1.20 tff(887,plain,
% 1.04/1.20 (b(s(elem!1), elem!1) <=> b(s(z), elem!1)),
% 1.04/1.20 inference(symmetry,[status(thm)],[886])).
% 1.04/1.20 tff(888,plain,
% 1.04/1.20 (b(s(z), elem!1)),
% 1.04/1.20 inference(modus_ponens,[status(thm)],[870, 887])).
% 1.04/1.20 tff(889,assumption,(r(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 1.04/1.20 tff(890,plain,
% 1.04/1.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(891,plain,
% 1.04/1.20 (((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(892,plain,
% 1.04/1.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z))))),
% 1.04/1.20 inference(monotonicity,[status(thm)],[891])).
% 1.04/1.20 tff(893,plain,
% 1.04/1.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)))),
% 1.04/1.20 inference(transitivity,[status(thm)],[892, 890])).
% 1.04/1.20 tff(894,plain,
% 1.04/1.20 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)))),
% 1.04/1.20 inference(quant_inst,[status(thm)],[])).
% 1.04/1.20 tff(895,plain,
% 1.04/1.20 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z))),
% 1.04/1.20 inference(modus_ponens,[status(thm)],[894, 893])).
% 1.04/1.20 tff(896,plain,
% 1.04/1.20 (~r(s(s(s(z))), z)),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[895, 297, 732, 889])).
% 1.04/1.20 tff(897,plain,
% 1.04/1.20 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(z))) = z))),
% 1.04/1.20 inference(quant_inst,[status(thm)],[])).
% 1.04/1.20 tff(898,plain,
% 1.04/1.20 (~(s(s(s(z))) = z)),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[897, 26])).
% 1.04/1.20 tff(899,plain,
% 1.04/1.20 (((~![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))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(900,plain,
% 1.04/1.20 ((~![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))),
% 1.04/1.20 inference(quant_inst,[status(thm)],[])).
% 1.04/1.20 tff(901,plain,
% 1.04/1.20 ((~![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)),
% 1.04/1.20 inference(modus_ponens,[status(thm)],[900, 899])).
% 1.04/1.20 tff(902,plain,
% 1.04/1.20 (b(s(s(s(z))), z)),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[901, 51, 898, 896])).
% 1.04/1.20 tff(903,assumption,(r(s(z), s(s(z)))), introduced(assumption)).
% 1.04/1.20 tff(904,plain,
% 1.04/1.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(905,plain,
% 1.04/1.20 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))))),
% 1.04/1.20 inference(quant_inst,[status(thm)],[])).
% 1.04/1.20 tff(906,plain,
% 1.04/1.20 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z)))),
% 1.04/1.20 inference(modus_ponens,[status(thm)],[905, 904])).
% 1.04/1.20 tff(907,plain,
% 1.04/1.20 (~r(s(s(s(z))), s(z))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[906, 297, 903, 889])).
% 1.04/1.20 tff(908,plain,
% 1.04/1.20 (((~![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)))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(909,plain,
% 1.04/1.20 ((~![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)))),
% 1.04/1.20 inference(quant_inst,[status(thm)],[])).
% 1.04/1.20 tff(910,plain,
% 1.04/1.20 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 1.04/1.20 inference(modus_ponens,[status(thm)],[909, 908])).
% 1.04/1.20 tff(911,plain,
% 1.04/1.20 (b(s(s(s(z))), s(z))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[910, 51, 30, 907])).
% 1.04/1.20 tff(912,assumption,(b(s(z), elem!1)), introduced(assumption)).
% 1.04/1.20 tff(913,assumption,(z = s(z)), introduced(assumption)).
% 1.04/1.20 tff(914,plain,
% 1.04/1.20 (s(z) = z),
% 1.04/1.20 inference(symmetry,[status(thm)],[913])).
% 1.04/1.20 tff(915,plain,
% 1.04/1.20 ($false),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[62, 914])).
% 1.04/1.20 tff(916,plain,(~(z = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.20 tff(917,assumption,(r(z, s(z))), introduced(assumption)).
% 1.04/1.20 tff(918,plain,
% 1.04/1.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(919,plain,
% 1.04/1.20 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))),
% 1.04/1.20 inference(quant_inst,[status(thm)],[])).
% 1.04/1.20 tff(920,plain,
% 1.04/1.20 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z)))),
% 1.04/1.20 inference(modus_ponens,[status(thm)],[919, 918])).
% 1.04/1.20 tff(921,plain,
% 1.04/1.20 ($false),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[920, 297, 903, 732, 917])).
% 1.04/1.20 tff(922,plain,((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.20 tff(923,plain,
% 1.04/1.20 (~r(z, s(z))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[922, 903, 732])).
% 1.04/1.20 tff(924,plain,
% 1.04/1.20 (((~![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)))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(925,plain,
% 1.04/1.20 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(z)) | b(z, s(z)) | r(z, s(z)))),
% 1.04/1.20 inference(quant_inst,[status(thm)],[])).
% 1.04/1.20 tff(926,plain,
% 1.04/1.20 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 1.04/1.20 inference(modus_ponens,[status(thm)],[925, 924])).
% 1.04/1.20 tff(927,plain,
% 1.04/1.20 (b(z, s(z))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[926, 51, 923, 916])).
% 1.04/1.20 tff(928,plain,
% 1.04/1.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(929,plain,
% 1.04/1.20 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(930,plain,
% 1.04/1.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z)))))),
% 1.04/1.20 inference(monotonicity,[status(thm)],[929])).
% 1.04/1.20 tff(931,plain,
% 1.04/1.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))))),
% 1.04/1.21 inference(transitivity,[status(thm)],[930, 928])).
% 1.04/1.21 tff(932,plain,
% 1.04/1.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)))),
% 1.04/1.21 inference(quant_inst,[status(thm)],[])).
% 1.04/1.21 tff(933,plain,
% 1.04/1.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z)))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[932, 931])).
% 1.04/1.21 tff(934,plain,
% 1.04/1.21 ($false),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[933, 319, 927, 912, 911, 902])).
% 1.04/1.21 tff(935,plain,((~r(s(s(s(z))), s(s(z)))) | (~b(s(z), elem!1)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.21 tff(936,plain,
% 1.04/1.21 (~r(s(s(s(z))), s(s(z)))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[935, 888, 885, 881])).
% 1.04/1.21 tff(937,plain,
% 1.04/1.21 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[133])).
% 1.04/1.21 tff(938,plain,
% 1.04/1.21 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[937, 133])).
% 1.04/1.21 tff(939,plain,
% 1.04/1.21 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(z)))),
% 1.04/1.21 inference(symmetry,[status(thm)],[938])).
% 1.04/1.21 tff(940,plain,
% 1.04/1.21 (r(s(s(s(z))), s(s(z)))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[335, 939])).
% 1.04/1.21 tff(941,assumption,(~r(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 1.04/1.21 tff(942,plain,
% 1.04/1.21 ($false),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[941, 940])).
% 1.04/1.21 tff(943,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | r(s(s(s(z))), s(s(z))) | (~(s(s(z)) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.21 tff(944,plain,
% 1.04/1.21 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[943, 936, 133])).
% 1.04/1.21 tff(945,plain,
% 1.04/1.21 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[348, 944, 232])).
% 1.04/1.21 tff(946,plain,
% 1.04/1.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(s(elem!1))), s(s(elem!1)))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(947,plain,
% 1.04/1.21 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), 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(s(elem!1))), s(s(elem!1)))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(948,plain,
% 1.04/1.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(s(elem!1))), s(s(elem!1))))))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[947])).
% 1.04/1.21 tff(949,plain,
% 1.04/1.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(s(elem!1))), s(s(elem!1)))))),
% 1.04/1.21 inference(transitivity,[status(thm)],[948, 946])).
% 1.04/1.21 tff(950,plain,
% 1.04/1.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.04/1.21 inference(quant_inst,[status(thm)],[])).
% 1.04/1.21 tff(951,plain,
% 1.04/1.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[950, 949])).
% 1.04/1.21 tff(952,plain,
% 1.04/1.21 ($false),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[951, 319, 449, 548, 274, 116])).
% 1.04/1.21 tff(953,plain,((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.21 tff(954,plain,
% 1.04/1.21 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[953, 945, 873, 870])).
% 1.04/1.21 tff(955,assumption,(~r(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 1.04/1.21 tff(956,assumption,(~b(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 1.04/1.21 tff(957,plain,
% 1.04/1.21 ($false),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[521, 51, 956, 176, 955])).
% 1.04/1.21 tff(958,plain,(r(s(s(s(elem!1))), s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.21 tff(959,plain,
% 1.04/1.21 (r(s(s(s(elem!1))), s(elem!1))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[958, 954, 183])).
% 1.04/1.21 tff(960,plain,
% 1.04/1.21 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[937])).
% 1.04/1.21 tff(961,plain,
% 1.04/1.21 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.04/1.21 inference(symmetry,[status(thm)],[960])).
% 1.04/1.21 tff(962,plain,
% 1.04/1.21 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.04/1.21 inference(symmetry,[status(thm)],[937])).
% 1.04/1.21 tff(963,plain,
% 1.04/1.21 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[962, 961])).
% 1.04/1.21 tff(964,plain,
% 1.04/1.21 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.04/1.21 inference(symmetry,[status(thm)],[963])).
% 1.04/1.21 tff(965,plain,
% 1.04/1.21 ((s(s(s(z))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[937, 960])).
% 1.04/1.21 tff(966,plain,
% 1.04/1.21 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(s(z))) = s(s(s(s(z)))))),
% 1.04/1.21 inference(symmetry,[status(thm)],[965])).
% 1.04/1.21 tff(967,plain,
% 1.04/1.21 ((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(z))) = s(s(s(s(z))))))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[966])).
% 1.04/1.21 tff(968,plain,
% 1.04/1.21 (~(s(s(s(z))) = s(s(s(s(z)))))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[538, 967])).
% 1.04/1.21 tff(969,plain,
% 1.04/1.21 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[962, 961])).
% 1.04/1.21 tff(970,plain,
% 1.04/1.21 ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) <=> (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[969])).
% 1.04/1.21 tff(971,plain,
% 1.04/1.21 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[178, 183])).
% 1.04/1.21 tff(972,plain,
% 1.04/1.21 (~r(z, s(z))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[922, 881, 885])).
% 1.04/1.21 tff(973,plain,
% 1.04/1.21 (r(z, s(z)) <=> r(elem!1, s(elem!1))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[187, 135])).
% 1.04/1.21 tff(974,plain,
% 1.04/1.21 (r(elem!1, s(elem!1)) <=> r(z, s(z))),
% 1.04/1.21 inference(symmetry,[status(thm)],[973])).
% 1.04/1.21 tff(975,plain,
% 1.04/1.21 (r(z, s(z))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[419, 974])).
% 1.04/1.21 tff(976,assumption,(~r(z, s(z))), introduced(assumption)).
% 1.04/1.21 tff(977,plain,
% 1.04/1.21 ($false),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[976, 975])).
% 1.04/1.21 tff(978,plain,((~r(elem!1, s(elem!1))) | r(z, s(z)) | (~(s(s(z)) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.21 tff(979,plain,
% 1.04/1.21 (~r(elem!1, s(elem!1))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[978, 972, 133])).
% 1.04/1.21 tff(980,plain,
% 1.04/1.21 (b(elem!1, s(elem!1))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[389, 979, 272])).
% 1.04/1.21 tff(981,plain,
% 1.04/1.21 (r(elem!1, s(s(elem!1))) <=> r(z, s(s(elem!1)))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[233])).
% 1.04/1.21 tff(982,plain,
% 1.04/1.21 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 1.04/1.21 inference(symmetry,[status(thm)],[981])).
% 1.04/1.21 tff(983,plain,
% 1.04/1.21 (r(elem!1, s(s(elem!1)))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[857, 982])).
% 1.04/1.21 tff(984,assumption,(r(s(s(s(s(elem!1)))), s(s(elem!1)))), introduced(assumption)).
% 1.04/1.21 tff(985,plain,
% 1.04/1.21 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[649, 297, 197, 984])).
% 1.04/1.21 tff(986,plain,
% 1.04/1.21 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[595, 985, 590])).
% 1.04/1.21 tff(987,assumption,(~(s(s(s(s(elem!1)))) = elem!1)), introduced(assumption)).
% 1.04/1.21 tff(988,assumption,(r(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.04/1.21 tff(989,plain,
% 1.04/1.21 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(990,plain,
% 1.04/1.21 (((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(991,plain,
% 1.04/1.21 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[990])).
% 1.04/1.21 tff(992,plain,
% 1.04/1.21 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.04/1.21 inference(transitivity,[status(thm)],[991, 989])).
% 1.04/1.21 tff(993,plain,
% 1.04/1.21 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.04/1.21 inference(quant_inst,[status(thm)],[])).
% 1.04/1.21 tff(994,plain,
% 1.04/1.21 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[993, 992])).
% 1.04/1.21 tff(995,plain,
% 1.04/1.21 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[994, 297, 984, 988])).
% 1.04/1.21 tff(996,plain,
% 1.04/1.21 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[616, 995, 987])).
% 1.04/1.21 tff(997,plain,
% 1.04/1.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(998,plain,
% 1.04/1.21 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(999,plain,
% 1.04/1.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[998])).
% 1.04/1.21 tff(1000,plain,
% 1.04/1.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.04/1.21 inference(transitivity,[status(thm)],[999, 997])).
% 1.04/1.21 tff(1001,plain,
% 1.04/1.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.04/1.21 inference(quant_inst,[status(thm)],[])).
% 1.04/1.21 tff(1002,plain,
% 1.04/1.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[1001, 1000])).
% 1.04/1.21 tff(1003,plain,
% 1.04/1.21 ($false),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[1002, 319, 275, 449, 996, 986])).
% 1.04/1.21 tff(1004,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (s(s(s(s(elem!1)))) = elem!1) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.21 tff(1005,plain,
% 1.04/1.21 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[1004, 983, 980, 605, 587, 870, 197])).
% 1.04/1.21 tff(1006,plain,
% 1.04/1.21 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[571, 1005, 971])).
% 1.04/1.21 tff(1007,plain,
% 1.04/1.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(1008,plain,
% 1.04/1.21 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(1009,plain,
% 1.04/1.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[1008])).
% 1.04/1.21 tff(1010,plain,
% 1.04/1.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.04/1.21 inference(transitivity,[status(thm)],[1009, 1007])).
% 1.04/1.21 tff(1011,plain,
% 1.04/1.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.04/1.21 inference(quant_inst,[status(thm)],[])).
% 1.04/1.21 tff(1012,plain,
% 1.04/1.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[1011, 1010])).
% 1.04/1.21 tff(1013,plain,
% 1.04/1.21 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[1012, 319, 873, 945, 1006])).
% 1.04/1.21 tff(1014,plain,
% 1.04/1.21 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[1013, 970])).
% 1.04/1.21 tff(1015,plain,
% 1.04/1.21 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(1016,plain,
% 1.04/1.21 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))),
% 1.04/1.21 inference(quant_inst,[status(thm)],[])).
% 1.04/1.21 tff(1017,plain,
% 1.04/1.21 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[1016, 1015])).
% 1.04/1.21 tff(1018,plain,
% 1.04/1.21 ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[1017, 51])).
% 1.04/1.21 tff(1019,plain,
% 1.04/1.21 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[1018, 1014, 968])).
% 1.04/1.21 tff(1020,plain,
% 1.04/1.21 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[1019, 964])).
% 1.04/1.21 tff(1021,assumption,(b(s(s(s(s(elem!1)))), s(s(elem!1)))), introduced(assumption)).
% 1.04/1.21 tff(1022,plain,
% 1.04/1.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(1023,plain,
% 1.04/1.21 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(1024,plain,
% 1.04/1.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[1023])).
% 1.04/1.21 tff(1025,plain,
% 1.04/1.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.04/1.21 inference(transitivity,[status(thm)],[1024, 1022])).
% 1.04/1.21 tff(1026,plain,
% 1.04/1.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.04/1.21 inference(quant_inst,[status(thm)],[])).
% 1.04/1.21 tff(1027,plain,
% 1.04/1.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[1026, 1025])).
% 1.04/1.21 tff(1028,plain,
% 1.04/1.21 ($false),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[1027, 319, 449, 274, 1021, 547])).
% 1.04/1.21 tff(1029,plain,((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.21 tff(1030,plain,
% 1.04/1.21 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[1029, 870, 873, 1006])).
% 1.04/1.21 tff(1031,plain,
% 1.04/1.21 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[595, 1030, 587])).
% 1.04/1.21 tff(1032,plain,
% 1.04/1.21 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(1033,plain,
% 1.04/1.22 (((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(1034,plain,
% 1.04/1.22 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[1033])).
% 1.04/1.22 tff(1035,plain,
% 1.04/1.22 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.04/1.22 inference(transitivity,[status(thm)],[1034, 1032])).
% 1.04/1.22 tff(1036,plain,
% 1.04/1.22 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.04/1.22 inference(quant_inst,[status(thm)],[])).
% 1.04/1.22 tff(1037,plain,
% 1.04/1.22 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[1036, 1035])).
% 1.04/1.22 tff(1038,plain,
% 1.04/1.22 ($false),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[1037, 297, 1031, 1020, 959])).
% 1.04/1.22 tff(1039,plain,((~r(s(elem!1), s(s(elem!1)))) | (~(s(s(z)) = s(s(elem!1)))) | r(s(s(z)), s(s(elem!1))) | r(s(s(elem!1)), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.22 tff(1040,plain,
% 1.04/1.22 (~r(s(elem!1), s(s(elem!1)))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[1039, 132, 69, 180])).
% 1.04/1.22 tff(1041,plain,
% 1.04/1.22 ((~r(s(elem!1), s(s(elem!1)))) <=> (~r(s(z), s(s(elem!1))))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[196])).
% 1.04/1.22 tff(1042,assumption,(~r(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 1.04/1.22 tff(1043,plain,
% 1.04/1.22 (~r(s(z), s(s(elem!1)))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[1042, 1041])).
% 1.04/1.22 tff(1044,plain,
% 1.04/1.22 ($false),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[444, 1043])).
% 1.04/1.22 tff(1045,plain,((~(s(s(z)) = s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | r(s(elem!1), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.22 tff(1046,plain,
% 1.04/1.22 (~r(s(z), s(s(elem!1)))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[1045, 1040, 132])).
% 1.04/1.22 tff(1047,plain,
% 1.04/1.22 (b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[846, 814])).
% 1.04/1.22 tff(1048,plain,
% 1.04/1.22 (b(s(z), s(s(elem!1)))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[1047, 1046])).
% 1.04/1.22 tff(1049,plain,
% 1.04/1.22 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.04/1.22 inference(symmetry,[status(thm)],[162])).
% 1.04/1.22 tff(1050,plain,
% 1.04/1.22 (s(elem!1) = s(z)),
% 1.04/1.22 inference(transitivity,[status(thm)],[206, 1049, 126])).
% 1.04/1.22 tff(1051,plain,
% 1.04/1.22 ((s(elem!1) = s(s(elem!1))) <=> (s(z) = s(s(elem!1)))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[1050])).
% 1.04/1.22 tff(1052,plain,
% 1.04/1.22 ((s(elem!1) = s(s(elem!1))) <=> (s(s(elem!1)) = s(z))),
% 1.04/1.22 inference(transitivity,[status(thm)],[1051, 809])).
% 1.04/1.22 tff(1053,plain,
% 1.04/1.22 ((s(s(elem!1)) = s(z)) <=> (s(elem!1) = s(s(elem!1)))),
% 1.04/1.22 inference(symmetry,[status(thm)],[1052])).
% 1.04/1.22 tff(1054,plain,
% 1.04/1.22 ((~(s(s(elem!1)) = s(z))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[1053])).
% 1.04/1.22 tff(1055,plain,
% 1.04/1.22 (~(s(elem!1) = s(s(elem!1)))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[209, 1054])).
% 1.04/1.22 tff(1056,plain,
% 1.04/1.22 (b(s(elem!1), s(s(elem!1)))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[807, 1040, 1055])).
% 1.04/1.22 tff(1057,plain,
% 1.04/1.22 ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) <=> (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[963])).
% 1.04/1.22 tff(1058,plain,
% 1.04/1.22 ((s(s(s(s(s(elem!1))))) = z) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 1.04/1.22 inference(monotonicity,[status(thm)],[187])).
% 1.04/1.22 tff(1059,plain,
% 1.04/1.22 ((~(s(s(s(s(s(elem!1))))) = z)) <=> (~(s(s(s(s(s(elem!1))))) = elem!1))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[1058])).
% 1.04/1.22 tff(1060,plain,
% 1.04/1.22 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[153, 1059])).
% 1.04/1.22 tff(1061,plain,
% 1.04/1.22 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), z)),
% 1.04/1.22 inference(symmetry,[status(thm)],[440])).
% 1.04/1.22 tff(1062,plain,
% 1.04/1.22 ((~r(s(s(elem!1)), elem!1)) <=> (~r(s(s(elem!1)), z))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[1061])).
% 1.04/1.22 tff(1063,plain,
% 1.04/1.22 (r(elem!1, s(s(s(elem!1)))) <=> r(z, s(s(s(elem!1))))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[233])).
% 1.04/1.22 tff(1064,plain,
% 1.04/1.22 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.04/1.22 inference(symmetry,[status(thm)],[1063])).
% 1.04/1.22 tff(1065,plain,
% 1.04/1.22 (b(elem!1, s(s(s(elem!1)))) <=> b(z, s(s(s(elem!1))))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[233])).
% 1.04/1.22 tff(1066,plain,
% 1.04/1.22 ((~b(elem!1, s(s(s(elem!1))))) <=> (~b(z, s(s(s(elem!1)))))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[1065])).
% 1.04/1.22 tff(1067,plain,
% 1.04/1.22 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.04/1.22 inference(symmetry,[status(thm)],[969])).
% 1.04/1.22 tff(1068,plain,
% 1.04/1.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(1069,plain,
% 1.04/1.22 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(1070,plain,
% 1.04/1.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[1069])).
% 1.04/1.22 tff(1071,plain,
% 1.04/1.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.04/1.22 inference(transitivity,[status(thm)],[1070, 1068])).
% 1.04/1.22 tff(1072,plain,
% 1.04/1.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))),
% 1.04/1.22 inference(quant_inst,[status(thm)],[])).
% 1.04/1.22 tff(1073,plain,
% 1.04/1.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[1072, 1071])).
% 1.04/1.22 tff(1074,plain,
% 1.04/1.22 (~b(s(s(s(elem!1))), z)),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[1073, 319, 1, 202, 116])).
% 1.04/1.22 tff(1075,plain,
% 1.04/1.22 (((~![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))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(1076,plain,
% 1.04/1.22 ((~![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))),
% 1.04/1.22 inference(quant_inst,[status(thm)],[])).
% 1.04/1.22 tff(1077,plain,
% 1.04/1.22 ((~![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)),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[1076, 1075])).
% 1.04/1.22 tff(1078,plain,
% 1.04/1.22 (r(s(s(s(elem!1))), z)),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[1077, 51, 160, 1074])).
% 1.04/1.22 tff(1079,plain,
% 1.04/1.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), 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(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), 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(elem!1))), s(z))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(1080,plain,
% 1.04/1.22 (((~b(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(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(z), 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(elem!1))), s(z))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(1081,plain,
% 1.04/1.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1))), s(s(elem!1)))) | (~b(s(z), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), 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(elem!1))), s(z)))))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[1080])).
% 1.04/1.22 tff(1082,plain,
% 1.04/1.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1))), s(s(elem!1)))) | (~b(s(z), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), 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(elem!1))), s(z))))),
% 1.04/1.22 inference(transitivity,[status(thm)],[1081, 1079])).
% 1.04/1.22 tff(1083,plain,
% 1.04/1.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.04/1.22 inference(quant_inst,[status(thm)],[])).
% 1.04/1.22 tff(1084,plain,
% 1.04/1.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), 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(elem!1))), s(z)))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[1083, 1082])).
% 1.04/1.22 tff(1085,plain,
% 1.04/1.22 (~b(s(s(s(elem!1))), s(z))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[1084, 319, 1, 817, 116])).
% 1.04/1.22 tff(1086,plain,
% 1.04/1.22 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z)))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(1087,plain,
% 1.04/1.22 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z)))),
% 1.04/1.22 inference(quant_inst,[status(thm)],[])).
% 1.04/1.22 tff(1088,plain,
% 1.04/1.22 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[1087, 1086])).
% 1.04/1.22 tff(1089,plain,
% 1.04/1.22 (r(s(s(s(elem!1))), s(z))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[1088, 51, 171, 1085])).
% 1.04/1.22 tff(1090,plain,
% 1.04/1.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(1091,plain,
% 1.04/1.22 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(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(z))) | (~b(z, s(z))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(1092,plain,
% 1.04/1.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z)))))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[1091])).
% 1.04/1.22 tff(1093,plain,
% 1.04/1.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))))),
% 1.04/1.22 inference(transitivity,[status(thm)],[1092, 1090])).
% 1.04/1.22 tff(1094,plain,
% 1.04/1.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))))),
% 1.04/1.22 inference(quant_inst,[status(thm)],[])).
% 1.04/1.22 tff(1095,plain,
% 1.04/1.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z)))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[1094, 1093])).
% 1.04/1.22 tff(1096,plain,
% 1.04/1.22 (~b(z, s(z))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[1095, 319, 1, 817, 202])).
% 1.04/1.22 tff(1097,assumption,(~b(z, s(z))), introduced(assumption)).
% 1.04/1.22 tff(1098,plain,
% 1.04/1.22 ($false),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[926, 51, 1097, 976, 916])).
% 1.04/1.22 tff(1099,plain,(b(z, s(z)) | r(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.22 tff(1100,plain,
% 1.04/1.22 (r(z, s(z))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[1099, 1096])).
% 1.04/1.22 tff(1101,plain,
% 1.04/1.22 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(1102,plain,
% 1.04/1.22 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))),
% 1.04/1.22 inference(quant_inst,[status(thm)],[])).
% 1.04/1.22 tff(1103,plain,
% 1.04/1.22 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[1102, 1101])).
% 1.04/1.22 tff(1104,plain,
% 1.04/1.22 ($false),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[1103, 297, 1100, 1089, 1078])).
% 1.04/1.22 tff(1105,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.22 tff(1106,plain,
% 1.04/1.22 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[1105, 202, 1, 817])).
% 1.04/1.22 tff(1107,plain,
% 1.04/1.22 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[348, 1106, 232])).
% 1.04/1.22 tff(1108,plain,
% 1.04/1.22 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[578, 297, 1107, 984])).
% 1.04/1.22 tff(1109,plain,
% 1.04/1.22 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[1108, 1057])).
% 1.04/1.22 tff(1110,plain,
% 1.04/1.22 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[1018, 1109, 968])).
% 1.04/1.22 tff(1111,plain,
% 1.04/1.22 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[1110, 1067])).
% 1.04/1.22 tff(1112,plain,
% 1.04/1.22 ((s(s(s(elem!1))) = s(z)) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.04/1.22 inference(transitivity,[status(thm)],[181, 277])).
% 1.04/1.22 tff(1113,plain,
% 1.04/1.22 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[1112])).
% 1.04/1.22 tff(1114,plain,
% 1.04/1.22 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[171, 1113])).
% 1.04/1.22 tff(1115,plain,
% 1.04/1.22 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[187])).
% 1.04/1.22 tff(1116,plain,
% 1.04/1.22 (b(elem!1, s(s(elem!1)))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[202, 1115])).
% 1.04/1.22 tff(1117,assumption,(r(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 1.04/1.22 tff(1118,plain,
% 1.04/1.22 ($false),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[994, 297, 1117, 984, 988])).
% 1.04/1.22 tff(1119,plain,((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.22 tff(1120,plain,
% 1.04/1.22 (~r(elem!1, s(s(elem!1)))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[1119, 1117, 984])).
% 1.04/1.22 tff(1121,plain,
% 1.04/1.22 (((~![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))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(1122,plain,
% 1.04/1.22 ((~![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))))),
% 1.04/1.22 inference(quant_inst,[status(thm)],[])).
% 1.04/1.22 tff(1123,plain,
% 1.04/1.22 ((~![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)))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[1122, 1121])).
% 1.04/1.22 tff(1124,plain,
% 1.04/1.22 (b(elem!1, s(s(elem!1)))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[1123, 51, 254, 1120])).
% 1.04/1.22 tff(1125,plain,
% 1.04/1.22 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[534, 1124, 219, 249, 286, 183])).
% 1.04/1.22 tff(1126,plain,
% 1.04/1.22 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[348, 1125, 232])).
% 1.04/1.22 tff(1127,plain,
% 1.04/1.22 (r(elem!1, s(s(elem!1))) <=> r(z, s(s(elem!1)))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[392])).
% 1.04/1.22 tff(1128,plain,
% 1.04/1.22 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 1.04/1.22 inference(symmetry,[status(thm)],[1127])).
% 1.04/1.22 tff(1129,plain,
% 1.04/1.22 ((s(elem!1) = z) <=> (s(elem!1) = elem!1)),
% 1.04/1.22 inference(monotonicity,[status(thm)],[391])).
% 1.04/1.22 tff(1130,plain,
% 1.04/1.22 ((s(elem!1) = z) <=> (elem!1 = s(elem!1))),
% 1.04/1.22 inference(transitivity,[status(thm)],[1129, 184])).
% 1.04/1.22 tff(1131,plain,
% 1.04/1.22 ((s(elem!1) = z) <=> (s(elem!1) = elem!1)),
% 1.04/1.22 inference(transitivity,[status(thm)],[1130, 185])).
% 1.04/1.22 tff(1132,plain,
% 1.04/1.22 ((~(s(elem!1) = z)) <=> (~(s(elem!1) = elem!1))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[1131])).
% 1.04/1.22 tff(1133,plain,
% 1.04/1.22 (~(s(elem!1) = elem!1)),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[193, 1132])).
% 1.04/1.22 tff(1134,assumption,(r(s(s(s(s(s(elem!1))))), elem!1)), introduced(assumption)).
% 1.04/1.22 tff(1135,plain,
% 1.04/1.22 ((s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))),
% 1.04/1.22 inference(commutativity,[status(thm)],[])).
% 1.04/1.22 tff(1136,plain,
% 1.04/1.22 ((s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))),
% 1.04/1.22 inference(symmetry,[status(thm)],[1135])).
% 1.04/1.22 tff(1137,plain,
% 1.04/1.22 ((~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[1136])).
% 1.04/1.22 tff(1138,plain,
% 1.04/1.22 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[101, 99])).
% 1.04/1.22 tff(1139,plain,
% 1.04/1.22 (~(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[1138, 1137])).
% 1.04/1.22 tff(1140,plain,
% 1.04/1.22 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(1141,plain,
% 1.04/1.22 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.04/1.22 inference(quant_inst,[status(thm)],[])).
% 1.04/1.22 tff(1142,plain,
% 1.04/1.22 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[1141, 1140])).
% 1.04/1.22 tff(1143,plain,
% 1.04/1.22 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[1142, 297, 1117, 1134])).
% 1.04/1.22 tff(1144,plain,
% 1.04/1.22 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(1145,plain,
% 1.04/1.22 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.04/1.22 inference(quant_inst,[status(thm)],[])).
% 1.04/1.22 tff(1146,plain,
% 1.04/1.22 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[1145, 1144])).
% 1.04/1.22 tff(1147,plain,
% 1.04/1.22 ((s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[1146, 51, 1143])).
% 1.04/1.22 tff(1148,plain,
% 1.04/1.22 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[1147, 1139])).
% 1.04/1.22 tff(1149,plain,
% 1.04/1.22 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(elem!1))) = z)),
% 1.04/1.22 inference(monotonicity,[status(thm)],[392])).
% 1.04/1.22 tff(1150,plain,
% 1.04/1.22 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 1.04/1.22 inference(symmetry,[status(thm)],[1149])).
% 1.04/1.22 tff(1151,plain,
% 1.04/1.22 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[1150])).
% 1.04/1.22 tff(1152,plain,
% 1.04/1.22 (~(s(s(s(elem!1))) = elem!1)),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[160, 1151])).
% 1.04/1.22 tff(1153,plain,
% 1.04/1.22 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[586, 1152])).
% 1.04/1.22 tff(1154,plain,
% 1.04/1.22 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 1.04/1.22 inference(monotonicity,[status(thm)],[391])).
% 1.04/1.22 tff(1155,plain,
% 1.04/1.22 ((~(s(elem!1) = z)) <=> (~(elem!1 = s(elem!1)))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[1130])).
% 1.04/1.22 tff(1156,plain,
% 1.04/1.22 (~(elem!1 = s(elem!1))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[193, 1155])).
% 1.04/1.22 tff(1157,plain,
% 1.04/1.22 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.04/1.22 inference(monotonicity,[status(thm)],[391])).
% 1.04/1.22 tff(1158,plain,
% 1.04/1.22 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.04/1.22 inference(transitivity,[status(thm)],[1157, 597])).
% 1.04/1.22 tff(1159,plain,
% 1.04/1.22 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[1158])).
% 1.04/1.22 tff(1160,plain,
% 1.04/1.22 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[604, 1159])).
% 1.04/1.22 tff(1161,plain,
% 1.04/1.22 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.04/1.22 inference(transitivity,[status(thm)],[1158, 598])).
% 1.04/1.22 tff(1162,plain,
% 1.04/1.22 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[1161])).
% 1.04/1.22 tff(1163,plain,
% 1.04/1.22 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[604, 1162])).
% 1.04/1.22 tff(1164,plain,
% 1.04/1.22 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(1165,plain,
% 1.04/1.22 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.04/1.22 inference(quant_inst,[status(thm)],[])).
% 1.04/1.22 tff(1166,plain,
% 1.04/1.22 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[1165, 1164])).
% 1.04/1.22 tff(1167,plain,
% 1.04/1.22 ($false),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[1166, 297, 286, 1117, 620])).
% 1.04/1.22 tff(1168,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.22 tff(1169,plain,
% 1.04/1.22 (~r(s(elem!1), elem!1)),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[1168, 620, 1117])).
% 1.04/1.22 tff(1170,plain,
% 1.04/1.22 (b(s(elem!1), elem!1)),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[375, 1169, 1133])).
% 1.04/1.22 tff(1171,plain,
% 1.04/1.22 (b(s(elem!1), z) <=> b(s(elem!1), elem!1)),
% 1.04/1.22 inference(monotonicity,[status(thm)],[391])).
% 1.04/1.22 tff(1172,plain,
% 1.04/1.22 (b(s(elem!1), elem!1) <=> b(s(elem!1), z)),
% 1.04/1.22 inference(symmetry,[status(thm)],[1171])).
% 1.04/1.22 tff(1173,plain,
% 1.04/1.22 (b(s(elem!1), z)),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[449, 1172])).
% 1.04/1.22 tff(1174,assumption,(~b(s(elem!1), z)), introduced(assumption)).
% 1.04/1.22 tff(1175,plain,
% 1.04/1.22 ($false),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[1174, 1173])).
% 1.04/1.23 tff(1176,plain,((~b(s(elem!1), elem!1)) | b(s(elem!1), z) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.23 tff(1177,plain,
% 1.04/1.23 (b(s(elem!1), z)),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[1176, 1170, 391])).
% 1.04/1.23 tff(1178,plain,
% 1.04/1.23 (~b(z, s(s(elem!1)))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[794, 1177, 1, 785])).
% 1.04/1.23 tff(1179,plain,
% 1.04/1.23 (r(z, s(s(elem!1)))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[56, 1178])).
% 1.04/1.23 tff(1180,plain,
% 1.04/1.23 (r(elem!1, s(s(elem!1)))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[1179, 1128])).
% 1.04/1.23 tff(1181,plain,
% 1.04/1.23 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(1182,plain,
% 1.04/1.23 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.04/1.23 inference(quant_inst,[status(thm)],[])).
% 1.04/1.23 tff(1183,plain,
% 1.04/1.23 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[1182, 1181])).
% 1.04/1.23 tff(1184,plain,
% 1.04/1.23 (~r(s(s(s(elem!1))), elem!1)),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[1183, 297, 335, 988])).
% 1.04/1.23 tff(1185,assumption,(~(elem!1 = s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.04/1.23 tff(1186,plain,
% 1.04/1.23 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[578, 297, 335, 984])).
% 1.04/1.23 tff(1187,plain,
% 1.04/1.23 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[558, 51, 99, 1186])).
% 1.04/1.23 tff(1188,plain,
% 1.04/1.23 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(1189,plain,
% 1.04/1.23 (((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1))))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(1190,plain,
% 1.04/1.23 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 1.04/1.23 inference(monotonicity,[status(thm)],[1189])).
% 1.04/1.23 tff(1191,plain,
% 1.04/1.23 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.04/1.23 inference(transitivity,[status(thm)],[1190, 1188])).
% 1.04/1.23 tff(1192,plain,
% 1.04/1.23 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.04/1.23 inference(quant_inst,[status(thm)],[])).
% 1.04/1.23 tff(1193,plain,
% 1.04/1.23 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[1192, 1191])).
% 1.04/1.23 tff(1194,plain,
% 1.04/1.23 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[1193, 297, 984, 988])).
% 1.04/1.23 tff(1195,plain,
% 1.04/1.23 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[634, 1194, 1185])).
% 1.04/1.23 tff(1196,plain,
% 1.04/1.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(1197,plain,
% 1.04/1.23 (((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(1198,plain,
% 1.04/1.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.04/1.23 inference(monotonicity,[status(thm)],[1197])).
% 1.04/1.23 tff(1199,plain,
% 1.04/1.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.04/1.23 inference(transitivity,[status(thm)],[1198, 1196])).
% 1.04/1.23 tff(1200,plain,
% 1.04/1.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.04/1.23 inference(quant_inst,[status(thm)],[])).
% 1.04/1.23 tff(1201,plain,
% 1.04/1.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[1200, 1199])).
% 1.04/1.23 tff(1202,plain,
% 1.04/1.23 ($false),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[1201, 319, 1195, 448, 996, 1187])).
% 1.04/1.23 tff(1203,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (elem!1 = s(s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = elem!1) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.23 tff(1204,plain,
% 1.04/1.23 (~b(s(s(s(elem!1))), elem!1)),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[1203, 988, 99, 1185, 987, 335, 984])).
% 1.04/1.23 tff(1205,plain,
% 1.04/1.23 ($false),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[361, 1204, 1184, 512])).
% 1.04/1.23 tff(1206,plain,((~r(elem!1, s(s(elem!1)))) | (s(s(s(elem!1))) = elem!1) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (elem!1 = s(s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = elem!1) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.23 tff(1207,plain,
% 1.04/1.23 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[1206, 1180, 99, 1160, 1163, 335, 1152])).
% 1.04/1.23 tff(1208,plain,
% 1.04/1.23 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[571, 1207, 560])).
% 1.04/1.23 tff(1209,assumption,(~(elem!1 = s(elem!1))), introduced(assumption)).
% 1.04/1.23 tff(1210,plain,
% 1.04/1.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(1211,plain,
% 1.04/1.23 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(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(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(1212,plain,
% 1.04/1.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1))))))),
% 1.04/1.23 inference(monotonicity,[status(thm)],[1211])).
% 1.04/1.23 tff(1213,plain,
% 1.04/1.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.04/1.23 inference(transitivity,[status(thm)],[1212, 1210])).
% 1.04/1.23 tff(1214,plain,
% 1.04/1.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 1.04/1.23 inference(quant_inst,[status(thm)],[])).
% 1.04/1.23 tff(1215,plain,
% 1.04/1.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1))))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[1214, 1213])).
% 1.04/1.23 tff(1216,plain,
% 1.04/1.23 ($false),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[1215, 319, 275, 274, 785, 308])).
% 1.04/1.23 tff(1217,plain,((~b(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)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.23 tff(1218,plain,
% 1.04/1.23 (~b(elem!1, s(elem!1))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[1217, 308, 785, 274])).
% 1.04/1.23 tff(1219,plain,
% 1.04/1.23 (r(elem!1, s(elem!1))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[389, 1218, 1209])).
% 1.04/1.23 tff(1220,plain,
% 1.04/1.23 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[611, 297, 1219, 620])).
% 1.04/1.23 tff(1221,plain,
% 1.04/1.23 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[616, 1220, 987])).
% 1.04/1.23 tff(1222,plain,
% 1.04/1.23 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[629, 1219, 620])).
% 1.04/1.23 tff(1223,plain,
% 1.04/1.23 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[634, 1222, 1185])).
% 1.04/1.23 tff(1224,plain,
% 1.04/1.23 ($false),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[641, 319, 1223, 308, 1221, 1021])).
% 1.04/1.23 tff(1225,plain,((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (s(s(s(s(elem!1)))) = elem!1) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (elem!1 = s(s(s(s(elem!1))))) | (elem!1 = s(elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.23 tff(1226,plain,
% 1.04/1.23 (~b(s(s(elem!1)), elem!1)),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[1225, 1208, 1163, 620, 1160, 1156, 785, 274])).
% 1.04/1.23 tff(1227,plain,
% 1.04/1.23 (~b(s(s(elem!1)), z)),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[500, 1226, 391])).
% 1.04/1.23 tff(1228,plain,
% 1.04/1.23 (r(s(s(elem!1)), z)),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[75, 1227])).
% 1.04/1.23 tff(1229,plain,
% 1.04/1.23 (r(s(s(elem!1)), elem!1)),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[1228, 1154])).
% 1.04/1.23 tff(1230,plain,
% 1.04/1.23 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(1231,plain,
% 1.04/1.23 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.04/1.23 inference(quant_inst,[status(thm)],[])).
% 1.04/1.23 tff(1232,plain,
% 1.04/1.23 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[1231, 1230])).
% 1.04/1.23 tff(1233,plain,
% 1.04/1.23 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[1232, 297, 1229, 1134])).
% 1.04/1.23 tff(1234,assumption,(s(s(s(s(s(elem!1))))) = s(s(elem!1))), introduced(assumption)).
% 1.04/1.23 tff(1235,plain,
% 1.04/1.23 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(elem!1)))),
% 1.04/1.23 inference(monotonicity,[status(thm)],[1234])).
% 1.04/1.23 tff(1236,plain,
% 1.04/1.23 (s(s(s(s(elem!1)))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.04/1.23 inference(symmetry,[status(thm)],[95])).
% 1.04/1.23 tff(1237,plain,
% 1.04/1.23 (s(s(s(s(elem!1)))) = s(elem!1)),
% 1.04/1.23 inference(transitivity,[status(thm)],[1236, 1235, 118])).
% 1.04/1.23 tff(1238,plain,
% 1.04/1.23 ($false),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[590, 1237])).
% 1.04/1.23 tff(1239,plain,((~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.23 tff(1240,plain,
% 1.04/1.23 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[1239, 1153])).
% 1.04/1.23 tff(1241,plain,
% 1.04/1.23 (((~![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))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(1242,plain,
% 1.04/1.23 ((~![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))))),
% 1.04/1.23 inference(quant_inst,[status(thm)],[])).
% 1.04/1.23 tff(1243,plain,
% 1.04/1.23 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | b(s(s(s(s(s(elem!1))))), s(s(elem!1))) | r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[1242, 1241])).
% 1.04/1.23 tff(1244,plain,
% 1.04/1.23 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[1243, 51, 1240, 1233])).
% 1.04/1.23 tff(1245,assumption,(s(s(elem!1)) = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.04/1.23 tff(1246,plain,
% 1.04/1.23 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.04/1.23 inference(symmetry,[status(thm)],[1245])).
% 1.04/1.23 tff(1247,plain,
% 1.04/1.23 ($false),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[560, 1246])).
% 1.04/1.23 tff(1248,plain,((~(s(s(elem!1)) = s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.23 tff(1249,plain,
% 1.04/1.23 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[1248, 560])).
% 1.04/1.23 tff(1250,plain,
% 1.04/1.23 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(1251,plain,
% 1.04/1.23 (((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(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)))))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(1252,plain,
% 1.04/1.23 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 1.04/1.23 inference(monotonicity,[status(thm)],[1251])).
% 1.04/1.23 tff(1253,plain,
% 1.04/1.23 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.04/1.23 inference(transitivity,[status(thm)],[1252, 1250])).
% 1.04/1.23 tff(1254,plain,
% 1.04/1.23 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.04/1.23 inference(quant_inst,[status(thm)],[])).
% 1.04/1.23 tff(1255,plain,
% 1.04/1.23 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[1254, 1253])).
% 1.04/1.23 tff(1256,plain,
% 1.04/1.23 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[1255, 297, 1229, 1117])).
% 1.04/1.23 tff(1257,plain,
% 1.04/1.23 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(1258,plain,
% 1.04/1.23 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.04/1.23 inference(quant_inst,[status(thm)],[])).
% 1.04/1.23 tff(1259,plain,
% 1.04/1.23 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[1258, 1257])).
% 1.04/1.23 tff(1260,plain,
% 1.04/1.23 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[1259, 51, 1256, 1249])).
% 1.04/1.23 tff(1261,plain,
% 1.04/1.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(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(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(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(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(1262,plain,
% 1.04/1.23 (((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), 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(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(1263,plain,
% 1.04/1.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(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(s(elem!1))))), s(s(s(s(elem!1))))))))),
% 1.04/1.23 inference(monotonicity,[status(thm)],[1262])).
% 1.04/1.23 tff(1264,plain,
% 1.04/1.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(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(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.04/1.23 inference(transitivity,[status(thm)],[1263, 1261])).
% 1.04/1.23 tff(1265,plain,
% 1.04/1.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), 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)))))),
% 1.04/1.23 inference(quant_inst,[status(thm)],[])).
% 1.04/1.23 tff(1266,plain,
% 1.04/1.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[1265, 1264])).
% 1.04/1.23 tff(1267,plain,
% 1.04/1.23 ($false),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[1266, 319, 274, 785, 1208, 1260, 1148, 1244])).
% 1.04/1.23 tff(1268,plain,((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~(z = elem!1)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.24 tff(1269,plain,
% 1.04/1.24 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[1268, 1117, 785, 1134, 274, 391, 560, 99, 335, 1])).
% 1.04/1.24 tff(1270,plain,
% 1.04/1.24 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[595, 1269, 1153])).
% 1.04/1.24 tff(1271,assumption,(b(s(s(s(s(s(elem!1))))), s(elem!1))), introduced(assumption)).
% 1.04/1.24 tff(1272,assumption,(b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.04/1.24 tff(1273,plain,
% 1.04/1.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(1274,plain,
% 1.04/1.24 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(1275,plain,
% 1.04/1.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[1274])).
% 1.04/1.24 tff(1276,plain,
% 1.04/1.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.04/1.24 inference(transitivity,[status(thm)],[1275, 1273])).
% 1.04/1.24 tff(1277,plain,
% 1.04/1.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(1278,plain,
% 1.04/1.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[1277, 1276])).
% 1.04/1.24 tff(1279,plain,
% 1.04/1.24 ($false),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[1278, 319, 785, 547, 1272, 1271])).
% 1.04/1.24 tff(1280,plain,((~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.24 tff(1281,plain,
% 1.04/1.24 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[1280, 1270, 785, 1148])).
% 1.04/1.24 tff(1282,assumption,(s(s(s(s(s(elem!1))))) = s(elem!1)), introduced(assumption)).
% 1.04/1.24 tff(1283,plain,
% 1.04/1.24 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(elem!1))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[1282])).
% 1.04/1.24 tff(1284,plain,
% 1.04/1.24 (inj_0(s(elem!1)) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.04/1.24 inference(symmetry,[status(thm)],[1283])).
% 1.04/1.24 tff(1285,plain,
% 1.04/1.24 (elem!1 = s(s(s(s(elem!1))))),
% 1.04/1.24 inference(transitivity,[status(thm)],[258, 1284, 95])).
% 1.04/1.24 tff(1286,plain,
% 1.04/1.24 ($false),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[1185, 1285])).
% 1.04/1.24 tff(1287,plain,((~(s(s(s(s(s(elem!1))))) = s(elem!1))) | (elem!1 = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.24 tff(1288,plain,
% 1.04/1.24 (~(s(s(s(s(s(elem!1))))) = s(elem!1))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[1287, 1160])).
% 1.04/1.24 tff(1289,plain,
% 1.04/1.24 (((~![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)))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(1290,plain,
% 1.04/1.24 ((~![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)))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(1291,plain,
% 1.04/1.24 ((~![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))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[1290, 1289])).
% 1.04/1.24 tff(1292,plain,
% 1.04/1.24 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[1291, 51, 1288, 1281])).
% 1.04/1.24 tff(1293,assumption,(r(s(s(s(s(s(elem!1))))), s(elem!1))), introduced(assumption)).
% 1.04/1.24 tff(1294,plain,
% 1.04/1.24 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(1295,plain,
% 1.04/1.24 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(1296,plain,
% 1.04/1.24 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[1295, 1294])).
% 1.04/1.24 tff(1297,plain,
% 1.04/1.24 ($false),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[1296, 297, 286, 1134, 1293])).
% 1.04/1.24 tff(1298,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,[]))).
% 1.04/1.24 tff(1299,plain,
% 1.04/1.24 (~r(s(elem!1), elem!1)),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[1298, 1292, 1134])).
% 1.04/1.24 tff(1300,plain,
% 1.04/1.24 (b(s(elem!1), elem!1)),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[375, 1299, 1133])).
% 1.04/1.24 tff(1301,plain,
% 1.04/1.24 (b(s(elem!1), z)),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[1176, 1300, 391])).
% 1.04/1.24 tff(1302,plain,
% 1.04/1.24 (~b(z, s(s(elem!1)))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[794, 1301, 1, 785])).
% 1.04/1.24 tff(1303,plain,
% 1.04/1.24 (r(z, s(s(elem!1)))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[56, 1302])).
% 1.04/1.24 tff(1304,plain,
% 1.04/1.24 (r(elem!1, s(s(elem!1)))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[1303, 1128])).
% 1.04/1.24 tff(1305,plain,
% 1.04/1.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(1306,plain,
% 1.04/1.24 (((~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(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(1307,plain,
% 1.04/1.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[1306])).
% 1.04/1.24 tff(1308,plain,
% 1.04/1.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.04/1.24 inference(transitivity,[status(thm)],[1307, 1305])).
% 1.04/1.24 tff(1309,plain,
% 1.04/1.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(1310,plain,
% 1.04/1.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[1309, 1308])).
% 1.04/1.24 tff(1311,plain,
% 1.04/1.24 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[1310, 319, 274, 785, 1270])).
% 1.04/1.24 tff(1312,plain,
% 1.04/1.24 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[571, 1311, 560])).
% 1.04/1.24 tff(1313,plain,
% 1.04/1.24 (~r(elem!1, s(s(elem!1)))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[1206, 1312, 99, 1160, 1163, 335, 1152])).
% 1.04/1.24 tff(1314,plain,
% 1.04/1.24 ($false),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[1313, 1304])).
% 1.04/1.24 tff(1315,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (~(z = elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.24 tff(1316,plain,
% 1.04/1.24 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[1315, 1126, 1, 187, 785, 538, 1117, 971, 219])).
% 1.04/1.24 tff(1317,plain,
% 1.04/1.24 (((~![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))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(1318,plain,
% 1.04/1.24 ((~![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))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(1319,plain,
% 1.04/1.24 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = elem!1) | b(s(s(s(s(s(elem!1))))), elem!1) | r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[1318, 1317])).
% 1.04/1.24 tff(1320,plain,
% 1.04/1.24 ((s(s(s(s(s(elem!1))))) = elem!1) | b(s(s(s(s(s(elem!1))))), elem!1) | r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[1319, 51])).
% 1.04/1.24 tff(1321,plain,
% 1.04/1.24 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[1320, 1316, 1060])).
% 1.04/1.24 tff(1322,plain,
% 1.04/1.24 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[962])).
% 1.04/1.24 tff(1323,plain,
% 1.04/1.24 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.04/1.24 inference(symmetry,[status(thm)],[1322])).
% 1.04/1.24 tff(1324,plain,
% 1.04/1.24 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.04/1.24 inference(commutativity,[status(thm)],[])).
% 1.04/1.24 tff(1325,plain,
% 1.04/1.24 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[937])).
% 1.04/1.24 tff(1326,plain,
% 1.04/1.24 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.04/1.24 inference(transitivity,[status(thm)],[1325, 1324])).
% 1.04/1.24 tff(1327,assumption,(s(s(s(s(elem!1)))) = s(s(s(z)))), introduced(assumption)).
% 1.04/1.24 tff(1328,plain,
% 1.04/1.24 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[1327, 1326])).
% 1.04/1.24 tff(1329,plain,
% 1.04/1.24 ($false),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[538, 1328])).
% 1.04/1.24 tff(1330,plain,((~(s(s(s(s(elem!1)))) = s(s(s(z))))) | (~(s(s(z)) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.24 tff(1331,plain,
% 1.04/1.24 (~(s(s(s(s(elem!1)))) = s(s(s(z))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[1330, 133])).
% 1.04/1.24 tff(1332,plain,
% 1.04/1.24 (r(s(s(s(s(elem!1)))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[937])).
% 1.04/1.24 tff(1333,plain,
% 1.04/1.24 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.04/1.24 inference(symmetry,[status(thm)],[1332])).
% 1.04/1.24 tff(1334,plain,
% 1.04/1.24 ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[1333])).
% 1.04/1.24 tff(1335,assumption,(r(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 1.04/1.24 tff(1336,plain,
% 1.04/1.24 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(1337,plain,
% 1.04/1.24 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(1338,plain,
% 1.04/1.24 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[1337, 1336])).
% 1.04/1.24 tff(1339,plain,
% 1.04/1.24 ($false),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[1338, 297, 335, 984, 1335])).
% 1.04/1.24 tff(1340,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.24 tff(1341,plain,
% 1.04/1.24 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[1340, 1126, 984])).
% 1.04/1.24 tff(1342,plain,
% 1.04/1.24 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[1341, 1334])).
% 1.04/1.24 tff(1343,plain,
% 1.04/1.24 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(z)))) | b(s(s(s(s(elem!1)))), s(s(s(z)))) | r(s(s(s(s(elem!1)))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(z)))) | b(s(s(s(s(elem!1)))), s(s(s(z)))) | r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(1344,plain,
% 1.04/1.24 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(z)))) | b(s(s(s(s(elem!1)))), s(s(s(z)))) | r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(1345,plain,
% 1.04/1.24 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(z)))) | b(s(s(s(s(elem!1)))), s(s(s(z)))) | r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[1344, 1343])).
% 1.04/1.24 tff(1346,plain,
% 1.04/1.24 ((s(s(s(s(elem!1)))) = s(s(s(z)))) | b(s(s(s(s(elem!1)))), s(s(s(z)))) | r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[1345, 51])).
% 1.04/1.24 tff(1347,plain,
% 1.04/1.24 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[1346, 1342, 1331])).
% 1.04/1.24 tff(1348,plain,
% 1.04/1.24 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[1347, 1323])).
% 1.04/1.24 tff(1349,plain,
% 1.04/1.24 ((s(s(s(s(z)))) = s(z)) <=> (s(z) = s(s(s(s(z)))))),
% 1.04/1.24 inference(commutativity,[status(thm)],[])).
% 1.04/1.24 tff(1350,plain,
% 1.04/1.24 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(z))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[961, 216])).
% 1.04/1.24 tff(1351,plain,
% 1.04/1.24 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(z) = s(s(s(s(z)))))),
% 1.04/1.24 inference(transitivity,[status(thm)],[1350, 1349])).
% 1.04/1.24 tff(1352,plain,
% 1.04/1.24 ((s(z) = s(s(s(s(z))))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 1.04/1.24 inference(symmetry,[status(thm)],[1351])).
% 1.04/1.24 tff(1353,assumption,(s(z) = s(s(s(s(z))))), introduced(assumption)).
% 1.04/1.24 tff(1354,plain,
% 1.04/1.24 (s(s(s(s(elem!1)))) = s(elem!1)),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[1353, 1352])).
% 1.04/1.24 tff(1355,plain,
% 1.04/1.24 ($false),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[587, 1354])).
% 1.04/1.24 tff(1356,plain,((~(s(z) = s(s(s(s(z)))))) | (~(s(s(z)) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.24 tff(1357,plain,
% 1.04/1.24 (~(s(z) = s(s(s(s(z)))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[1356, 133])).
% 1.04/1.24 tff(1358,plain,
% 1.04/1.24 (r(s(elem!1), s(s(s(s(elem!1))))) <=> r(s(z), s(s(s(s(z)))))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[216, 961])).
% 1.04/1.24 tff(1359,plain,
% 1.04/1.24 ((~r(s(elem!1), s(s(s(s(elem!1)))))) <=> (~r(s(z), s(s(s(s(z))))))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[1358])).
% 1.04/1.24 tff(1360,plain,
% 1.04/1.24 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(1361,plain,
% 1.04/1.24 (((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(1362,plain,
% 1.04/1.24 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[1361])).
% 1.04/1.24 tff(1363,plain,
% 1.04/1.24 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.04/1.24 inference(transitivity,[status(thm)],[1362, 1360])).
% 1.04/1.24 tff(1364,plain,
% 1.04/1.24 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(1365,plain,
% 1.04/1.24 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1))))))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[1364, 1363])).
% 1.04/1.24 tff(1366,plain,
% 1.04/1.24 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[1365, 297, 286, 1117])).
% 1.04/1.24 tff(1367,plain,
% 1.04/1.24 (~r(s(z), s(s(s(s(z)))))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[1366, 1359])).
% 1.04/1.24 tff(1368,plain,
% 1.04/1.24 (((~![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))))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(1369,plain,
% 1.04/1.24 ((~![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))))))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(1370,plain,
% 1.04/1.24 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[1369, 1368])).
% 1.04/1.24 tff(1371,plain,
% 1.04/1.24 ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[1370, 51])).
% 1.04/1.24 tff(1372,plain,
% 1.04/1.24 (b(s(z), s(s(s(s(z)))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[1371, 1367, 1357])).
% 1.04/1.24 tff(1373,plain,
% 1.04/1.24 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(z)))))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[216, 961])).
% 1.04/1.24 tff(1374,plain,
% 1.04/1.24 (b(s(z), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.04/1.24 inference(symmetry,[status(thm)],[1373])).
% 1.04/1.24 tff(1375,assumption,(b(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 1.04/1.24 tff(1376,plain,
% 1.04/1.24 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[1375, 1374])).
% 1.04/1.24 tff(1377,assumption,(~b(s(elem!1), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.04/1.24 tff(1378,plain,
% 1.04/1.24 ($false),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[1377, 1376])).
% 1.04/1.24 tff(1379,plain,(b(s(elem!1), s(s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~(s(s(z)) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.24 tff(1380,plain,
% 1.04/1.24 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[1379, 1372, 133])).
% 1.04/1.24 tff(1381,plain,
% 1.04/1.24 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[578, 297, 1126, 984])).
% 1.04/1.24 tff(1382,plain,
% 1.04/1.24 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[1381, 1057])).
% 1.04/1.24 tff(1383,plain,
% 1.04/1.24 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[1018, 1382, 968])).
% 1.04/1.24 tff(1384,plain,
% 1.04/1.24 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[1383, 1067])).
% 1.04/1.24 tff(1385,plain,
% 1.04/1.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(1386,plain,
% 1.04/1.24 (((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(1387,plain,
% 1.04/1.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[1386])).
% 1.04/1.24 tff(1388,plain,
% 1.04/1.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.04/1.24 inference(transitivity,[status(thm)],[1387, 1385])).
% 1.04/1.24 tff(1389,plain,
% 1.04/1.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(1390,plain,
% 1.04/1.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[1389, 1388])).
% 1.04/1.24 tff(1391,plain,
% 1.04/1.24 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[1390, 319, 1384, 1380, 1348])).
% 1.04/1.24 tff(1392,plain,
% 1.04/1.24 (r(s(elem!1), s(s(s(elem!1))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[434, 1391, 1114])).
% 1.04/1.24 tff(1393,plain,
% 1.04/1.24 ($false),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[368, 297, 286, 461, 334])).
% 1.04/1.24 tff(1394,plain,((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.24 tff(1395,plain,
% 1.04/1.24 (~r(s(s(s(elem!1))), elem!1)),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[1394, 1392, 286])).
% 1.04/1.24 tff(1396,plain,
% 1.04/1.24 (b(s(s(s(elem!1))), elem!1)),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[361, 1395, 249])).
% 1.04/1.25 tff(1397,plain,
% 1.04/1.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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))))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(1398,plain,
% 1.04/1.25 (((~b(elem!1, s(s(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(elem!1))), elem!1)) | (~b(s(s(s(s(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(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(1399,plain,
% 1.04/1.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(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(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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)))))))),
% 1.04/1.25 inference(monotonicity,[status(thm)],[1398])).
% 1.04/1.25 tff(1400,plain,
% 1.04/1.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(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(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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))))))),
% 1.04/1.25 inference(transitivity,[status(thm)],[1399, 1397])).
% 1.04/1.25 tff(1401,plain,
% 1.04/1.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(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(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
% 1.04/1.25 tff(1402,plain,
% 1.04/1.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[1401, 1400])).
% 1.04/1.25 tff(1403,plain,
% 1.04/1.25 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[1402, 319, 1396, 1124, 1321])).
% 1.04/1.25 tff(1404,assumption,(s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))), introduced(assumption)).
% 1.04/1.25 tff(1405,plain,
% 1.04/1.25 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(elem!1))))),
% 1.04/1.25 inference(monotonicity,[status(thm)],[1404])).
% 1.04/1.25 tff(1406,plain,
% 1.04/1.25 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.04/1.25 inference(transitivity,[status(thm)],[1236, 1405, 83])).
% 1.04/1.25 tff(1407,plain,
% 1.04/1.25 ($false),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[560, 1406])).
% 1.04/1.25 tff(1408,plain,((~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.25 tff(1409,plain,
% 1.04/1.25 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[1408, 971])).
% 1.04/1.25 tff(1410,plain,
% 1.04/1.25 (((~![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)))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(1411,plain,
% 1.04/1.25 ((~![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)))))),
% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
% 1.04/1.25 tff(1412,plain,
% 1.04/1.25 ((~![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))))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[1411, 1410])).
% 1.04/1.25 tff(1413,plain,
% 1.04/1.25 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[1412, 51, 1409, 1403])).
% 1.04/1.25 tff(1414,plain,
% 1.04/1.25 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(1415,plain,
% 1.04/1.25 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
% 1.04/1.25 tff(1416,plain,
% 1.04/1.25 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[1415, 1414])).
% 1.04/1.25 tff(1417,plain,
% 1.04/1.25 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[1416, 297, 1392, 1413])).
% 1.04/1.25 tff(1418,plain,
% 1.04/1.25 (~(s(s(s(s(s(elem!1))))) = s(elem!1))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[1287, 619])).
% 1.04/1.25 tff(1419,plain,
% 1.04/1.25 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[1291, 51, 1418, 1417])).
% 1.04/1.25 tff(1420,plain,
% 1.04/1.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(1421,plain,
% 1.04/1.25 (((~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(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~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))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(1422,plain,
% 1.04/1.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))))),
% 1.04/1.25 inference(monotonicity,[status(thm)],[1421])).
% 1.04/1.25 tff(1423,plain,
% 1.04/1.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.04/1.25 inference(transitivity,[status(thm)],[1422, 1420])).
% 1.04/1.25 tff(1424,plain,
% 1.04/1.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
% 1.04/1.25 tff(1425,plain,
% 1.04/1.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[1424, 1423])).
% 1.04/1.25 tff(1426,plain,
% 1.04/1.25 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[1425, 319, 219, 785, 1419])).
% 1.04/1.25 tff(1427,plain,
% 1.04/1.25 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[1239, 587])).
% 1.04/1.25 tff(1428,plain,
% 1.04/1.25 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[1243, 51, 1427, 1426])).
% 1.04/1.25 tff(1429,plain,
% 1.04/1.25 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(1430,plain,
% 1.04/1.25 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
% 1.04/1.25 tff(1431,plain,
% 1.04/1.25 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[1430, 1429])).
% 1.04/1.25 tff(1432,plain,
% 1.04/1.25 ($false),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[1431, 297, 1126, 1413, 1428])).
% 1.04/1.25 tff(1433,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~(s(s(z)) = s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.25 tff(1434,plain,
% 1.04/1.25 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[1433, 286, 785, 133, 984, 1])).
% 1.04/1.25 tff(1435,plain,
% 1.04/1.25 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[616, 1434, 605])).
% 1.04/1.25 tff(1436,plain,
% 1.04/1.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(1437,plain,
% 1.04/1.25 (((~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(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(1438,plain,
% 1.04/1.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1))))))),
% 1.04/1.25 inference(monotonicity,[status(thm)],[1437])).
% 1.04/1.25 tff(1439,plain,
% 1.04/1.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.04/1.25 inference(transitivity,[status(thm)],[1438, 1436])).
% 1.04/1.25 tff(1440,plain,
% 1.04/1.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))))),
% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
% 1.04/1.25 tff(1441,plain,
% 1.04/1.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1))))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[1440, 1439])).
% 1.04/1.25 tff(1442,plain,
% 1.04/1.25 (~b(elem!1, s(elem!1))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[1441, 319, 219, 785, 1116])).
% 1.04/1.25 tff(1443,plain,
% 1.04/1.25 (r(elem!1, s(elem!1))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[389, 1442, 272])).
% 1.04/1.25 tff(1444,assumption,(b(s(s(s(elem!1))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.04/1.25 tff(1445,assumption,(b(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 1.04/1.25 tff(1446,plain,
% 1.04/1.25 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[178, 176])).
% 1.04/1.25 tff(1447,plain,
% 1.04/1.25 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[580, 547, 99, 274, 1446, 335, 309])).
% 1.04/1.25 tff(1448,plain,
% 1.04/1.25 (r(s(s(s(elem!1))), s(elem!1))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[958, 1447, 176])).
% 1.04/1.25 tff(1449,plain,
% 1.04/1.25 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(elem!1))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(1450,plain,
% 1.04/1.25 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(elem!1))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(1451,plain,
% 1.04/1.25 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(elem!1)))))),
% 1.04/1.25 inference(monotonicity,[status(thm)],[1450])).
% 1.04/1.25 tff(1452,plain,
% 1.04/1.25 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(elem!1))))),
% 1.04/1.25 inference(transitivity,[status(thm)],[1451, 1449])).
% 1.04/1.25 tff(1453,plain,
% 1.04/1.25 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
% 1.04/1.25 tff(1454,plain,
% 1.04/1.25 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(elem!1)))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[1453, 1452])).
% 1.04/1.25 tff(1455,plain,
% 1.04/1.25 (~r(s(s(s(elem!1))), elem!1)),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[1454, 297, 419, 1448])).
% 1.04/1.25 tff(1456,plain,
% 1.04/1.25 (b(s(s(s(elem!1))), elem!1)),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[361, 1455, 512])).
% 1.04/1.25 tff(1457,plain,
% 1.04/1.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(1458,plain,
% 1.04/1.25 (((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(1459,plain,
% 1.04/1.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.04/1.25 inference(monotonicity,[status(thm)],[1458])).
% 1.04/1.25 tff(1460,plain,
% 1.04/1.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.04/1.25 inference(transitivity,[status(thm)],[1459, 1457])).
% 1.04/1.25 tff(1461,plain,
% 1.04/1.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
% 1.04/1.25 tff(1462,plain,
% 1.04/1.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[1461, 1460])).
% 1.04/1.25 tff(1463,plain,
% 1.04/1.25 ($false),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[1462, 319, 785, 1456, 1445, 397, 547, 1444])).
% 1.04/1.25 tff(1464,plain,((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (s(s(s(elem!1))) = elem!1) | (~r(elem!1, s(elem!1))) | (s(s(s(elem!1))) = s(elem!1)) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.25 tff(1465,plain,
% 1.04/1.25 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[1464, 1111, 785, 1435, 1116, 249, 547, 183, 538, 219, 1107, 1443])).
% 1.04/1.25 tff(1466,plain,
% 1.04/1.25 (r(s(elem!1), s(s(s(elem!1))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[434, 1465, 1114])).
% 1.04/1.25 tff(1467,plain,
% 1.04/1.25 (~r(s(s(s(elem!1))), elem!1)),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[1394, 1466, 286])).
% 1.04/1.25 tff(1468,plain,
% 1.04/1.25 (b(s(s(s(elem!1))), elem!1)),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[361, 1467, 249])).
% 1.04/1.25 tff(1469,plain,
% 1.04/1.25 ($false),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[1462, 319, 785, 1468, 1435, 1116, 547, 1111])).
% 1.04/1.25 tff(1470,plain,((~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~(s(s(z)) = s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.25 tff(1471,plain,
% 1.04/1.25 (~b(z, s(s(elem!1)))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[1470, 286, 547, 785, 133, 984, 1, 817])).
% 1.04/1.25 tff(1472,plain,
% 1.04/1.25 (r(z, s(s(elem!1)))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[56, 1471])).
% 1.04/1.25 tff(1473,plain,
% 1.04/1.25 (r(elem!1, s(s(elem!1)))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[70, 1128])).
% 1.04/1.25 tff(1474,assumption,(~r(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.04/1.25 tff(1475,plain,
% 1.04/1.25 ($false),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[1474, 1473])).
% 1.04/1.25 tff(1476,plain,((~r(z, s(s(elem!1)))) | r(elem!1, s(s(elem!1))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.25 tff(1477,plain,
% 1.04/1.25 (r(elem!1, s(s(elem!1)))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[1476, 1472, 187])).
% 1.04/1.25 tff(1478,plain,
% 1.04/1.25 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[1206, 1477, 538, 619, 605, 984, 249])).
% 1.04/1.25 tff(1479,plain,
% 1.04/1.25 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[348, 1478, 232])).
% 1.04/1.25 tff(1480,plain,
% 1.04/1.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(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)))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(1481,plain,
% 1.04/1.26 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(1482,plain,
% 1.04/1.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(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))))))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[1481])).
% 1.04/1.26 tff(1483,plain,
% 1.04/1.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(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)))))),
% 1.04/1.26 inference(transitivity,[status(thm)],[1482, 1480])).
% 1.04/1.26 tff(1484,plain,
% 1.04/1.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(1485,plain,
% 1.04/1.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(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))))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[1484, 1483])).
% 1.04/1.26 tff(1486,plain,
% 1.04/1.26 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[1485, 319, 219, 785, 1479])).
% 1.04/1.26 tff(1487,plain,
% 1.04/1.26 (r(s(elem!1), s(s(s(elem!1))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[434, 1486, 1114])).
% 1.04/1.26 tff(1488,plain,
% 1.04/1.26 (~r(s(s(s(elem!1))), elem!1)),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[1394, 1487, 286])).
% 1.04/1.26 tff(1489,plain,
% 1.04/1.26 (b(s(s(s(elem!1))), elem!1)),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[361, 1488, 249])).
% 1.04/1.26 tff(1490,plain,
% 1.04/1.26 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[1193, 297, 984, 1477])).
% 1.04/1.26 tff(1491,plain,
% 1.04/1.26 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[634, 1490, 619])).
% 1.04/1.26 tff(1492,plain,
% 1.04/1.26 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[101, 538])).
% 1.04/1.26 tff(1493,plain,
% 1.04/1.26 (~(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[107, 1492])).
% 1.04/1.26 tff(1494,plain,
% 1.04/1.26 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[960, 937])).
% 1.04/1.26 tff(1495,plain,
% 1.04/1.26 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(z)))))),
% 1.04/1.26 inference(commutativity,[status(thm)],[])).
% 1.04/1.26 tff(1496,plain,
% 1.04/1.26 ((s(s(s(z))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 1.04/1.26 inference(symmetry,[status(thm)],[1495])).
% 1.04/1.26 tff(1497,plain,
% 1.04/1.26 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 1.04/1.26 inference(transitivity,[status(thm)],[966, 1496])).
% 1.04/1.26 tff(1498,plain,
% 1.04/1.26 ((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(z)))) = s(s(s(z)))))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[1497])).
% 1.04/1.26 tff(1499,plain,
% 1.04/1.26 (~(s(s(s(s(z)))) = s(s(s(z))))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[538, 1498])).
% 1.04/1.26 tff(1500,plain,
% 1.04/1.26 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[960])).
% 1.04/1.26 tff(1501,plain,
% 1.04/1.26 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.04/1.26 inference(symmetry,[status(thm)],[1500])).
% 1.04/1.26 tff(1502,plain,
% 1.04/1.26 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.04/1.26 inference(transitivity,[status(thm)],[1322, 1501])).
% 1.04/1.26 tff(1503,plain,
% 1.04/1.26 ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[1502])).
% 1.04/1.26 tff(1504,assumption,(b(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 1.04/1.26 tff(1505,assumption,(b(elem!1, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.04/1.26 tff(1506,plain,
% 1.04/1.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(1507,plain,
% 1.04/1.26 (((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(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(elem!1)))), s(s(s(elem!1))))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(1508,plain,
% 1.04/1.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[1507])).
% 1.04/1.26 tff(1509,plain,
% 1.04/1.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.04/1.26 inference(transitivity,[status(thm)],[1508, 1506])).
% 1.04/1.26 tff(1510,plain,
% 1.04/1.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(1511,plain,
% 1.04/1.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[1510, 1509])).
% 1.04/1.26 tff(1512,plain,
% 1.04/1.26 ($false),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[1511, 319, 1505, 448, 1445, 1504])).
% 1.04/1.26 tff(1513,plain,((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.26 tff(1514,plain,
% 1.04/1.26 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[1513, 1489, 1435, 1491])).
% 1.04/1.26 tff(1515,plain,
% 1.04/1.26 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[1514, 1503])).
% 1.04/1.26 tff(1516,plain,
% 1.04/1.26 (((~![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)))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(1517,plain,
% 1.04/1.26 ((~![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)))))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(1518,plain,
% 1.04/1.26 ((~![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))))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[1517, 1516])).
% 1.04/1.26 tff(1519,plain,
% 1.04/1.26 ((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))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[1518, 51])).
% 1.04/1.26 tff(1520,plain,
% 1.04/1.26 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[1519, 1515, 1499])).
% 1.04/1.26 tff(1521,plain,
% 1.04/1.26 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[1520, 1494])).
% 1.04/1.26 tff(1522,assumption,(~(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.04/1.26 tff(1523,assumption,(b(s(s(s(s(s(elem!1))))), elem!1)), introduced(assumption)).
% 1.04/1.26 tff(1524,plain,
% 1.04/1.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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)))))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(1525,plain,
% 1.04/1.26 (((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))) <=> ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(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)))))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(1526,plain,
% 1.04/1.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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))))))))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[1525])).
% 1.04/1.26 tff(1527,plain,
% 1.04/1.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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)))))))),
% 1.04/1.26 inference(transitivity,[status(thm)],[1526, 1524])).
% 1.04/1.26 tff(1528,plain,
% 1.04/1.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), 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)))))))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(1529,plain,
% 1.04/1.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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))))))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[1528, 1527])).
% 1.04/1.26 tff(1530,plain,
% 1.04/1.26 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[1529, 319, 1505, 1445, 1523])).
% 1.04/1.26 tff(1531,plain,
% 1.04/1.26 (r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[1146, 51, 1530, 1522])).
% 1.04/1.26 tff(1532,plain,
% 1.04/1.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(1533,plain,
% 1.04/1.26 (((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(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)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(1534,plain,
% 1.04/1.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[1533])).
% 1.04/1.26 tff(1535,plain,
% 1.04/1.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.04/1.26 inference(transitivity,[status(thm)],[1534, 1532])).
% 1.04/1.26 tff(1536,plain,
% 1.04/1.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(1537,plain,
% 1.04/1.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[1536, 1535])).
% 1.04/1.26 tff(1538,plain,
% 1.04/1.26 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[1537, 319, 1505, 448, 1523])).
% 1.04/1.26 tff(1539,assumption,(~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))), introduced(assumption)).
% 1.04/1.26 tff(1540,plain,
% 1.04/1.26 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[1412, 51, 1539, 1538])).
% 1.04/1.26 tff(1541,plain,
% 1.04/1.26 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(1542,plain,
% 1.04/1.26 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(1543,plain,
% 1.04/1.26 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[1542, 1541])).
% 1.04/1.26 tff(1544,plain,
% 1.04/1.26 ($false),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[1543, 297, 1335, 1540, 1531])).
% 1.04/1.26 tff(1545,plain,((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))) | (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(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.26 tff(1546,plain,
% 1.04/1.26 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[1545, 1521, 1493, 1409, 1491, 1435, 1489])).
% 1.04/1.26 tff(1547,plain,
% 1.04/1.26 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[1320, 1546, 1060])).
% 1.04/1.26 tff(1548,plain,
% 1.04/1.26 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[133])).
% 1.04/1.26 tff(1549,plain,
% 1.04/1.26 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 1.04/1.26 inference(symmetry,[status(thm)],[1548])).
% 1.04/1.26 tff(1550,plain,
% 1.04/1.26 ((~r(s(s(elem!1)), s(s(s(elem!1))))) <=> (~r(s(s(z)), s(s(s(elem!1)))))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[1549])).
% 1.04/1.26 tff(1551,plain,
% 1.04/1.26 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[1248, 971])).
% 1.04/1.26 tff(1552,plain,
% 1.04/1.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(1553,plain,
% 1.04/1.26 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(1554,plain,
% 1.04/1.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[1553])).
% 1.04/1.26 tff(1555,plain,
% 1.04/1.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.04/1.26 inference(transitivity,[status(thm)],[1554, 1552])).
% 1.04/1.26 tff(1556,plain,
% 1.04/1.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(1557,plain,
% 1.04/1.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[1556, 1555])).
% 1.04/1.26 tff(1558,plain,
% 1.04/1.26 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[1557, 319, 219, 785, 547])).
% 1.04/1.26 tff(1559,plain,
% 1.04/1.26 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[1259, 51, 1558, 1551])).
% 1.04/1.26 tff(1560,assumption,(r(s(s(elem!1)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.04/1.26 tff(1561,plain,
% 1.04/1.26 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(1562,plain,
% 1.04/1.26 (((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(1563,plain,
% 1.04/1.27 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[1562])).
% 1.04/1.27 tff(1564,plain,
% 1.04/1.27 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.04/1.27 inference(transitivity,[status(thm)],[1563, 1561])).
% 1.04/1.27 tff(1565,plain,
% 1.04/1.27 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(1566,plain,
% 1.04/1.27 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[1565, 1564])).
% 1.04/1.27 tff(1567,plain,
% 1.04/1.27 ($false),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1566, 297, 460, 1335, 1560])).
% 1.04/1.27 tff(1568,plain,((~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))))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.27 tff(1569,plain,
% 1.04/1.27 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1568, 1559, 1521])).
% 1.04/1.27 tff(1570,plain,
% 1.04/1.27 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[1569, 1550])).
% 1.04/1.27 tff(1571,plain,
% 1.04/1.27 (b(s(s(z)), s(s(s(elem!1)))) | r(s(s(z)), s(s(s(elem!1))))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[476, 231])).
% 1.04/1.27 tff(1572,plain,
% 1.04/1.27 (b(s(s(z)), s(s(s(elem!1))))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1571, 1570])).
% 1.04/1.27 tff(1573,plain,
% 1.04/1.27 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[1572, 437])).
% 1.04/1.27 tff(1574,plain,
% 1.04/1.27 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.04/1.27 inference(symmetry,[status(thm)],[1065])).
% 1.04/1.27 tff(1575,plain,
% 1.04/1.27 ((~r(elem!1, s(s(s(elem!1))))) <=> (~r(z, s(s(s(elem!1)))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[1063])).
% 1.04/1.27 tff(1576,plain,
% 1.04/1.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(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(s(elem!1))), s(s(elem!1)))))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(1577,plain,
% 1.04/1.27 (((~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(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(s(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(s(elem!1))), s(s(elem!1)))))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(1578,plain,
% 1.04/1.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(elem!1))), s(s(elem!1))))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[1577])).
% 1.04/1.27 tff(1579,plain,
% 1.04/1.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(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(s(elem!1))), s(s(elem!1)))))),
% 1.04/1.27 inference(transitivity,[status(thm)],[1578, 1576])).
% 1.04/1.27 tff(1580,plain,
% 1.04/1.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(1581,plain,
% 1.04/1.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(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(s(elem!1))), s(s(elem!1))))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[1580, 1579])).
% 1.04/1.27 tff(1582,plain,
% 1.04/1.27 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1581, 319, 219, 785, 1479])).
% 1.04/1.27 tff(1583,plain,
% 1.04/1.27 (r(s(s(s(elem!1))), s(elem!1))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[958, 1582, 183])).
% 1.04/1.27 tff(1584,plain,
% 1.04/1.27 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1201, 319, 1491, 1489, 1435])).
% 1.04/1.27 tff(1585,plain,
% 1.04/1.27 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[1584, 970])).
% 1.04/1.27 tff(1586,plain,
% 1.04/1.27 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1018, 1585, 968])).
% 1.04/1.27 tff(1587,plain,
% 1.04/1.27 (r(s(z), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.04/1.27 inference(symmetry,[status(thm)],[1358])).
% 1.04/1.27 tff(1588,assumption,(r(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 1.04/1.27 tff(1589,plain,
% 1.04/1.27 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[1588, 1587])).
% 1.04/1.27 tff(1590,assumption,(r(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 1.04/1.27 tff(1591,plain,
% 1.04/1.27 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[1590, 964])).
% 1.04/1.27 tff(1592,plain,
% 1.04/1.27 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(1593,plain,
% 1.04/1.27 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(elem!1)))))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(1594,plain,
% 1.04/1.27 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[1593])).
% 1.04/1.27 tff(1595,plain,
% 1.04/1.27 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.04/1.27 inference(transitivity,[status(thm)],[1594, 1592])).
% 1.04/1.27 tff(1596,plain,
% 1.04/1.27 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(1597,plain,
% 1.04/1.27 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[1596, 1595])).
% 1.04/1.27 tff(1598,plain,
% 1.04/1.27 ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1597, 297, 334])).
% 1.04/1.27 tff(1599,plain,
% 1.04/1.27 ($false),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1598, 1591, 1589])).
% 1.04/1.27 tff(1600,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~(s(s(z)) = s(s(elem!1)))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.27 tff(1601,plain,
% 1.04/1.27 (~r(s(z), s(s(s(s(z)))))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1600, 1586, 133, 1487])).
% 1.04/1.27 tff(1602,plain,
% 1.04/1.27 (b(s(z), s(s(s(s(z)))))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1371, 1601, 1357])).
% 1.04/1.27 tff(1603,plain,
% 1.04/1.27 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1379, 1602, 133])).
% 1.04/1.27 tff(1604,plain,
% 1.04/1.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(1605,plain,
% 1.04/1.27 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(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(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(1606,plain,
% 1.04/1.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[1605])).
% 1.04/1.27 tff(1607,plain,
% 1.04/1.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.04/1.27 inference(transitivity,[status(thm)],[1606, 1604])).
% 1.04/1.27 tff(1608,plain,
% 1.04/1.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))))),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(1609,plain,
% 1.04/1.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[1608, 1607])).
% 1.04/1.27 tff(1610,plain,
% 1.04/1.27 (~b(elem!1, s(elem!1))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1609, 319, 1491, 1435, 1603])).
% 1.04/1.27 tff(1611,plain,
% 1.04/1.27 (r(elem!1, s(elem!1))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[389, 1610, 272])).
% 1.04/1.27 tff(1612,plain,
% 1.04/1.27 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(1613,plain,
% 1.04/1.27 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(1614,plain,
% 1.04/1.27 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1)))))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[1613, 1612])).
% 1.04/1.27 tff(1615,plain,
% 1.04/1.27 (~r(elem!1, s(s(s(elem!1))))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1614, 297, 1611, 1583])).
% 1.04/1.27 tff(1616,plain,
% 1.04/1.27 (~r(z, s(s(s(elem!1))))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[1615, 1575])).
% 1.04/1.27 tff(1617,plain,
% 1.04/1.27 (b(z, s(s(s(elem!1))))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[416, 1616])).
% 1.04/1.27 tff(1618,plain,
% 1.04/1.27 (b(elem!1, s(s(s(elem!1))))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[1617, 1574])).
% 1.04/1.27 tff(1619,plain,
% 1.04/1.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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(elem!1)), s(s(s(elem!1))))))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(1620,plain,
% 1.04/1.27 (((~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(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(1621,plain,
% 1.04/1.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1)), s(s(s(elem!1))))) | (~b(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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(elem!1)), s(s(s(elem!1)))))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[1620])).
% 1.04/1.27 tff(1622,plain,
% 1.04/1.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1)), s(s(s(elem!1))))) | (~b(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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(elem!1)), s(s(s(elem!1))))))),
% 1.04/1.27 inference(transitivity,[status(thm)],[1621, 1619])).
% 1.04/1.27 tff(1623,plain,
% 1.04/1.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(1624,plain,
% 1.04/1.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[1623, 1622])).
% 1.04/1.27 tff(1625,plain,
% 1.04/1.27 (~b(s(s(elem!1)), elem!1)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1624, 319, 1489, 1618, 1573])).
% 1.04/1.27 tff(1626,plain,
% 1.04/1.27 (~b(s(s(elem!1)), z)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[500, 1625, 187])).
% 1.04/1.27 tff(1627,plain,
% 1.04/1.27 (r(s(s(elem!1)), z)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[75, 1626])).
% 1.04/1.27 tff(1628,plain,
% 1.04/1.27 (r(s(s(elem!1)), elem!1)),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[1627, 440])).
% 1.04/1.27 tff(1629,plain,
% 1.04/1.27 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1232, 297, 1628, 1547])).
% 1.04/1.27 tff(1630,plain,
% 1.04/1.27 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1243, 51, 1427, 1629])).
% 1.04/1.27 tff(1631,plain,
% 1.04/1.27 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1298, 1547, 286])).
% 1.04/1.27 tff(1632,plain,
% 1.04/1.27 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1291, 51, 1418, 1631])).
% 1.04/1.27 tff(1633,plain,
% 1.04/1.27 ($false),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1425, 319, 219, 785, 1632, 1630])).
% 1.04/1.27 tff(1634,plain,((~r(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~(s(s(z)) = s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.27 tff(1635,plain,
% 1.04/1.27 (~r(s(elem!1), elem!1)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1634, 547, 133, 785, 984, 1, 817])).
% 1.04/1.27 tff(1636,plain,
% 1.04/1.27 (b(s(elem!1), elem!1)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[375, 1635, 194])).
% 1.04/1.27 tff(1637,plain,
% 1.04/1.27 (b(s(elem!1), z)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1176, 1636, 187])).
% 1.04/1.27 tff(1638,plain,
% 1.04/1.27 (~b(z, s(s(elem!1)))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[794, 1637, 1, 785])).
% 1.04/1.27 tff(1639,plain,
% 1.04/1.27 (r(z, s(s(elem!1)))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[56, 1638])).
% 1.04/1.27 tff(1640,plain,
% 1.04/1.27 (r(elem!1, s(s(elem!1)))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1476, 1639, 187])).
% 1.04/1.27 tff(1641,plain,
% 1.04/1.27 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1119, 1640, 984])).
% 1.04/1.27 tff(1642,plain,
% 1.04/1.27 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[616, 1641, 605])).
% 1.04/1.27 tff(1643,plain,
% 1.04/1.27 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1193, 297, 984, 1640])).
% 1.04/1.27 tff(1644,plain,
% 1.04/1.27 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[634, 1643, 619])).
% 1.04/1.27 tff(1645,plain,
% 1.04/1.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(1646,plain,
% 1.04/1.27 (((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(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(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(1647,plain,
% 1.04/1.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[1646])).
% 1.04/1.27 tff(1648,plain,
% 1.04/1.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.04/1.27 inference(transitivity,[status(thm)],[1647, 1645])).
% 1.04/1.27 tff(1649,plain,
% 1.04/1.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(1650,plain,
% 1.04/1.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[1649, 1648])).
% 1.04/1.27 tff(1651,plain,
% 1.04/1.27 ($false),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1650, 319, 1636, 1644, 1642, 547])).
% 1.04/1.27 tff(1652,plain,((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~(s(s(z)) = s(s(elem!1)))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.27 tff(1653,plain,
% 1.04/1.27 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1652, 984, 1, 785, 133, 817])).
% 1.04/1.27 tff(1654,plain,
% 1.04/1.27 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[595, 1653, 587])).
% 1.04/1.27 tff(1655,plain,
% 1.04/1.27 (b(s(elem!1), z)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1176, 449, 187])).
% 1.04/1.27 tff(1656,plain,
% 1.04/1.27 (~b(z, s(s(elem!1)))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[794, 1655, 1, 785])).
% 1.04/1.27 tff(1657,plain,
% 1.04/1.27 (r(z, s(s(elem!1)))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[56, 1656])).
% 1.04/1.27 tff(1658,plain,
% 1.04/1.27 (r(elem!1, s(s(elem!1)))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1476, 1657, 187])).
% 1.04/1.27 tff(1659,plain,
% 1.04/1.27 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1119, 1658, 984])).
% 1.04/1.27 tff(1660,plain,
% 1.04/1.27 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[616, 1659, 605])).
% 1.04/1.27 tff(1661,plain,
% 1.04/1.27 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1206, 1658, 538, 619, 605, 984, 249])).
% 1.04/1.27 tff(1662,plain,
% 1.04/1.27 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[348, 1661, 232])).
% 1.04/1.27 tff(1663,plain,
% 1.04/1.27 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1485, 319, 219, 785, 1662])).
% 1.04/1.27 tff(1664,plain,
% 1.04/1.27 (r(s(elem!1), s(s(s(elem!1))))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[434, 1663, 1114])).
% 1.04/1.27 tff(1665,plain,
% 1.04/1.27 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1193, 297, 984, 1658])).
% 1.04/1.27 tff(1666,plain,
% 1.04/1.27 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[634, 1665, 619])).
% 1.04/1.27 tff(1667,plain,
% 1.04/1.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(1668,plain,
% 1.04/1.27 (((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(1669,plain,
% 1.04/1.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[1668])).
% 1.04/1.27 tff(1670,plain,
% 1.04/1.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.04/1.27 inference(transitivity,[status(thm)],[1669, 1667])).
% 1.04/1.27 tff(1671,plain,
% 1.04/1.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(1672,plain,
% 1.04/1.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[1671, 1670])).
% 1.04/1.28 tff(1673,plain,
% 1.04/1.28 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1672, 319, 449, 1666, 1660])).
% 1.04/1.28 tff(1674,plain,
% 1.04/1.28 (~b(s(z), s(s(s(s(z)))))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1379, 1673, 133])).
% 1.04/1.28 tff(1675,plain,
% 1.04/1.28 (r(s(z), s(s(s(s(z)))))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1371, 1674, 1357])).
% 1.04/1.28 tff(1676,plain,
% 1.04/1.28 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1600, 1675, 133, 1664])).
% 1.04/1.28 tff(1677,plain,
% 1.04/1.28 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1018, 1676, 968])).
% 1.04/1.28 tff(1678,plain,
% 1.04/1.28 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[1677, 1067])).
% 1.04/1.28 tff(1679,plain,
% 1.04/1.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(1680,plain,
% 1.04/1.28 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(1681,plain,
% 1.04/1.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[1680])).
% 1.04/1.28 tff(1682,plain,
% 1.04/1.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.04/1.28 inference(transitivity,[status(thm)],[1681, 1679])).
% 1.04/1.28 tff(1683,plain,
% 1.04/1.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.04/1.28 inference(quant_inst,[status(thm)],[])).
% 1.04/1.28 tff(1684,plain,
% 1.04/1.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[1683, 1682])).
% 1.04/1.28 tff(1685,plain,
% 1.04/1.28 (~b(elem!1, s(s(s(elem!1))))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1684, 319, 1666, 1660, 1678])).
% 1.04/1.28 tff(1686,plain,
% 1.04/1.28 (~b(z, s(s(s(elem!1))))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[1685, 1066])).
% 1.04/1.28 tff(1687,plain,
% 1.04/1.28 (r(z, s(s(s(elem!1))))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[416, 1686])).
% 1.04/1.28 tff(1688,plain,
% 1.04/1.28 (r(elem!1, s(s(s(elem!1))))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[1687, 1064])).
% 1.04/1.28 tff(1689,plain,
% 1.04/1.28 (~r(elem!1, s(elem!1))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[425, 297, 1664, 1688])).
% 1.04/1.28 tff(1690,plain,
% 1.04/1.28 (b(elem!1, s(elem!1))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[389, 1689, 272])).
% 1.04/1.28 tff(1691,plain,
% 1.04/1.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(1692,plain,
% 1.04/1.28 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))) <=> ((~b(elem!1, s(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)))))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(1693,plain,
% 1.04/1.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[1692])).
% 1.04/1.28 tff(1694,plain,
% 1.04/1.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.04/1.28 inference(transitivity,[status(thm)],[1693, 1691])).
% 1.04/1.28 tff(1695,plain,
% 1.04/1.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), 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)))))))),
% 1.04/1.28 inference(quant_inst,[status(thm)],[])).
% 1.04/1.28 tff(1696,plain,
% 1.04/1.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[1695, 1694])).
% 1.04/1.28 tff(1697,plain,
% 1.04/1.28 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1696, 319, 275, 1445, 1523])).
% 1.04/1.28 tff(1698,plain,
% 1.04/1.28 (r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1146, 51, 1697, 1522])).
% 1.04/1.28 tff(1699,plain,
% 1.04/1.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(1700,plain,
% 1.04/1.28 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(1701,plain,
% 1.04/1.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[1700])).
% 1.04/1.28 tff(1702,plain,
% 1.04/1.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.04/1.28 inference(transitivity,[status(thm)],[1701, 1699])).
% 1.04/1.28 tff(1703,plain,
% 1.04/1.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.04/1.28 inference(quant_inst,[status(thm)],[])).
% 1.04/1.28 tff(1704,plain,
% 1.04/1.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[1703, 1702])).
% 1.04/1.28 tff(1705,plain,
% 1.04/1.28 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1704, 319, 275, 449, 1523])).
% 1.04/1.28 tff(1706,assumption,(~(s(s(s(s(s(elem!1))))) = s(elem!1))), introduced(assumption)).
% 1.04/1.28 tff(1707,plain,
% 1.04/1.28 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1291, 51, 1706, 1705])).
% 1.04/1.28 tff(1708,plain,
% 1.04/1.28 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(1709,plain,
% 1.04/1.28 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.04/1.28 inference(quant_inst,[status(thm)],[])).
% 1.04/1.28 tff(1710,plain,
% 1.04/1.28 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[1709, 1708])).
% 1.04/1.28 tff(1711,plain,
% 1.04/1.28 ($false),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1710, 297, 620, 1707, 1698])).
% 1.04/1.28 tff(1712,plain,((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))) | (s(s(s(s(s(elem!1))))) = s(elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.28 tff(1713,plain,
% 1.04/1.28 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1712, 1690, 1493, 1418, 620, 1660, 449])).
% 1.04/1.28 tff(1714,plain,
% 1.04/1.28 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1320, 1713, 1060])).
% 1.04/1.28 tff(1715,plain,
% 1.04/1.28 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(1716,plain,
% 1.04/1.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[1715])).
% 1.04/1.28 tff(1717,plain,
% 1.04/1.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.04/1.28 inference(transitivity,[status(thm)],[1716, 1196])).
% 1.04/1.28 tff(1718,plain,
% 1.04/1.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.04/1.28 inference(quant_inst,[status(thm)],[])).
% 1.04/1.28 tff(1719,plain,
% 1.04/1.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[1718, 1717])).
% 1.04/1.28 tff(1720,plain,
% 1.04/1.28 (~b(s(s(s(elem!1))), elem!1)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1719, 319, 1666, 1660, 1678])).
% 1.04/1.28 tff(1721,plain,
% 1.04/1.28 (r(s(s(s(elem!1))), elem!1)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[361, 1720, 249])).
% 1.04/1.28 tff(1722,plain,
% 1.04/1.28 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(1723,plain,
% 1.04/1.28 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.04/1.28 inference(quant_inst,[status(thm)],[])).
% 1.04/1.28 tff(1724,plain,
% 1.04/1.28 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[1723, 1722])).
% 1.04/1.28 tff(1725,plain,
% 1.04/1.28 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1724, 297, 1721, 1714])).
% 1.04/1.28 tff(1726,plain,
% 1.04/1.28 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1412, 51, 1409, 1725])).
% 1.04/1.28 tff(1727,plain,
% 1.04/1.28 (~b(s(s(elem!1)), elem!1)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1217, 1690, 785, 219])).
% 1.04/1.28 tff(1728,plain,
% 1.04/1.28 (~b(s(s(elem!1)), z)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[500, 1727, 187])).
% 1.04/1.28 tff(1729,plain,
% 1.04/1.28 (r(s(s(elem!1)), z)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[75, 1728])).
% 1.04/1.28 tff(1730,plain,
% 1.04/1.28 (r(s(s(elem!1)), elem!1)),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[1729, 440])).
% 1.04/1.28 tff(1731,plain,
% 1.04/1.28 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1232, 297, 1730, 1714])).
% 1.04/1.28 tff(1732,plain,
% 1.04/1.28 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1243, 51, 1427, 1731])).
% 1.04/1.28 tff(1733,plain,
% 1.04/1.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), 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))))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(1734,plain,
% 1.04/1.28 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(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)))))) <=> ((~b(s(s(elem!1)), 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))))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(1735,plain,
% 1.04/1.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), 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)))))))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[1734])).
% 1.04/1.28 tff(1736,plain,
% 1.04/1.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), 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))))))),
% 1.04/1.28 inference(transitivity,[status(thm)],[1735, 1733])).
% 1.04/1.28 tff(1737,plain,
% 1.04/1.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(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))))))),
% 1.04/1.28 inference(quant_inst,[status(thm)],[])).
% 1.04/1.28 tff(1738,plain,
% 1.04/1.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[1737, 1736])).
% 1.04/1.28 tff(1739,plain,
% 1.04/1.28 ($false),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1738, 319, 219, 1662, 1732, 1726])).
% 1.04/1.28 tff(1740,plain,((~b(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~(s(s(z)) = s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.28 tff(1741,plain,
% 1.04/1.28 (~b(s(elem!1), elem!1)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1740, 1654, 785, 133, 984, 1])).
% 1.04/1.28 tff(1742,plain,
% 1.04/1.28 (r(s(elem!1), elem!1)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[375, 1741, 194])).
% 1.04/1.28 tff(1743,plain,
% 1.04/1.28 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1433, 1742, 785, 133, 984, 1])).
% 1.04/1.28 tff(1744,plain,
% 1.04/1.28 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[616, 1743, 605])).
% 1.04/1.28 tff(1745,plain,
% 1.04/1.28 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[629, 1443, 1654])).
% 1.04/1.28 tff(1746,plain,
% 1.04/1.28 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[634, 1745, 619])).
% 1.04/1.28 tff(1747,plain,
% 1.04/1.28 (~b(elem!1, s(s(s(elem!1))))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1684, 319, 1746, 1744, 1111])).
% 1.04/1.28 tff(1748,plain,
% 1.04/1.28 (~b(z, s(s(s(elem!1))))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[1747, 1066])).
% 1.04/1.28 tff(1749,plain,
% 1.04/1.28 (r(z, s(s(s(elem!1))))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[416, 1748])).
% 1.04/1.28 tff(1750,plain,
% 1.04/1.28 (r(elem!1, s(s(s(elem!1))))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[1749, 1064])).
% 1.04/1.28 tff(1751,plain,
% 1.04/1.28 ((~b(s(s(elem!1)), s(s(s(elem!1))))) <=> (~b(s(s(z)), s(s(s(elem!1)))))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[436])).
% 1.04/1.28 tff(1752,plain,
% 1.04/1.28 (~b(s(s(s(elem!1))), elem!1)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1719, 319, 1746, 1744, 1111])).
% 1.04/1.28 tff(1753,plain,
% 1.04/1.28 (r(s(s(s(elem!1))), elem!1)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[361, 1752, 249])).
% 1.04/1.28 tff(1754,plain,
% 1.04/1.28 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[517, 297, 1742, 1753])).
% 1.04/1.28 tff(1755,plain,
% 1.04/1.28 (b(s(s(s(elem!1))), s(elem!1))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[958, 1754, 183])).
% 1.04/1.28 tff(1756,plain,
% 1.04/1.28 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1394, 1753, 1742])).
% 1.04/1.28 tff(1757,plain,
% 1.04/1.28 (b(s(elem!1), s(s(s(elem!1))))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[434, 1756, 1114])).
% 1.04/1.28 tff(1758,plain,
% 1.04/1.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(1759,plain,
% 1.04/1.29 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), 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))))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(1760,plain,
% 1.04/1.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[1759])).
% 1.04/1.29 tff(1761,plain,
% 1.04/1.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.04/1.29 inference(transitivity,[status(thm)],[1760, 1758])).
% 1.04/1.29 tff(1762,plain,
% 1.04/1.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.04/1.29 inference(quant_inst,[status(thm)],[])).
% 1.04/1.29 tff(1763,plain,
% 1.04/1.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[1762, 1761])).
% 1.04/1.29 tff(1764,plain,
% 1.04/1.29 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1763, 319, 1757, 1755, 219])).
% 1.04/1.29 tff(1765,plain,
% 1.04/1.29 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[1764, 1751])).
% 1.04/1.29 tff(1766,plain,
% 1.04/1.29 (r(s(s(z)), s(s(s(elem!1))))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1571, 1765])).
% 1.04/1.29 tff(1767,plain,
% 1.04/1.29 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[1766, 1548])).
% 1.04/1.29 tff(1768,plain,
% 1.04/1.29 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(1769,plain,
% 1.04/1.29 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(1770,plain,
% 1.04/1.29 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1)))))))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[1769])).
% 1.04/1.29 tff(1771,plain,
% 1.04/1.29 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.04/1.29 inference(transitivity,[status(thm)],[1770, 1768])).
% 1.04/1.29 tff(1772,plain,
% 1.04/1.29 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))),
% 1.04/1.29 inference(quant_inst,[status(thm)],[])).
% 1.04/1.29 tff(1773,plain,
% 1.04/1.29 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1)))))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[1772, 1771])).
% 1.04/1.29 tff(1774,plain,
% 1.04/1.29 (~r(s(s(elem!1)), elem!1)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1773, 297, 1767, 1750])).
% 1.04/1.29 tff(1775,plain,
% 1.04/1.29 (~r(s(s(elem!1)), z)),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[1774, 1062])).
% 1.04/1.29 tff(1776,plain,
% 1.04/1.29 (b(s(s(elem!1)), z)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[75, 1775])).
% 1.04/1.29 tff(1777,plain,
% 1.04/1.29 (b(s(s(elem!1)), elem!1)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[500, 1776, 187])).
% 1.04/1.29 tff(1778,plain,
% 1.04/1.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(1779,plain,
% 1.04/1.29 (((~b(elem!1, s(s(s(s(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(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(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)))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(1780,plain,
% 1.04/1.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[1779])).
% 1.04/1.29 tff(1781,plain,
% 1.04/1.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.04/1.29 inference(transitivity,[status(thm)],[1780, 1778])).
% 1.04/1.29 tff(1782,plain,
% 1.04/1.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.04/1.29 inference(quant_inst,[status(thm)],[])).
% 1.04/1.29 tff(1783,plain,
% 1.04/1.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[1782, 1781])).
% 1.04/1.29 tff(1784,plain,
% 1.04/1.29 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1783, 319, 1505, 308, 1523])).
% 1.04/1.29 tff(1785,assumption,(~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))), introduced(assumption)).
% 1.04/1.29 tff(1786,plain,
% 1.04/1.29 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1243, 51, 1785, 1784])).
% 1.04/1.29 tff(1787,plain,
% 1.04/1.29 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(1788,plain,
% 1.04/1.29 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.04/1.29 inference(quant_inst,[status(thm)],[])).
% 1.04/1.29 tff(1789,plain,
% 1.04/1.29 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[1788, 1787])).
% 1.04/1.29 tff(1790,plain,
% 1.04/1.29 ($false),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1789, 297, 984, 1786, 1531])).
% 1.04/1.29 tff(1791,plain,((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.29 tff(1792,plain,
% 1.04/1.29 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1791, 1746, 1493, 1427, 984, 1744, 1777])).
% 1.04/1.29 tff(1793,plain,
% 1.04/1.29 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1320, 1792, 1060])).
% 1.04/1.29 tff(1794,plain,
% 1.04/1.29 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1724, 297, 1753, 1793])).
% 1.04/1.29 tff(1795,plain,
% 1.04/1.29 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1412, 51, 1409, 1794])).
% 1.04/1.29 tff(1796,plain,
% 1.04/1.29 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1298, 1793, 1742])).
% 1.04/1.29 tff(1797,plain,
% 1.04/1.29 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1291, 51, 1418, 1796])).
% 1.04/1.29 tff(1798,plain,
% 1.04/1.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(1799,plain,
% 1.04/1.29 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(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(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))))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(1800,plain,
% 1.04/1.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(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(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)))))))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[1799])).
% 1.04/1.29 tff(1801,plain,
% 1.04/1.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(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(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))))))),
% 1.04/1.29 inference(transitivity,[status(thm)],[1800, 1798])).
% 1.04/1.29 tff(1802,plain,
% 1.04/1.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(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(s(elem!1))))))),
% 1.04/1.29 inference(quant_inst,[status(thm)],[])).
% 1.04/1.29 tff(1803,plain,
% 1.04/1.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[1802, 1801])).
% 1.04/1.29 tff(1804,plain,
% 1.04/1.29 ($false),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1803, 319, 1757, 1755, 1797, 1795])).
% 1.04/1.29 tff(1805,plain,((~b(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~(s(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))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.29 tff(1806,plain,
% 1.04/1.29 (~b(z, s(s(elem!1)))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1805, 984, 133, 785, 1, 817])).
% 1.04/1.29 tff(1807,plain,
% 1.04/1.29 (r(z, s(s(elem!1)))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[56, 1806])).
% 1.04/1.29 tff(1808,plain,
% 1.04/1.29 (r(elem!1, s(s(elem!1)))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1476, 1807, 187])).
% 1.04/1.29 tff(1809,plain,
% 1.04/1.29 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1206, 1808, 538, 619, 605, 984, 249])).
% 1.04/1.29 tff(1810,plain,
% 1.04/1.29 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[348, 1809, 232])).
% 1.04/1.29 tff(1811,plain,
% 1.04/1.29 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1581, 319, 219, 785, 1810])).
% 1.04/1.29 tff(1812,plain,
% 1.04/1.29 (r(s(s(s(elem!1))), s(elem!1))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[958, 1811, 183])).
% 1.04/1.29 tff(1813,plain,
% 1.04/1.29 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1037, 297, 1654, 1812])).
% 1.04/1.29 tff(1814,plain,
% 1.04/1.29 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[1813, 1057])).
% 1.04/1.29 tff(1815,plain,
% 1.04/1.29 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1485, 319, 219, 785, 1810])).
% 1.04/1.29 tff(1816,plain,
% 1.04/1.29 (r(s(elem!1), s(s(s(elem!1))))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[434, 1815, 1114])).
% 1.04/1.29 tff(1817,plain,
% 1.04/1.29 (~r(s(s(s(elem!1))), elem!1)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1394, 1816, 1742])).
% 1.04/1.29 tff(1818,plain,
% 1.04/1.29 (b(s(s(s(elem!1))), elem!1)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[361, 1817, 249])).
% 1.04/1.29 tff(1819,plain,
% 1.04/1.29 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1193, 297, 984, 1808])).
% 1.04/1.29 tff(1820,plain,
% 1.04/1.29 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[634, 1819, 619])).
% 1.04/1.29 tff(1821,plain,
% 1.04/1.29 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1201, 319, 1820, 1818, 1744])).
% 1.04/1.29 tff(1822,plain,
% 1.04/1.29 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[1821, 970])).
% 1.04/1.29 tff(1823,plain,
% 1.04/1.29 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1018, 1822, 968])).
% 1.04/1.29 tff(1824,plain,
% 1.04/1.29 ($false),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1823, 1814])).
% 1.04/1.29 tff(1825,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~(s(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))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.29 tff(1826,plain,
% 1.04/1.29 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1825, 132, 1056, 872, 1048])).
% 1.04/1.29 tff(1827,plain,
% 1.04/1.29 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[571, 1826, 179])).
% 1.04/1.29 tff(1828,plain,
% 1.04/1.29 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.04/1.29 inference(monotonicity,[status(thm)],[149])).
% 1.04/1.29 tff(1829,plain,
% 1.04/1.29 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.04/1.29 inference(transitivity,[status(thm)],[1828, 597])).
% 1.04/1.29 tff(1830,plain,
% 1.04/1.29 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.04/1.29 inference(transitivity,[status(thm)],[1829, 598])).
% 1.04/1.29 tff(1831,plain,
% 1.04/1.29 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[1830])).
% 1.04/1.29 tff(1832,plain,
% 1.04/1.29 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[604, 1831])).
% 1.04/1.29 tff(1833,plain,
% 1.04/1.29 (((~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(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(1834,plain,
% 1.04/1.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[1833])).
% 1.04/1.29 tff(1835,plain,
% 1.04/1.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.04/1.29 inference(transitivity,[status(thm)],[1834, 1305])).
% 1.04/1.29 tff(1836,plain,
% 1.04/1.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.04/1.29 inference(quant_inst,[status(thm)],[])).
% 1.04/1.29 tff(1837,plain,
% 1.04/1.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[1836, 1835])).
% 1.04/1.29 tff(1838,plain,
% 1.04/1.29 ($false),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1837, 319, 274, 785, 1021, 547])).
% 1.04/1.29 tff(1839,plain,((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.29 tff(1840,plain,
% 1.04/1.29 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1839, 1021, 219, 785])).
% 1.04/1.29 tff(1841,plain,
% 1.04/1.29 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[595, 1840, 587])).
% 1.04/1.29 tff(1842,plain,
% 1.04/1.29 (~r(s(elem!1), elem!1)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1168, 1117, 1841])).
% 1.04/1.29 tff(1843,plain,
% 1.04/1.29 (b(s(elem!1), elem!1)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[375, 1842, 194])).
% 1.04/1.29 tff(1844,plain,
% 1.04/1.29 (b(s(elem!1), z)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1176, 1843, 187])).
% 1.04/1.29 tff(1845,plain,
% 1.04/1.29 (~b(z, s(s(elem!1)))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[794, 1844, 1, 785])).
% 1.04/1.29 tff(1846,plain,
% 1.04/1.29 (r(z, s(s(elem!1)))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[56, 1845])).
% 1.04/1.29 tff(1847,plain,
% 1.04/1.29 (r(elem!1, s(s(elem!1)))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1476, 1846, 187])).
% 1.04/1.29 tff(1848,plain,
% 1.04/1.29 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1012, 319, 274, 116, 1021])).
% 1.04/1.29 tff(1849,plain,
% 1.04/1.29 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[1848, 970])).
% 1.04/1.29 tff(1850,plain,
% 1.04/1.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(1851,plain,
% 1.04/1.29 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(1852,plain,
% 1.04/1.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[1851])).
% 1.04/1.29 tff(1853,plain,
% 1.04/1.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.04/1.29 inference(transitivity,[status(thm)],[1852, 1850])).
% 1.04/1.29 tff(1854,plain,
% 1.04/1.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.04/1.29 inference(quant_inst,[status(thm)],[])).
% 1.04/1.29 tff(1855,plain,
% 1.04/1.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[1854, 1853])).
% 1.04/1.29 tff(1856,plain,
% 1.04/1.29 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1855, 319, 274, 785, 1021])).
% 1.04/1.29 tff(1857,plain,
% 1.04/1.29 (~b(s(z), s(s(s(s(z)))))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1379, 1856, 133])).
% 1.04/1.29 tff(1858,plain,
% 1.04/1.29 (r(s(z), s(s(s(s(z)))))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1371, 1857, 1357])).
% 1.04/1.29 tff(1859,plain,
% 1.04/1.29 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1485, 319, 274, 785, 116])).
% 1.04/1.29 tff(1860,plain,
% 1.04/1.29 (r(s(elem!1), s(s(s(elem!1))))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[434, 1859, 1114])).
% 1.04/1.29 tff(1861,plain,
% 1.04/1.29 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1600, 1860, 133, 1858])).
% 1.04/1.29 tff(1862,plain,
% 1.04/1.29 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1018, 1861, 968])).
% 1.04/1.29 tff(1863,plain,
% 1.04/1.29 ($false),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1862, 1849])).
% 1.04/1.29 tff(1864,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~(s(s(z)) = s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.29 tff(1865,plain,
% 1.04/1.29 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1864, 133, 219, 785, 1021])).
% 1.04/1.29 tff(1866,plain,
% 1.04/1.29 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[348, 1865, 232])).
% 1.04/1.29 tff(1867,plain,
% 1.04/1.29 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(1868,plain,
% 1.04/1.29 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(1869,plain,
% 1.14/1.30 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1)))))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[1868])).
% 1.14/1.30 tff(1870,plain,
% 1.14/1.30 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.14/1.30 inference(transitivity,[status(thm)],[1869, 1867])).
% 1.14/1.30 tff(1871,plain,
% 1.14/1.30 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.14/1.30 inference(quant_inst,[status(thm)],[])).
% 1.14/1.30 tff(1872,plain,
% 1.14/1.30 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1)))))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[1871, 1870])).
% 1.14/1.30 tff(1873,plain,
% 1.14/1.30 (~r(elem!1, s(s(s(elem!1))))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1872, 297, 1866, 1847])).
% 1.14/1.30 tff(1874,plain,
% 1.14/1.30 (~r(z, s(s(s(elem!1))))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[1873, 1575])).
% 1.14/1.30 tff(1875,plain,
% 1.14/1.30 (b(z, s(s(s(elem!1))))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[416, 1874])).
% 1.14/1.30 tff(1876,plain,
% 1.14/1.30 (b(elem!1, s(s(s(elem!1))))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[1875, 1574])).
% 1.14/1.30 tff(1877,plain,
% 1.14/1.30 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1315, 1117, 1, 187, 785, 538, 1866, 971, 219])).
% 1.14/1.30 tff(1878,plain,
% 1.14/1.30 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1320, 1877, 1060])).
% 1.14/1.30 tff(1879,plain,
% 1.14/1.30 (~b(s(s(elem!1)), elem!1)),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1225, 1841, 605, 1021, 619, 272, 785, 219])).
% 1.14/1.30 tff(1880,plain,
% 1.14/1.30 (~b(s(s(elem!1)), z)),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[500, 1879, 187])).
% 1.14/1.30 tff(1881,plain,
% 1.14/1.30 (r(s(s(elem!1)), z)),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[75, 1880])).
% 1.14/1.30 tff(1882,plain,
% 1.14/1.30 (r(s(s(elem!1)), elem!1)),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[1881, 440])).
% 1.14/1.30 tff(1883,plain,
% 1.14/1.30 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[481, 297, 462, 461])).
% 1.14/1.30 tff(1884,plain,
% 1.14/1.30 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[348, 1883, 232])).
% 1.14/1.30 tff(1885,plain,
% 1.14/1.30 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1012, 319, 274, 1884, 1021])).
% 1.14/1.30 tff(1886,plain,
% 1.14/1.30 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[1885, 970])).
% 1.14/1.30 tff(1887,plain,
% 1.14/1.30 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(1888,plain,
% 1.14/1.30 (((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(1889,plain,
% 1.14/1.30 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[1888])).
% 1.14/1.30 tff(1890,plain,
% 1.14/1.30 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.14/1.30 inference(transitivity,[status(thm)],[1889, 1887])).
% 1.14/1.30 tff(1891,plain,
% 1.14/1.30 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.14/1.30 inference(quant_inst,[status(thm)],[])).
% 1.14/1.30 tff(1892,plain,
% 1.14/1.30 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[1891, 1890])).
% 1.14/1.30 tff(1893,plain,
% 1.14/1.30 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1892, 297, 461, 1117])).
% 1.14/1.30 tff(1894,plain,
% 1.14/1.30 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[1893, 1057])).
% 1.14/1.30 tff(1895,plain,
% 1.14/1.30 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1018, 1894, 968])).
% 1.14/1.30 tff(1896,plain,
% 1.14/1.30 ($false),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1895, 1886])).
% 1.14/1.30 tff(1897,plain,((~r(s(s(s(elem!1))), elem!1)) | (~(s(s(z)) = s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.30 tff(1898,plain,
% 1.14/1.30 (~r(s(s(s(elem!1))), elem!1)),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1897, 1117, 219, 1021, 133, 1882])).
% 1.14/1.30 tff(1899,plain,
% 1.14/1.30 (b(s(s(s(elem!1))), elem!1)),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[361, 1898, 249])).
% 1.14/1.30 tff(1900,plain,
% 1.14/1.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(1901,plain,
% 1.14/1.30 (((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(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)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(1902,plain,
% 1.14/1.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[1901])).
% 1.14/1.30 tff(1903,plain,
% 1.14/1.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.14/1.30 inference(transitivity,[status(thm)],[1902, 1900])).
% 1.14/1.30 tff(1904,plain,
% 1.14/1.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.14/1.30 inference(quant_inst,[status(thm)],[])).
% 1.14/1.30 tff(1905,plain,
% 1.14/1.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[1904, 1903])).
% 1.14/1.30 tff(1906,plain,
% 1.14/1.30 ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1905, 319, 1899, 1878])).
% 1.14/1.30 tff(1907,plain,
% 1.14/1.30 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1906, 1876])).
% 1.14/1.30 tff(1908,plain,
% 1.14/1.30 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1412, 51, 1409, 1907])).
% 1.14/1.30 tff(1909,plain,
% 1.14/1.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(1910,plain,
% 1.14/1.30 (((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(1911,plain,
% 1.14/1.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[1910])).
% 1.14/1.30 tff(1912,plain,
% 1.14/1.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.14/1.30 inference(transitivity,[status(thm)],[1911, 1909])).
% 1.14/1.30 tff(1913,plain,
% 1.14/1.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.14/1.30 inference(quant_inst,[status(thm)],[])).
% 1.14/1.30 tff(1914,plain,
% 1.14/1.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[1913, 1912])).
% 1.14/1.30 tff(1915,plain,
% 1.14/1.30 ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1914, 319, 1843, 1878])).
% 1.14/1.30 tff(1916,plain,
% 1.14/1.30 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1915, 1876])).
% 1.14/1.30 tff(1917,plain,
% 1.14/1.30 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1291, 51, 1418, 1916])).
% 1.14/1.30 tff(1918,plain,
% 1.14/1.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(1919,plain,
% 1.14/1.30 (((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(1920,plain,
% 1.14/1.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[1919])).
% 1.14/1.30 tff(1921,plain,
% 1.14/1.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.14/1.30 inference(transitivity,[status(thm)],[1920, 1918])).
% 1.14/1.30 tff(1922,plain,
% 1.14/1.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.14/1.30 inference(quant_inst,[status(thm)],[])).
% 1.14/1.30 tff(1923,plain,
% 1.14/1.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[1922, 1921])).
% 1.14/1.30 tff(1924,plain,
% 1.14/1.30 ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1923, 319, 1843, 1899])).
% 1.14/1.30 tff(1925,plain,
% 1.14/1.30 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1924, 1876])).
% 1.14/1.30 tff(1926,plain,
% 1.14/1.30 (r(s(s(s(elem!1))), s(elem!1))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[958, 1925, 183])).
% 1.14/1.30 tff(1927,plain,
% 1.14/1.30 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(1928,plain,
% 1.14/1.30 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.14/1.30 inference(quant_inst,[status(thm)],[])).
% 1.14/1.30 tff(1929,plain,
% 1.14/1.30 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[1928, 1927])).
% 1.14/1.30 tff(1930,plain,
% 1.14/1.30 ($false),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1929, 297, 1926, 1917, 1908])).
% 1.14/1.30 tff(1931,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~(s(s(z)) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.30 tff(1932,plain,
% 1.14/1.30 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1931, 1056, 872, 1827, 132])).
% 1.14/1.30 tff(1933,plain,
% 1.14/1.30 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[616, 1932, 1832])).
% 1.14/1.30 tff(1934,plain,
% 1.14/1.30 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(z))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[1050])).
% 1.14/1.30 tff(1935,plain,
% 1.14/1.30 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.14/1.30 inference(symmetry,[status(thm)],[1934])).
% 1.14/1.30 tff(1936,plain,
% 1.14/1.30 (b(s(s(elem!1)), s(elem!1))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[872, 1935])).
% 1.14/1.30 tff(1937,plain,
% 1.14/1.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(1938,plain,
% 1.14/1.30 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(1939,plain,
% 1.14/1.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[1938])).
% 1.14/1.30 tff(1940,plain,
% 1.14/1.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.14/1.30 inference(transitivity,[status(thm)],[1939, 1937])).
% 1.14/1.30 tff(1941,plain,
% 1.14/1.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.14/1.30 inference(quant_inst,[status(thm)],[])).
% 1.14/1.30 tff(1942,plain,
% 1.14/1.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[1941, 1940])).
% 1.14/1.30 tff(1943,plain,
% 1.14/1.30 ($false),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1942, 319, 274, 1445, 1021, 397])).
% 1.14/1.30 tff(1944,plain,((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.30 tff(1945,plain,
% 1.14/1.30 (~b(elem!1, s(s(elem!1)))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1944, 1936, 1933, 1827])).
% 1.14/1.30 tff(1946,plain,
% 1.14/1.30 ((elem!1 = s(s(elem!1))) <=> (z = s(s(elem!1)))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[155])).
% 1.14/1.30 tff(1947,plain,
% 1.14/1.30 ((elem!1 = s(s(elem!1))) <=> (s(s(elem!1)) = z)),
% 1.14/1.30 inference(transitivity,[status(thm)],[1946, 36])).
% 1.14/1.30 tff(1948,plain,
% 1.14/1.30 ((s(s(elem!1)) = z) <=> (elem!1 = s(s(elem!1)))),
% 1.14/1.30 inference(symmetry,[status(thm)],[1947])).
% 1.14/1.30 tff(1949,plain,
% 1.14/1.30 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = s(s(elem!1))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[1948])).
% 1.14/1.30 tff(1950,plain,
% 1.14/1.30 (~(elem!1 = s(s(elem!1)))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[40, 1949])).
% 1.14/1.30 tff(1951,plain,
% 1.14/1.30 (r(elem!1, s(s(elem!1)))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1123, 51, 1950, 1945])).
% 1.14/1.30 tff(1952,plain,
% 1.14/1.30 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[132])).
% 1.14/1.30 tff(1953,plain,
% 1.14/1.30 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 1.14/1.30 inference(transitivity,[status(thm)],[1952, 220])).
% 1.14/1.30 tff(1954,plain,
% 1.14/1.30 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[1953])).
% 1.14/1.30 tff(1955,plain,
% 1.14/1.30 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[231, 1954])).
% 1.14/1.30 tff(1956,plain,
% 1.14/1.30 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1864, 132, 1936, 1056, 1827])).
% 1.14/1.30 tff(1957,plain,
% 1.14/1.30 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[348, 1956, 1955])).
% 1.14/1.30 tff(1958,plain,
% 1.14/1.30 (~r(s(s(s(elem!1))), elem!1)),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1183, 297, 1957, 1951])).
% 1.14/1.30 tff(1959,plain,
% 1.14/1.30 (b(s(s(s(elem!1))), elem!1)),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[361, 1958, 161])).
% 1.14/1.30 tff(1960,plain,
% 1.14/1.30 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[132])).
% 1.14/1.30 tff(1961,plain,
% 1.14/1.30 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[1960])).
% 1.14/1.30 tff(1962,plain,
% 1.14/1.30 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[1961, 1960])).
% 1.14/1.31 tff(1963,plain,
% 1.14/1.31 ((s(s(s(z))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[1960, 1961])).
% 1.14/1.31 tff(1964,plain,
% 1.14/1.31 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(s(z))) = s(s(s(s(z)))))),
% 1.14/1.31 inference(symmetry,[status(thm)],[1963])).
% 1.14/1.31 tff(1965,plain,
% 1.14/1.31 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 1.14/1.31 inference(transitivity,[status(thm)],[1964, 1496])).
% 1.14/1.31 tff(1966,plain,
% 1.14/1.31 ((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(z)))) = s(s(s(z)))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[1965])).
% 1.14/1.31 tff(1967,plain,
% 1.14/1.31 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[92, 1955])).
% 1.14/1.31 tff(1968,plain,
% 1.14/1.31 (~(s(s(s(s(z)))) = s(s(s(z))))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[1967, 1966])).
% 1.14/1.31 tff(1969,plain,
% 1.14/1.31 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[1961])).
% 1.14/1.31 tff(1970,plain,
% 1.14/1.31 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.14/1.31 inference(symmetry,[status(thm)],[1969])).
% 1.14/1.31 tff(1971,plain,
% 1.14/1.31 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.14/1.31 inference(symmetry,[status(thm)],[1960])).
% 1.14/1.31 tff(1972,plain,
% 1.14/1.31 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[1971])).
% 1.14/1.31 tff(1973,plain,
% 1.14/1.31 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.14/1.31 inference(transitivity,[status(thm)],[1972, 1970])).
% 1.14/1.31 tff(1974,plain,
% 1.14/1.31 ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[1973])).
% 1.14/1.31 tff(1975,plain,
% 1.14/1.31 (b(elem!1, s(s(s(elem!1)))) <=> b(z, s(s(s(elem!1))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[155])).
% 1.14/1.31 tff(1976,plain,
% 1.14/1.31 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.14/1.31 inference(symmetry,[status(thm)],[1975])).
% 1.14/1.31 tff(1977,plain,
% 1.14/1.31 (r(elem!1, s(s(s(elem!1)))) <=> r(z, s(s(s(elem!1))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[155])).
% 1.14/1.31 tff(1978,plain,
% 1.14/1.31 ((~r(elem!1, s(s(s(elem!1))))) <=> (~r(z, s(s(s(elem!1)))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[1977])).
% 1.14/1.31 tff(1979,plain,
% 1.14/1.31 (~r(elem!1, s(s(s(elem!1))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1872, 297, 1957, 1951])).
% 1.14/1.31 tff(1980,plain,
% 1.14/1.31 (~r(z, s(s(s(elem!1))))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[1979, 1978])).
% 1.14/1.31 tff(1981,plain,
% 1.14/1.31 (b(z, s(s(s(elem!1))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[416, 1980])).
% 1.14/1.31 tff(1982,plain,
% 1.14/1.31 (b(elem!1, s(s(s(elem!1))))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[1981, 1976])).
% 1.14/1.31 tff(1983,plain,
% 1.14/1.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(1984,plain,
% 1.14/1.31 (((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(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)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(1985,plain,
% 1.14/1.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[1984])).
% 1.14/1.31 tff(1986,plain,
% 1.14/1.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.14/1.31 inference(transitivity,[status(thm)],[1985, 1983])).
% 1.14/1.31 tff(1987,plain,
% 1.14/1.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(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))))))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(1988,plain,
% 1.14/1.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[1987, 1986])).
% 1.14/1.31 tff(1989,plain,
% 1.14/1.31 ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1988, 319, 1959, 1933])).
% 1.14/1.31 tff(1990,plain,
% 1.14/1.31 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1989, 1982])).
% 1.14/1.31 tff(1991,plain,
% 1.14/1.31 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[1990, 1974])).
% 1.14/1.31 tff(1992,plain,
% 1.14/1.31 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1519, 1991, 1968])).
% 1.14/1.31 tff(1993,plain,
% 1.14/1.31 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[1992, 1962])).
% 1.14/1.31 tff(1994,plain,
% 1.14/1.31 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1408, 179])).
% 1.14/1.31 tff(1995,plain,
% 1.14/1.31 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[101, 1967])).
% 1.14/1.31 tff(1996,plain,
% 1.14/1.31 (~(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[107, 1995])).
% 1.14/1.31 tff(1997,plain,
% 1.14/1.31 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[1829])).
% 1.14/1.31 tff(1998,plain,
% 1.14/1.31 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[604, 1997])).
% 1.14/1.31 tff(1999,plain,
% 1.14/1.31 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[586, 161])).
% 1.14/1.31 tff(2000,plain,
% 1.14/1.31 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1839, 1827, 1936, 1056])).
% 1.14/1.31 tff(2001,plain,
% 1.14/1.31 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[595, 2000, 1999])).
% 1.14/1.31 tff(2002,plain,
% 1.14/1.31 ((s(elem!1) = z) <=> (s(elem!1) = elem!1)),
% 1.14/1.31 inference(monotonicity,[status(thm)],[149])).
% 1.14/1.31 tff(2003,plain,
% 1.14/1.31 ((s(elem!1) = z) <=> (elem!1 = s(elem!1))),
% 1.14/1.31 inference(transitivity,[status(thm)],[2002, 184])).
% 1.14/1.31 tff(2004,plain,
% 1.14/1.31 ((~(s(elem!1) = z)) <=> (~(elem!1 = s(elem!1)))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[2003])).
% 1.14/1.31 tff(2005,plain,
% 1.14/1.31 (~(elem!1 = s(elem!1))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[193, 2004])).
% 1.14/1.31 tff(2006,plain,
% 1.14/1.31 (~(s(z) = s(s(s(s(z)))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1356, 132])).
% 1.14/1.31 tff(2007,plain,
% 1.14/1.31 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1855, 319, 1936, 1056, 1827])).
% 1.14/1.31 tff(2008,plain,
% 1.14/1.31 (~b(s(z), s(s(s(s(z)))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1379, 2007, 132])).
% 1.14/1.31 tff(2009,plain,
% 1.14/1.31 (r(s(z), s(s(s(s(z)))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1371, 2008, 2006])).
% 1.14/1.31 tff(2010,plain,
% 1.14/1.31 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.14/1.31 inference(symmetry,[status(thm)],[1961])).
% 1.14/1.31 tff(2011,plain,
% 1.14/1.31 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[1971, 2010])).
% 1.14/1.31 tff(2012,plain,
% 1.14/1.31 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.14/1.31 inference(symmetry,[status(thm)],[2011])).
% 1.14/1.31 tff(2013,plain,
% 1.14/1.31 ((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(z))) = s(s(s(s(z))))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[1964])).
% 1.14/1.31 tff(2014,plain,
% 1.14/1.31 (~(s(s(s(z))) = s(s(s(s(z)))))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[1967, 2013])).
% 1.14/1.31 tff(2015,plain,
% 1.14/1.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(2016,plain,
% 1.14/1.31 (((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(2017,plain,
% 1.14/1.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[2016])).
% 1.14/1.31 tff(2018,plain,
% 1.14/1.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.14/1.31 inference(transitivity,[status(thm)],[2017, 2015])).
% 1.14/1.31 tff(2019,plain,
% 1.14/1.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(2020,plain,
% 1.14/1.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[2019, 2018])).
% 1.14/1.31 tff(2021,plain,
% 1.14/1.31 ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[2020, 319, 1959, 1933])).
% 1.14/1.31 tff(2022,plain,
% 1.14/1.31 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[2021, 1982])).
% 1.14/1.31 tff(2023,assumption,(b(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 1.14/1.31 tff(2024,plain,
% 1.14/1.31 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[2023, 1067])).
% 1.14/1.31 tff(2025,assumption,(~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.14/1.31 tff(2026,plain,
% 1.14/1.31 ($false),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[2025, 2024])).
% 1.14/1.31 tff(2027,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (~(s(s(z)) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.31 tff(2028,plain,
% 1.14/1.31 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[2027, 2022, 132])).
% 1.14/1.31 tff(2029,plain,
% 1.14/1.31 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1018, 2028, 2014])).
% 1.14/1.31 tff(2030,plain,
% 1.14/1.31 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[2029, 2012])).
% 1.14/1.31 tff(2031,assumption,(r(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 1.14/1.31 tff(2032,assumption,(r(s(s(s(elem!1))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.14/1.31 tff(2033,plain,
% 1.14/1.31 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(2034,plain,
% 1.14/1.31 (((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(2035,plain,
% 1.14/1.31 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[2034])).
% 1.14/1.31 tff(2036,plain,
% 1.14/1.31 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.14/1.31 inference(transitivity,[status(thm)],[2035, 2033])).
% 1.14/1.31 tff(2037,plain,
% 1.14/1.31 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(2038,plain,
% 1.14/1.31 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[2037, 2036])).
% 1.14/1.31 tff(2039,plain,
% 1.14/1.31 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[2038, 297, 2032, 2031])).
% 1.14/1.31 tff(2040,plain,
% 1.14/1.31 ($false),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[2039, 1589])).
% 1.14/1.31 tff(2041,plain,((~r(s(z), s(s(s(s(z)))))) | (~(s(s(z)) = s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.31 tff(2042,plain,
% 1.14/1.31 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[2041, 2030, 2009, 132])).
% 1.14/1.31 tff(2043,plain,
% 1.14/1.31 (b(s(s(s(elem!1))), s(elem!1))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[958, 2042, 172])).
% 1.14/1.31 tff(2044,plain,
% 1.14/1.31 ((s(s(s(elem!1))) = s(z)) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.14/1.31 inference(transitivity,[status(thm)],[164, 277])).
% 1.14/1.31 tff(2045,plain,
% 1.14/1.31 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[2044])).
% 1.14/1.31 tff(2046,plain,
% 1.14/1.31 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[171, 2045])).
% 1.14/1.31 tff(2047,plain,
% 1.14/1.31 ((~b(s(elem!1), s(s(s(s(elem!1)))))) <=> (~b(s(z), s(s(s(s(z))))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[1373])).
% 1.14/1.31 tff(2048,plain,
% 1.14/1.31 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1206, 988, 538, 619, 605, 335, 249])).
% 1.14/1.31 tff(2049,plain,
% 1.14/1.31 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[571, 2048, 971])).
% 1.14/1.31 tff(2050,plain,
% 1.14/1.31 ((s(elem!1) = s(s(elem!1))) <=> (s(z) = s(s(elem!1)))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[216])).
% 1.14/1.31 tff(2051,plain,
% 1.14/1.31 ((s(elem!1) = s(s(elem!1))) <=> (s(s(elem!1)) = s(z))),
% 1.14/1.31 inference(transitivity,[status(thm)],[2050, 809])).
% 1.14/1.31 tff(2052,plain,
% 1.14/1.31 ((s(s(elem!1)) = s(z)) <=> (s(elem!1) = s(s(elem!1)))),
% 1.14/1.31 inference(symmetry,[status(thm)],[2051])).
% 1.14/1.31 tff(2053,plain,
% 1.14/1.31 ((~(s(s(elem!1)) = s(z))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[2052])).
% 1.14/1.31 tff(2054,plain,
% 1.14/1.31 (~(s(elem!1) = s(s(elem!1)))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[209, 2053])).
% 1.14/1.31 tff(2055,plain,
% 1.14/1.31 (~r(s(elem!1), s(s(elem!1)))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[343, 334, 335])).
% 1.14/1.31 tff(2056,plain,
% 1.14/1.31 (b(s(elem!1), s(s(elem!1)))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[807, 2055, 2054])).
% 1.14/1.31 tff(2057,plain,
% 1.14/1.31 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1855, 319, 274, 2056, 2049])).
% 1.14/1.31 tff(2058,plain,
% 1.14/1.31 (~b(s(z), s(s(s(s(z)))))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[2057, 2047])).
% 1.14/1.31 tff(2059,plain,
% 1.14/1.31 (r(s(z), s(s(s(s(z)))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1371, 2058, 1357])).
% 1.14/1.31 tff(2060,plain,
% 1.14/1.31 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1600, 2059, 133, 334])).
% 1.14/1.31 tff(2061,plain,
% 1.14/1.31 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1018, 2060, 968])).
% 1.14/1.31 tff(2062,plain,
% 1.14/1.31 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[2061, 1067])).
% 1.14/1.31 tff(2063,plain,
% 1.14/1.31 (~r(elem!1, s(s(s(elem!1))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1872, 297, 335, 988])).
% 1.14/1.31 tff(2064,plain,
% 1.14/1.31 (~r(z, s(s(s(elem!1))))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[2063, 1575])).
% 1.14/1.31 tff(2065,plain,
% 1.14/1.31 (b(z, s(s(s(elem!1))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[416, 2064])).
% 1.14/1.31 tff(2066,plain,
% 1.14/1.31 (b(elem!1, s(s(s(elem!1))))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[2065, 1574])).
% 1.14/1.31 tff(2067,plain,
% 1.14/1.31 (b(s(s(s(elem!1))), elem!1)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[361, 1184, 249])).
% 1.14/1.31 tff(2068,plain,
% 1.14/1.31 ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[2020, 319, 2067, 1445])).
% 1.14/1.31 tff(2069,plain,
% 1.14/1.31 ($false),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[2068, 2066, 2062])).
% 1.14/1.31 tff(2070,plain,((~r(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~(s(s(z)) = s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.31 tff(2071,plain,
% 1.14/1.31 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[2070, 1951, 132, 1957, 1936, 1933])).
% 1.14/1.31 tff(2072,plain,
% 1.14/1.31 (b(s(elem!1), s(s(s(elem!1))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[434, 2071, 2046])).
% 1.14/1.31 tff(2073,plain,
% 1.14/1.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(2074,plain,
% 1.14/1.31 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1)))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(2075,plain,
% 1.14/1.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[2074])).
% 1.14/1.31 tff(2076,plain,
% 1.14/1.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.14/1.31 inference(transitivity,[status(thm)],[2075, 2073])).
% 1.14/1.31 tff(2077,plain,
% 1.14/1.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(2078,plain,
% 1.14/1.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[2077, 2076])).
% 1.14/1.31 tff(2079,plain,
% 1.14/1.31 (~b(elem!1, s(elem!1))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[2078, 319, 2072, 2043, 1982])).
% 1.14/1.31 tff(2080,plain,
% 1.14/1.31 (r(elem!1, s(elem!1))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[389, 2079, 2005])).
% 1.14/1.31 tff(2081,plain,
% 1.14/1.31 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[629, 2080, 2001])).
% 1.14/1.31 tff(2082,plain,
% 1.14/1.31 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[634, 2081, 1998])).
% 1.14/1.31 tff(2083,plain,
% 1.14/1.31 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1545, 2082, 1996, 1994, 1993, 1933, 1959])).
% 1.14/1.31 tff(2084,plain,
% 1.14/1.31 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1320, 2083, 154])).
% 1.14/1.31 tff(2085,plain,
% 1.14/1.31 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 1.14/1.31 inference(monotonicity,[status(thm)],[149])).
% 1.14/1.31 tff(2086,plain,
% 1.14/1.31 (~b(s(s(elem!1)), elem!1)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1225, 2001, 1832, 1827, 1998, 2005, 1056, 1936])).
% 1.14/1.31 tff(2087,plain,
% 1.14/1.31 (~b(s(s(elem!1)), z)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[500, 2086, 149])).
% 1.14/1.31 tff(2088,plain,
% 1.14/1.31 (r(s(s(elem!1)), z)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[75, 2087])).
% 1.14/1.32 tff(2089,plain,
% 1.14/1.32 (r(s(s(elem!1)), elem!1)),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[2088, 2085])).
% 1.14/1.32 tff(2090,plain,
% 1.14/1.32 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1232, 297, 2089, 2084])).
% 1.14/1.32 tff(2091,plain,
% 1.14/1.32 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1239, 1999])).
% 1.14/1.32 tff(2092,plain,
% 1.14/1.32 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1243, 51, 2091, 2090])).
% 1.14/1.32 tff(2093,plain,
% 1.14/1.32 ((s(elem!1) = z) <=> (s(elem!1) = elem!1)),
% 1.14/1.32 inference(transitivity,[status(thm)],[2003, 185])).
% 1.14/1.32 tff(2094,plain,
% 1.14/1.32 ((~(s(elem!1) = z)) <=> (~(s(elem!1) = elem!1))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[2093])).
% 1.14/1.32 tff(2095,plain,
% 1.14/1.32 (~(s(elem!1) = elem!1)),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[193, 2094])).
% 1.14/1.32 tff(2096,plain,
% 1.14/1.32 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.14/1.32 inference(symmetry,[status(thm)],[395])).
% 1.14/1.32 tff(2097,plain,
% 1.14/1.32 ((~r(elem!1, s(s(s(elem!1))))) <=> (~r(z, s(s(s(elem!1)))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[393])).
% 1.14/1.32 tff(2098,plain,
% 1.14/1.32 (b(s(elem!1), z)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1176, 449, 391])).
% 1.14/1.32 tff(2099,plain,
% 1.14/1.32 (~b(z, s(s(elem!1)))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[794, 2098, 1, 785])).
% 1.14/1.32 tff(2100,plain,
% 1.14/1.32 (r(z, s(s(elem!1)))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[56, 2099])).
% 1.14/1.32 tff(2101,plain,
% 1.14/1.32 (r(elem!1, s(s(elem!1)))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1476, 2100, 391])).
% 1.14/1.32 tff(2102,plain,
% 1.14/1.32 (~r(elem!1, s(s(s(elem!1))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1872, 297, 335, 2101])).
% 1.14/1.32 tff(2103,plain,
% 1.14/1.32 (~r(z, s(s(s(elem!1))))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[2102, 2097])).
% 1.14/1.32 tff(2104,plain,
% 1.14/1.32 (b(z, s(s(s(elem!1))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[416, 2103])).
% 1.14/1.32 tff(2105,plain,
% 1.14/1.32 (b(elem!1, s(s(s(elem!1))))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[2104, 2096])).
% 1.14/1.32 tff(2106,plain,
% 1.14/1.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(2107,plain,
% 1.14/1.32 (((~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(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(2108,plain,
% 1.14/1.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1), s(s(s(elem!1))))) | (~b(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[2107])).
% 1.14/1.32 tff(2109,plain,
% 1.14/1.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1), s(s(s(elem!1))))) | (~b(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.14/1.32 inference(transitivity,[status(thm)],[2108, 2106])).
% 1.14/1.32 tff(2110,plain,
% 1.14/1.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(2111,plain,
% 1.14/1.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[2110, 2109])).
% 1.14/1.32 tff(2112,plain,
% 1.14/1.32 (~b(elem!1, s(s(s(elem!1))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[2111, 319, 449, 309, 548])).
% 1.14/1.32 tff(2113,plain,
% 1.14/1.32 ($false),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[2112, 2105])).
% 1.14/1.32 tff(2114,plain,((~b(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))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.32 tff(2115,plain,
% 1.14/1.32 (~b(s(elem!1), elem!1)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[2114, 2043, 149, 2072, 1957, 872, 1056])).
% 1.14/1.32 tff(2116,plain,
% 1.14/1.32 (r(s(elem!1), elem!1)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[375, 2115, 2095])).
% 1.14/1.32 tff(2117,plain,
% 1.14/1.32 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1298, 2084, 2116])).
% 1.14/1.32 tff(2118,plain,
% 1.14/1.32 (~(s(s(s(s(s(elem!1))))) = s(elem!1))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1287, 1998])).
% 1.14/1.32 tff(2119,plain,
% 1.14/1.32 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1291, 51, 2118, 2117])).
% 1.14/1.32 tff(2120,plain,
% 1.14/1.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), 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(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), 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(s(s(s(elem!1))))), s(elem!1))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(2121,plain,
% 1.14/1.32 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~b(s(elem!1), 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(s(s(s(elem!1))))), s(elem!1))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(2122,plain,
% 1.14/1.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), 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(s(s(s(elem!1))))), s(elem!1)))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[2121])).
% 1.14/1.32 tff(2123,plain,
% 1.14/1.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), 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(s(s(s(elem!1))))), s(elem!1))))),
% 1.14/1.32 inference(transitivity,[status(thm)],[2122, 2120])).
% 1.14/1.32 tff(2124,plain,
% 1.14/1.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(2125,plain,
% 1.14/1.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[2124, 2123])).
% 1.14/1.32 tff(2126,plain,
% 1.14/1.32 ($false),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[2125, 319, 2072, 1936, 2119, 2092])).
% 1.14/1.32 tff(2127,plain,(r(s(s(z)), s(s(elem!1))) | r(s(s(elem!1)), s(z)) | b(s(s(z)), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.32 tff(2128,plain,
% 1.14/1.32 (r(s(s(elem!1)), s(z))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[2127, 33, 69])).
% 1.14/1.32 tff(2129,plain,
% 1.14/1.32 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.14/1.32 inference(symmetry,[status(thm)],[130])).
% 1.14/1.32 tff(2130,plain,
% 1.14/1.32 (r(s(s(elem!1)), s(s(s(s(elem!1))))) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[2129])).
% 1.14/1.32 tff(2131,plain,
% 1.14/1.32 ((s(s(elem!1)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.14/1.32 inference(commutativity,[status(thm)],[])).
% 1.14/1.32 tff(2132,plain,
% 1.14/1.32 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.14/1.32 inference(symmetry,[status(thm)],[2131])).
% 1.14/1.32 tff(2133,plain,
% 1.14/1.32 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[123])).
% 1.14/1.32 tff(2134,plain,
% 1.14/1.32 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.14/1.32 inference(transitivity,[status(thm)],[2133, 2132])).
% 1.14/1.32 tff(2135,plain,
% 1.14/1.32 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[2134])).
% 1.14/1.32 tff(2136,assumption,(s(s(s(s(elem!1)))) = s(s(z))), introduced(assumption)).
% 1.14/1.32 tff(2137,plain,
% 1.14/1.32 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(z)))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[2136])).
% 1.14/1.32 tff(2138,plain,
% 1.14/1.32 (s(s(s(elem!1))) = s(z)),
% 1.14/1.32 inference(transitivity,[status(thm)],[89, 2137, 126])).
% 1.14/1.32 tff(2139,plain,
% 1.14/1.32 ($false),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[171, 2138])).
% 1.14/1.32 tff(2140,plain,(~(s(s(s(s(elem!1)))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.32 tff(2141,plain,
% 1.14/1.32 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[2140, 2135])).
% 1.14/1.32 tff(2142,assumption,(~(s(elem!1) = s(s(elem!1)))), introduced(assumption)).
% 1.14/1.32 tff(2143,plain,
% 1.14/1.32 (s(z) = s(elem!1)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[138, 123])).
% 1.14/1.32 tff(2144,plain,
% 1.14/1.32 (z = elem!1),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[148, 2143])).
% 1.14/1.32 tff(2145,plain,
% 1.14/1.32 (r(elem!1, s(s(elem!1)))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1476, 2144, 70])).
% 1.14/1.32 tff(2146,assumption,(~(s(s(elem!1)) = s(s(s(elem!1))))), introduced(assumption)).
% 1.14/1.32 tff(2147,plain,
% 1.14/1.32 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 1.14/1.32 inference(monotonicity,[status(thm)],[2144])).
% 1.14/1.32 tff(2148,plain,
% 1.14/1.32 (r(s(s(elem!1)), elem!1)),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[115, 2147])).
% 1.14/1.32 tff(2149,assumption,(s(elem!1) = elem!1), introduced(assumption)).
% 1.14/1.32 tff(2150,plain,
% 1.14/1.32 (elem!1 = s(elem!1)),
% 1.14/1.32 inference(symmetry,[status(thm)],[2149])).
% 1.14/1.32 tff(2151,plain,
% 1.14/1.32 ((elem!1 = s(s(elem!1))) <=> (s(elem!1) = s(s(elem!1)))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[2150])).
% 1.14/1.32 tff(2152,plain,
% 1.14/1.32 ((s(elem!1) = s(s(elem!1))) <=> (elem!1 = s(s(elem!1)))),
% 1.14/1.32 inference(symmetry,[status(thm)],[2151])).
% 1.14/1.32 tff(2153,plain,
% 1.14/1.32 ((~(s(elem!1) = s(s(elem!1)))) <=> (~(elem!1 = s(s(elem!1))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[2152])).
% 1.14/1.32 tff(2154,plain,
% 1.14/1.32 (~(elem!1 = s(s(elem!1)))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[2142, 2153])).
% 1.14/1.32 tff(2155,plain,
% 1.14/1.32 (s(s(elem!1)) = s(elem!1)),
% 1.14/1.32 inference(monotonicity,[status(thm)],[2149])).
% 1.14/1.32 tff(2156,plain,
% 1.14/1.32 (s(elem!1) = s(s(elem!1))),
% 1.14/1.32 inference(symmetry,[status(thm)],[2155])).
% 1.14/1.32 tff(2157,plain,
% 1.14/1.32 (elem!1 = s(s(elem!1))),
% 1.14/1.32 inference(transitivity,[status(thm)],[2150, 2156])).
% 1.14/1.32 tff(2158,plain,
% 1.14/1.32 ($false),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[2157, 2154])).
% 1.14/1.32 tff(2159,plain,((~(s(elem!1) = elem!1)) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.32 tff(2160,plain,
% 1.14/1.32 (~(s(elem!1) = elem!1)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[2159, 2142])).
% 1.14/1.32 tff(2161,plain,
% 1.14/1.32 (~r(s(elem!1), elem!1)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[868, 123, 59])).
% 1.14/1.32 tff(2162,plain,
% 1.14/1.32 (b(s(elem!1), elem!1)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[375, 2161, 2160])).
% 1.14/1.32 tff(2163,assumption,(elem!1 = s(elem!1)), introduced(assumption)).
% 1.14/1.32 tff(2164,plain,
% 1.14/1.32 (s(elem!1) = elem!1),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[2163, 185])).
% 1.14/1.32 tff(2165,assumption,(~(s(elem!1) = elem!1)), introduced(assumption)).
% 1.14/1.32 tff(2166,plain,
% 1.14/1.32 ($false),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[2165, 2164])).
% 1.14/1.32 tff(2167,plain,((~(elem!1 = s(elem!1))) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.32 tff(2168,plain,
% 1.14/1.32 (~(elem!1 = s(elem!1))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[2167, 2160])).
% 1.14/1.32 tff(2169,assumption,(r(s(s(elem!1)), s(z))), introduced(assumption)).
% 1.14/1.32 tff(2170,plain,
% 1.14/1.32 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(2171,plain,
% 1.14/1.32 (((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(2172,plain,
% 1.14/1.32 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z)))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[2171])).
% 1.14/1.32 tff(2173,plain,
% 1.14/1.32 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))))),
% 1.14/1.32 inference(transitivity,[status(thm)],[2172, 2170])).
% 1.14/1.32 tff(2174,plain,
% 1.14/1.32 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(2175,plain,
% 1.14/1.32 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z)))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[2174, 2173])).
% 1.14/1.32 tff(2176,plain,
% 1.14/1.32 ($false),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[2175, 297, 2169, 70, 917])).
% 1.14/1.32 tff(2177,plain,((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.32 tff(2178,plain,
% 1.14/1.32 (~r(z, s(z))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[2177, 2128, 70])).
% 1.14/1.32 tff(2179,plain,
% 1.14/1.32 (~r(elem!1, s(elem!1))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[978, 123, 2178])).
% 1.14/1.32 tff(2180,plain,
% 1.14/1.32 (b(elem!1, s(elem!1))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[389, 2179, 2168])).
% 1.14/1.32 tff(2181,plain,
% 1.14/1.32 (~r(s(s(s(elem!1))), elem!1)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[470, 460, 462])).
% 1.14/1.32 tff(2182,plain,
% 1.14/1.32 (b(s(s(s(elem!1))), elem!1)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[361, 2181, 512])).
% 1.14/1.32 tff(2183,plain,
% 1.14/1.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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))), elem!1)))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(2184,plain,
% 1.14/1.32 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(2185,plain,
% 1.14/1.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))), elem!1))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[2184])).
% 1.14/1.32 tff(2186,plain,
% 1.14/1.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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))), elem!1)))),
% 1.14/1.32 inference(transitivity,[status(thm)],[2185, 2183])).
% 1.14/1.32 tff(2187,plain,
% 1.14/1.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(2188,plain,
% 1.14/1.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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))), elem!1))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[2187, 2186])).
% 1.14/1.32 tff(2189,plain,
% 1.14/1.32 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[2188, 319, 275, 449, 2182])).
% 1.14/1.32 tff(2190,plain,
% 1.14/1.32 (r(s(elem!1), s(s(s(elem!1))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[434, 2189, 430])).
% 1.14/1.32 tff(2191,plain,
% 1.14/1.32 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(2192,plain,
% 1.14/1.32 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(2193,plain,
% 1.14/1.32 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[2192])).
% 1.14/1.32 tff(2194,plain,
% 1.14/1.32 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.14/1.32 inference(transitivity,[status(thm)],[2193, 2191])).
% 1.14/1.32 tff(2195,plain,
% 1.14/1.32 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(2196,plain,
% 1.14/1.32 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1))))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[2195, 2194])).
% 1.14/1.32 tff(2197,plain,
% 1.14/1.32 ($false),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[2196, 297, 197, 2190, 460])).
% 1.14/1.32 tff(2198,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (s(elem!1) = s(s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (s(s(s(elem!1))) = elem!1) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.32 tff(2199,plain,
% 1.14/1.32 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[2198, 197, 275, 449, 462, 249, 1114])).
% 1.14/1.32 tff(2200,plain,
% 1.14/1.32 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[133])).
% 1.14/1.32 tff(2201,plain,
% 1.14/1.32 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[2200])).
% 1.14/1.32 tff(2202,plain,
% 1.14/1.32 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[2140, 2201])).
% 1.14/1.32 tff(2203,plain,
% 1.14/1.32 ((s(elem!1) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 1.14/1.32 inference(commutativity,[status(thm)],[])).
% 1.14/1.32 tff(2204,plain,
% 1.14/1.32 ((s(z) = s(s(s(s(elem!1))))) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[135])).
% 1.14/1.32 tff(2205,plain,
% 1.14/1.32 ((s(z) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 1.14/1.32 inference(transitivity,[status(thm)],[2204, 2203])).
% 1.14/1.32 tff(2206,plain,
% 1.14/1.32 ((~(s(z) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[2205])).
% 1.14/1.32 tff(2207,assumption,(s(z) = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.14/1.32 tff(2208,plain,
% 1.14/1.32 (inj_0(s(z)) = inj_0(s(s(s(s(elem!1)))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[2207])).
% 1.14/1.32 tff(2209,plain,
% 1.14/1.32 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(z))),
% 1.14/1.32 inference(symmetry,[status(thm)],[2208])).
% 1.14/1.32 tff(2210,plain,
% 1.14/1.32 (s(s(s(elem!1))) = z),
% 1.14/1.32 inference(transitivity,[status(thm)],[89, 2209, 13])).
% 1.14/1.32 tff(2211,plain,
% 1.14/1.32 ($false),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[160, 2210])).
% 1.14/1.32 tff(2212,plain,(~(s(z) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.32 tff(2213,plain,
% 1.14/1.32 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[2212, 2206])).
% 1.14/1.32 tff(2214,plain,
% 1.14/1.32 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1004, 197, 988, 275, 2213, 605, 449])).
% 1.14/1.32 tff(2215,plain,
% 1.14/1.32 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[571, 2214, 2202])).
% 1.14/1.32 tff(2216,plain,
% 1.14/1.32 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[960, 937])).
% 1.14/1.32 tff(2217,plain,
% 1.14/1.32 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.14/1.32 inference(symmetry,[status(thm)],[2216])).
% 1.14/1.32 tff(2218,plain,
% 1.14/1.32 ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[2217])).
% 1.14/1.32 tff(2219,assumption,(~r(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 1.14/1.32 tff(2220,plain,
% 1.14/1.32 (((~![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)))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(2221,plain,
% 1.14/1.32 ((~![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)))))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(2222,plain,
% 1.14/1.32 ((~![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))))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[2221, 2220])).
% 1.14/1.32 tff(2223,plain,
% 1.14/1.32 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[2222, 51, 2219, 2146])).
% 1.14/1.32 tff(2224,plain,
% 1.14/1.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(2225,plain,
% 1.14/1.32 (((~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(s(s(elem!1)))), 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(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(2226,plain,
% 1.14/1.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1)))), 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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[2225])).
% 1.14/1.32 tff(2227,plain,
% 1.14/1.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1)))), 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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.14/1.33 inference(transitivity,[status(thm)],[2226, 2224])).
% 1.14/1.33 tff(2228,plain,
% 1.14/1.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1)))), 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))))))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(2229,plain,
% 1.14/1.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2228, 2227])).
% 1.14/1.33 tff(2230,plain,
% 1.14/1.33 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2229, 319, 116, 1021, 2223])).
% 1.14/1.33 tff(2231,plain,
% 1.14/1.33 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2230, 2218])).
% 1.14/1.33 tff(2232,plain,
% 1.14/1.33 ((~(s(s(s(z))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(s(z)))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[1496])).
% 1.14/1.33 tff(2233,plain,
% 1.14/1.33 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 1.14/1.33 inference(commutativity,[status(thm)],[])).
% 1.14/1.33 tff(2234,assumption,(s(s(s(z))) = s(s(s(s(z))))), introduced(assumption)).
% 1.14/1.33 tff(2235,plain,
% 1.14/1.33 ((s(s(s(z))) = s(s(z))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[2234])).
% 1.14/1.33 tff(2236,plain,
% 1.14/1.33 ((s(s(s(z))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 1.14/1.33 inference(transitivity,[status(thm)],[2235, 2233])).
% 1.14/1.33 tff(2237,plain,
% 1.14/1.33 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(z))) = s(s(z)))),
% 1.14/1.33 inference(symmetry,[status(thm)],[2236])).
% 1.14/1.33 tff(2238,plain,
% 1.14/1.33 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(z))))) = s(s(s(z))))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(2239,plain,
% 1.14/1.33 (inj_0(s(s(s(s(z))))) = s(s(s(z)))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2238, 11])).
% 1.14/1.33 tff(2240,plain,
% 1.14/1.33 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(z)))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[2234])).
% 1.14/1.33 tff(2241,plain,
% 1.14/1.33 (s(s(z)) = s(s(s(s(z))))),
% 1.14/1.33 inference(transitivity,[status(thm)],[18, 2240, 2239, 2234])).
% 1.14/1.33 tff(2242,plain,
% 1.14/1.33 (s(s(s(z))) = s(s(z))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2241, 2237])).
% 1.14/1.33 tff(2243,assumption,(s(s(s(z))) = s(s(z))), introduced(assumption)).
% 1.14/1.33 tff(2244,plain,
% 1.14/1.33 (s(s(z)) = s(s(s(z)))),
% 1.14/1.33 inference(symmetry,[status(thm)],[2243])).
% 1.14/1.33 tff(2245,plain,
% 1.14/1.33 (inj_0(s(s(z))) = inj_0(s(s(s(z))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[2244])).
% 1.14/1.33 tff(2246,plain,
% 1.14/1.33 (s(z) = s(s(z))),
% 1.14/1.33 inference(transitivity,[status(thm)],[127, 2245, 17])).
% 1.14/1.33 tff(2247,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[680, 2246])).
% 1.14/1.33 tff(2248,plain,(~(s(s(s(z))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.33 tff(2249,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2248, 2242])).
% 1.14/1.33 tff(2250,plain,(~(s(s(s(z))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.33 tff(2251,plain,
% 1.14/1.33 (~(s(s(s(s(z)))) = s(s(s(z))))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2250, 2232])).
% 1.14/1.33 tff(2252,plain,
% 1.14/1.33 (b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1519, 2251])).
% 1.14/1.33 tff(2253,plain,
% 1.14/1.33 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2252, 2231])).
% 1.14/1.33 tff(2254,plain,
% 1.14/1.33 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2253, 1494])).
% 1.14/1.33 tff(2255,plain,
% 1.14/1.33 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(2256,plain,
% 1.14/1.33 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(2257,plain,
% 1.14/1.33 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2256, 2255])).
% 1.14/1.33 tff(2258,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2257, 297, 461, 1117, 1335])).
% 1.14/1.33 tff(2259,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.33 tff(2260,plain,
% 1.14/1.33 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2259, 2254, 461])).
% 1.14/1.33 tff(2261,plain,
% 1.14/1.33 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[616, 2260, 605])).
% 1.14/1.33 tff(2262,plain,
% 1.14/1.33 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1002, 319, 275, 449, 2261])).
% 1.14/1.33 tff(2263,plain,
% 1.14/1.33 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[595, 2262, 2213])).
% 1.14/1.33 tff(2264,plain,
% 1.14/1.33 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1712, 2263, 449, 1418, 1522, 275, 2261])).
% 1.14/1.33 tff(2265,plain,
% 1.14/1.33 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1320, 2264, 1060])).
% 1.14/1.33 tff(2266,plain,
% 1.14/1.33 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1724, 297, 461, 2265])).
% 1.14/1.33 tff(2267,plain,
% 1.14/1.33 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1408, 2202])).
% 1.14/1.33 tff(2268,plain,
% 1.14/1.33 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1412, 51, 2267, 2266])).
% 1.14/1.33 tff(2269,plain,
% 1.14/1.33 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1232, 297, 462, 2265])).
% 1.14/1.33 tff(2270,plain,
% 1.14/1.33 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1239, 2213])).
% 1.14/1.33 tff(2271,plain,
% 1.14/1.33 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1243, 51, 2270, 2269])).
% 1.14/1.33 tff(2272,plain,
% 1.14/1.33 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[937, 960])).
% 1.14/1.33 tff(2273,plain,
% 1.14/1.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(2274,plain,
% 1.14/1.33 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(2275,plain,
% 1.14/1.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[2274])).
% 1.14/1.33 tff(2276,plain,
% 1.14/1.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.14/1.33 inference(transitivity,[status(thm)],[2275, 2273])).
% 1.14/1.33 tff(2277,plain,
% 1.14/1.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(2278,plain,
% 1.14/1.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2277, 2276])).
% 1.14/1.33 tff(2279,plain,
% 1.14/1.33 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2278, 319, 116, 1021, 2223])).
% 1.14/1.33 tff(2280,plain,
% 1.14/1.33 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2027, 2279, 133])).
% 1.14/1.33 tff(2281,plain,
% 1.14/1.33 (b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1018, 2250])).
% 1.14/1.33 tff(2282,plain,
% 1.14/1.33 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2281, 2280])).
% 1.14/1.33 tff(2283,plain,
% 1.14/1.33 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2282, 2272])).
% 1.14/1.33 tff(2284,assumption,(b(s(elem!1), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.14/1.33 tff(2285,plain,
% 1.14/1.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(2286,plain,
% 1.14/1.33 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(2287,plain,
% 1.14/1.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[2286])).
% 1.14/1.33 tff(2288,plain,
% 1.14/1.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.14/1.33 inference(transitivity,[status(thm)],[2287, 2285])).
% 1.14/1.33 tff(2289,plain,
% 1.14/1.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(2290,plain,
% 1.14/1.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2289, 2288])).
% 1.14/1.33 tff(2291,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2290, 319, 275, 449, 1445, 2284])).
% 1.14/1.33 tff(2292,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.33 tff(2293,plain,
% 1.14/1.33 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2292, 2261, 449, 275])).
% 1.14/1.33 tff(2294,plain,
% 1.14/1.33 (~b(s(z), s(s(s(s(z)))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1379, 2293, 133])).
% 1.14/1.33 tff(2295,plain,
% 1.14/1.33 (inj_0(s(z)) = inj_0(s(s(s(s(z)))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[1353])).
% 1.14/1.33 tff(2296,plain,
% 1.14/1.33 (inj_0(s(s(s(s(z))))) = inj_0(s(z))),
% 1.14/1.33 inference(symmetry,[status(thm)],[2295])).
% 1.14/1.33 tff(2297,plain,
% 1.14/1.33 (s(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 1.14/1.33 inference(symmetry,[status(thm)],[2239])).
% 1.14/1.33 tff(2298,plain,
% 1.14/1.33 (s(s(s(z))) = z),
% 1.14/1.33 inference(transitivity,[status(thm)],[2297, 2296, 13])).
% 1.14/1.33 tff(2299,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[898, 2298])).
% 1.14/1.33 tff(2300,plain,(~(s(z) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.33 tff(2301,plain,
% 1.14/1.33 (b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1371, 2300])).
% 1.14/1.33 tff(2302,plain,
% 1.14/1.33 (r(s(z), s(s(s(s(z)))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2301, 2294])).
% 1.14/1.33 tff(2303,plain,
% 1.14/1.33 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2041, 2302, 2283, 133])).
% 1.14/1.33 tff(2304,plain,
% 1.14/1.33 (b(s(s(s(elem!1))), s(elem!1))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[958, 2303, 183])).
% 1.14/1.33 tff(2305,plain,
% 1.14/1.33 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1600, 2302, 133, 2282])).
% 1.14/1.33 tff(2306,plain,
% 1.14/1.33 (b(s(elem!1), s(s(s(elem!1))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[434, 2305, 1114])).
% 1.14/1.33 tff(2307,plain,
% 1.14/1.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(2308,plain,
% 1.14/1.33 (((~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(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(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(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(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(2309,plain,
% 1.14/1.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[2308])).
% 1.14/1.33 tff(2310,plain,
% 1.14/1.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.14/1.33 inference(transitivity,[status(thm)],[2309, 2307])).
% 1.14/1.33 tff(2311,plain,
% 1.14/1.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(2312,plain,
% 1.14/1.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2311, 2310])).
% 1.14/1.33 tff(2313,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2312, 319, 2306, 2304, 116, 2223, 2271, 2268])).
% 1.14/1.33 tff(2314,plain,((~r(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~(s(s(z)) = s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.33 tff(2315,plain,
% 1.14/1.33 (~r(s(s(s(elem!1))), elem!1)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2314, 2215, 462, 449, 1522, 275, 133, 116, 2199, 2146])).
% 1.14/1.33 tff(2316,plain,
% 1.14/1.33 (b(s(s(s(elem!1))), elem!1)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[361, 2315, 249])).
% 1.14/1.33 tff(2317,plain,
% 1.14/1.33 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2188, 319, 275, 449, 2316])).
% 1.14/1.33 tff(2318,plain,
% 1.14/1.33 (r(s(elem!1), s(s(s(elem!1))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[434, 2317, 1114])).
% 1.14/1.33 tff(2319,plain,
% 1.14/1.33 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2222, 51, 2199, 2146])).
% 1.14/1.33 tff(2320,plain,
% 1.14/1.33 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2278, 319, 116, 2215, 2319])).
% 1.14/1.33 tff(2321,plain,
% 1.14/1.33 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2027, 2320, 133])).
% 1.14/1.33 tff(2322,plain,
% 1.14/1.33 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2281, 2321])).
% 1.14/1.33 tff(2323,plain,
% 1.14/1.33 (~r(s(z), s(s(s(s(z)))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1600, 2322, 133, 2318])).
% 1.14/1.33 tff(2324,plain,
% 1.14/1.33 (b(s(z), s(s(s(s(z)))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2301, 2323])).
% 1.14/1.33 tff(2325,plain,
% 1.14/1.33 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1379, 2324, 133])).
% 1.14/1.33 tff(2326,plain,
% 1.14/1.33 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2292, 2325, 449, 275])).
% 1.14/1.33 tff(2327,plain,
% 1.14/1.33 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[616, 2326, 605])).
% 1.14/1.33 tff(2328,plain,
% 1.14/1.33 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.14/1.33 inference(transitivity,[status(thm)],[2200, 2132])).
% 1.14/1.33 tff(2329,plain,
% 1.14/1.33 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[2328])).
% 1.14/1.33 tff(2330,plain,
% 1.14/1.33 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2140, 2329])).
% 1.14/1.33 tff(2331,plain,
% 1.14/1.33 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1255, 297, 462, 2327])).
% 1.14/1.33 tff(2332,plain,
% 1.14/1.33 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1259, 51, 2331, 2330])).
% 1.14/1.33 tff(2333,plain,
% 1.14/1.33 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1232, 297, 462, 1134])).
% 1.14/1.33 tff(2334,plain,
% 1.14/1.33 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1243, 51, 1785, 2333])).
% 1.14/1.33 tff(2335,plain,
% 1.14/1.33 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1146, 51, 1522, 1143])).
% 1.14/1.33 tff(2336,assumption,(b(s(s(elem!1)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.14/1.33 tff(2337,plain,
% 1.14/1.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(2338,plain,
% 1.14/1.33 (((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), 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(s(elem!1))))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(2339,plain,
% 1.14/1.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), 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(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[2338])).
% 1.14/1.33 tff(2340,plain,
% 1.14/1.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), 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(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.14/1.33 inference(transitivity,[status(thm)],[2339, 2337])).
% 1.14/1.33 tff(2341,plain,
% 1.14/1.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), 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(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(2342,plain,
% 1.14/1.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[2341, 2340])).
% 1.14/1.33 tff(2343,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2342, 319, 1021, 2336, 2335, 2334])).
% 1.14/1.33 tff(2344,plain,((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.33 tff(2345,plain,
% 1.14/1.33 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2344, 2215, 2332, 1522, 2270, 2327, 462])).
% 1.14/1.33 tff(2346,plain,
% 1.14/1.33 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1320, 2345, 1060])).
% 1.14/1.33 tff(2347,plain,
% 1.14/1.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(2348,plain,
% 1.14/1.33 (((~b(elem!1, s(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(elem!1))), 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))), 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))))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(2349,plain,
% 1.14/1.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[2348])).
% 1.14/1.34 tff(2350,plain,
% 1.14/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.14/1.34 inference(transitivity,[status(thm)],[2349, 2347])).
% 1.14/1.34 tff(2351,plain,
% 1.14/1.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(2352,plain,
% 1.14/1.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[2351, 2350])).
% 1.14/1.34 tff(2353,plain,
% 1.14/1.34 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2352, 319, 275, 2316, 2346])).
% 1.14/1.34 tff(2354,plain,
% 1.14/1.34 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1412, 51, 2267, 2353])).
% 1.14/1.34 tff(2355,plain,
% 1.14/1.34 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1704, 319, 275, 449, 2346])).
% 1.14/1.34 tff(2356,plain,
% 1.14/1.34 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1291, 51, 1418, 2355])).
% 1.14/1.34 tff(2357,plain,
% 1.14/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(2358,plain,
% 1.14/1.34 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(2359,plain,
% 1.14/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[2358])).
% 1.14/1.34 tff(2360,plain,
% 1.14/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.14/1.34 inference(transitivity,[status(thm)],[2359, 2357])).
% 1.14/1.34 tff(2361,plain,
% 1.14/1.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(2362,plain,
% 1.14/1.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[2361, 2360])).
% 1.14/1.34 tff(2363,plain,
% 1.14/1.34 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2362, 319, 275, 449, 2316])).
% 1.14/1.34 tff(2364,plain,
% 1.14/1.34 (r(s(s(s(elem!1))), s(elem!1))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[958, 2363, 183])).
% 1.14/1.34 tff(2365,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1929, 297, 2364, 2356, 2354])).
% 1.14/1.34 tff(2366,plain,((~r(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~(s(s(z)) = s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(2367,plain,
% 1.14/1.34 (~r(s(elem!1), s(s(elem!1)))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2366, 2180, 2162, 1522, 2148, 123, 116, 2146, 2145])).
% 1.14/1.34 tff(2368,plain,
% 1.14/1.34 (b(s(elem!1), s(s(elem!1)))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[807, 2367, 2142])).
% 1.14/1.34 tff(2369,plain,
% 1.14/1.34 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[2133])).
% 1.14/1.34 tff(2370,plain,
% 1.14/1.34 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[2140, 2369])).
% 1.14/1.34 tff(2371,plain,
% 1.14/1.34 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.14/1.34 inference(symmetry,[status(thm)],[124])).
% 1.14/1.34 tff(2372,plain,
% 1.14/1.34 (s(elem!1) = s(z)),
% 1.14/1.34 inference(transitivity,[status(thm)],[206, 2371, 126])).
% 1.14/1.34 tff(2373,plain,
% 1.14/1.34 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(z))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[2372])).
% 1.14/1.34 tff(2374,plain,
% 1.14/1.34 (r(s(s(elem!1)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 1.14/1.34 inference(symmetry,[status(thm)],[2373])).
% 1.14/1.34 tff(2375,plain,
% 1.14/1.34 (r(s(s(elem!1)), s(elem!1))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[2128, 2374])).
% 1.14/1.34 tff(2376,plain,
% 1.14/1.34 ((s(z) = s(s(s(s(elem!1))))) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[128])).
% 1.14/1.34 tff(2377,plain,
% 1.14/1.34 ((s(z) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 1.14/1.34 inference(transitivity,[status(thm)],[2376, 2203])).
% 1.14/1.34 tff(2378,plain,
% 1.14/1.34 ((~(s(z) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[2377])).
% 1.14/1.34 tff(2379,plain,
% 1.14/1.34 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[2212, 2378])).
% 1.14/1.34 tff(2380,plain,
% 1.14/1.34 (b(z, s(elem!1)) <=> b(elem!1, s(elem!1))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[2144])).
% 1.14/1.34 tff(2381,plain,
% 1.14/1.34 (b(elem!1, s(elem!1)) <=> b(z, s(elem!1))),
% 1.14/1.34 inference(symmetry,[status(thm)],[2380])).
% 1.14/1.34 tff(2382,plain,
% 1.14/1.34 (b(z, s(elem!1))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[2180, 2381])).
% 1.14/1.34 tff(2383,plain,
% 1.14/1.34 (b(s(elem!1), z)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1176, 2162, 2144])).
% 1.14/1.34 tff(2384,plain,
% 1.14/1.34 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.14/1.34 inference(monotonicity,[status(thm)],[391])).
% 1.14/1.34 tff(2385,plain,
% 1.14/1.34 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(elem!1)))), z)),
% 1.14/1.34 inference(symmetry,[status(thm)],[2384])).
% 1.14/1.34 tff(2386,plain,
% 1.14/1.34 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1119, 984, 988])).
% 1.14/1.34 tff(2387,plain,
% 1.14/1.34 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[616, 2386, 1163])).
% 1.14/1.34 tff(2388,plain,
% 1.14/1.34 (b(s(s(s(s(elem!1)))), z)),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[2387, 2385])).
% 1.14/1.34 tff(2389,assumption,(b(z, s(elem!1))), introduced(assumption)).
% 1.14/1.34 tff(2390,assumption,(r(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 1.14/1.34 tff(2391,plain,
% 1.14/1.34 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(2392,plain,
% 1.14/1.34 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(2393,plain,
% 1.14/1.34 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[2392, 2391])).
% 1.14/1.34 tff(2394,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2393, 297, 2390, 984, 620])).
% 1.14/1.34 tff(2395,plain,((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(2396,plain,
% 1.14/1.34 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2395, 984, 2390])).
% 1.14/1.34 tff(2397,plain,
% 1.14/1.34 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[595, 2396, 590])).
% 1.14/1.34 tff(2398,assumption,(b(s(s(s(s(elem!1)))), z)), introduced(assumption)).
% 1.14/1.34 tff(2399,plain,
% 1.14/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(2400,plain,
% 1.14/1.34 (((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(2401,plain,
% 1.14/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[2400])).
% 1.14/1.34 tff(2402,plain,
% 1.14/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.14/1.34 inference(transitivity,[status(thm)],[2401, 2399])).
% 1.14/1.34 tff(2403,plain,
% 1.14/1.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(2404,plain,
% 1.14/1.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[2403, 2402])).
% 1.14/1.34 tff(2405,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2404, 319, 2389, 786, 547, 2398])).
% 1.14/1.34 tff(2406,plain,((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(2407,plain,
% 1.14/1.34 (~b(s(s(s(s(elem!1)))), z)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2406, 2397, 786, 2389])).
% 1.14/1.34 tff(2408,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2407, 2388])).
% 1.14/1.34 tff(2409,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~(z = elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(2410,plain,
% 1.14/1.34 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2409, 2144, 2383, 2382, 2379, 2145, 2375])).
% 1.14/1.34 tff(2411,plain,
% 1.14/1.34 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[571, 2410, 2370])).
% 1.14/1.34 tff(2412,plain,
% 1.14/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(2413,plain,
% 1.14/1.34 (((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(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(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(2414,plain,
% 1.14/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[2413])).
% 1.14/1.34 tff(2415,plain,
% 1.14/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.14/1.34 inference(transitivity,[status(thm)],[2414, 2412])).
% 1.14/1.34 tff(2416,plain,
% 1.14/1.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(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))))))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(2417,plain,
% 1.14/1.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[2416, 2415])).
% 1.14/1.34 tff(2418,plain,
% 1.14/1.34 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2417, 319, 785, 116, 2336])).
% 1.14/1.34 tff(2419,plain,
% 1.14/1.34 (r(s(elem!1), s(s(s(elem!1))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[434, 2418, 1114])).
% 1.14/1.34 tff(2420,plain,
% 1.14/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(2421,plain,
% 1.14/1.34 (((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(2422,plain,
% 1.14/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[2421])).
% 1.14/1.34 tff(2423,plain,
% 1.14/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.14/1.34 inference(transitivity,[status(thm)],[2422, 2420])).
% 1.14/1.34 tff(2424,plain,
% 1.14/1.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(2425,plain,
% 1.14/1.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[2424, 2423])).
% 1.14/1.34 tff(2426,plain,
% 1.14/1.34 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2425, 319, 785, 1021, 2336])).
% 1.14/1.34 tff(2427,plain,
% 1.14/1.34 (~b(s(z), s(s(s(s(z)))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1379, 2426, 133])).
% 1.14/1.34 tff(2428,plain,
% 1.14/1.34 (r(s(z), s(s(s(s(z)))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2301, 2427])).
% 1.14/1.34 tff(2429,plain,
% 1.14/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(2430,plain,
% 1.14/1.34 (((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(2431,plain,
% 1.14/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[2430])).
% 1.14/1.34 tff(2432,plain,
% 1.14/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.14/1.34 inference(transitivity,[status(thm)],[2431, 2429])).
% 1.14/1.34 tff(2433,plain,
% 1.14/1.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(2434,plain,
% 1.14/1.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[2433, 2432])).
% 1.14/1.35 tff(2435,plain,
% 1.14/1.35 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2434, 319, 116, 1021, 2336])).
% 1.14/1.35 tff(2436,plain,
% 1.14/1.35 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2027, 2435, 133])).
% 1.14/1.35 tff(2437,plain,
% 1.14/1.35 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2281, 2436])).
% 1.14/1.35 tff(2438,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1600, 2437, 2428, 133, 2419])).
% 1.14/1.35 tff(2439,plain,((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~(s(s(z)) = s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(2440,plain,
% 1.14/1.35 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2439, 123, 116, 2411, 2368])).
% 1.14/1.35 tff(2441,plain,
% 1.14/1.35 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1259, 51, 2440, 2141])).
% 1.14/1.35 tff(2442,plain,
% 1.14/1.35 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[2441, 2130])).
% 1.14/1.35 tff(2443,assumption,(r(s(s(elem!1)), s(s(s(s(z)))))), introduced(assumption)).
% 1.14/1.35 tff(2444,assumption,(r(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.14/1.35 tff(2445,plain,
% 1.14/1.35 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(2446,plain,
% 1.14/1.35 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~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)))))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(2447,plain,
% 1.14/1.35 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[2446])).
% 1.14/1.35 tff(2448,plain,
% 1.14/1.35 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.14/1.35 inference(transitivity,[status(thm)],[2447, 2445])).
% 1.14/1.35 tff(2449,plain,
% 1.14/1.35 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(2450,plain,
% 1.14/1.35 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[2449, 2448])).
% 1.14/1.35 tff(2451,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2450, 297, 2169, 2444, 2443])).
% 1.14/1.35 tff(2452,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(2453,plain,
% 1.14/1.35 (~r(s(s(s(s(z)))), s(z))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2452, 2442, 2128])).
% 1.14/1.35 tff(2454,plain,
% 1.14/1.35 ((s(z) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(z))),
% 1.14/1.35 inference(symmetry,[status(thm)],[1349])).
% 1.14/1.35 tff(2455,plain,
% 1.14/1.35 ((~(s(z) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(z)))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[2454])).
% 1.14/1.35 tff(2456,plain,
% 1.14/1.35 (~(s(s(s(s(z)))) = s(z))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[2300, 2455])).
% 1.14/1.35 tff(2457,plain,
% 1.14/1.35 (((~![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)))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(2458,plain,
% 1.14/1.35 ((~![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)))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(2459,plain,
% 1.14/1.35 ((~![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))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[2458, 2457])).
% 1.14/1.35 tff(2460,plain,
% 1.14/1.35 ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2459, 51])).
% 1.14/1.35 tff(2461,plain,
% 1.14/1.35 (b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2460, 2456])).
% 1.14/1.35 tff(2462,plain,
% 1.14/1.35 (b(s(s(s(s(z)))), s(z))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2461, 2453])).
% 1.14/1.35 tff(2463,plain,
% 1.14/1.35 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[2462, 131])).
% 1.14/1.35 tff(2464,plain,
% 1.14/1.35 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.14/1.35 inference(monotonicity,[status(thm)],[130])).
% 1.14/1.35 tff(2465,plain,
% 1.14/1.35 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(z)))), elem!1)),
% 1.14/1.35 inference(monotonicity,[status(thm)],[2144])).
% 1.14/1.35 tff(2466,plain,
% 1.14/1.35 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.14/1.35 inference(transitivity,[status(thm)],[2465, 2464])).
% 1.14/1.35 tff(2467,assumption,(r(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.14/1.35 tff(2468,plain,
% 1.14/1.35 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(2469,plain,
% 1.14/1.35 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(2470,plain,
% 1.14/1.35 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[2469])).
% 1.14/1.35 tff(2471,plain,
% 1.14/1.35 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.14/1.35 inference(transitivity,[status(thm)],[2470, 2468])).
% 1.14/1.35 tff(2472,plain,
% 1.14/1.35 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(2473,plain,
% 1.14/1.35 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[2472, 2471])).
% 1.14/1.35 tff(2474,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2473, 297, 115, 2467, 2443])).
% 1.14/1.35 tff(2475,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(2476,plain,
% 1.14/1.35 (~r(s(s(s(s(z)))), z)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2475, 2442, 115])).
% 1.14/1.35 tff(2477,plain,
% 1.14/1.35 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(z)))) = z))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(2478,plain,
% 1.14/1.35 (~(s(s(s(s(z)))) = z)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2477, 26])).
% 1.14/1.35 tff(2479,plain,
% 1.14/1.35 (((~![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))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(2480,plain,
% 1.14/1.35 ((~![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))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(2481,plain,
% 1.14/1.35 ((~![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)),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[2480, 2479])).
% 1.14/1.35 tff(2482,plain,
% 1.14/1.35 (b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2481, 51, 2478])).
% 1.14/1.35 tff(2483,plain,
% 1.14/1.35 (b(s(s(s(s(z)))), z)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2482, 2476])).
% 1.14/1.35 tff(2484,plain,
% 1.14/1.35 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[2483, 2466])).
% 1.14/1.35 tff(2485,plain,
% 1.14/1.35 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(2486,plain,
% 1.14/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[2485])).
% 1.14/1.35 tff(2487,plain,
% 1.14/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.14/1.35 inference(transitivity,[status(thm)],[2486, 997])).
% 1.14/1.35 tff(2488,plain,
% 1.14/1.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(2489,plain,
% 1.14/1.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[2488, 2487])).
% 1.14/1.35 tff(2490,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2489, 319, 2180, 2162, 2484, 2463])).
% 1.14/1.35 tff(2491,plain,(b(s(s(z)), s(s(elem!1))) | (~r(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | (s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | r(s(z), z) | r(s(s(z)), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(2492,plain,
% 1.14/1.35 (b(s(s(z)), s(s(elem!1)))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2491, 116, 115, 114, 108, 81, 70, 59, 69])).
% 1.14/1.35 tff(2493,assumption,(b(s(z), z)), introduced(assumption)).
% 1.14/1.35 tff(2494,plain,
% 1.14/1.35 ((s(s(elem!1)) = s(elem!1)) <=> (s(elem!1) = s(s(elem!1)))),
% 1.14/1.35 inference(commutativity,[status(thm)],[])).
% 1.14/1.35 tff(2495,plain,
% 1.14/1.35 ((s(elem!1) = s(s(elem!1))) <=> (s(s(elem!1)) = s(elem!1))),
% 1.14/1.35 inference(symmetry,[status(thm)],[2494])).
% 1.14/1.35 tff(2496,plain,
% 1.14/1.35 ((~(s(elem!1) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[2495])).
% 1.14/1.35 tff(2497,plain,
% 1.14/1.35 (~(s(s(elem!1)) = s(elem!1))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[114, 2496])).
% 1.14/1.35 tff(2498,plain,
% 1.14/1.35 (~(s(elem!1) = s(z))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[774, 772])).
% 1.14/1.35 tff(2499,plain,
% 1.14/1.35 ((s(elem!1) = s(z)) <=> (s(z) = s(elem!1))),
% 1.14/1.35 inference(commutativity,[status(thm)],[])).
% 1.14/1.35 tff(2500,plain,
% 1.14/1.35 ((s(z) = s(elem!1)) <=> (s(elem!1) = s(z))),
% 1.14/1.35 inference(symmetry,[status(thm)],[2499])).
% 1.14/1.35 tff(2501,plain,
% 1.14/1.35 (s(elem!1) = s(z)),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[142, 2500])).
% 1.14/1.35 tff(2502,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[776, 2501])).
% 1.14/1.35 tff(2503,plain,((~(s(z) = s(elem!1))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(2504,plain,
% 1.14/1.35 (~(s(z) = s(elem!1))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2503, 2498])).
% 1.14/1.35 tff(2505,assumption,(s(s(s(z))) = s(s(s(elem!1)))), introduced(assumption)).
% 1.14/1.35 tff(2506,plain,
% 1.14/1.35 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[2505])).
% 1.14/1.35 tff(2507,plain,
% 1.14/1.35 (s(s(z)) = s(s(elem!1))),
% 1.14/1.35 inference(transitivity,[status(thm)],[18, 2506, 83])).
% 1.14/1.35 tff(2508,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[772, 2507])).
% 1.14/1.35 tff(2509,plain,((~(s(s(s(z))) = s(s(s(elem!1))))) | (s(s(z)) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(2510,plain,
% 1.14/1.35 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2509, 772])).
% 1.14/1.35 tff(2511,assumption,(r(s(s(z)), s(z))), introduced(assumption)).
% 1.14/1.35 tff(2512,assumption,(~b(s(elem!1), s(s(z)))), introduced(assumption)).
% 1.14/1.35 tff(2513,plain,
% 1.14/1.35 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(z)) = s(s(s(elem!1))))),
% 1.14/1.35 inference(commutativity,[status(thm)],[])).
% 1.14/1.35 tff(2514,plain,
% 1.14/1.35 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 1.14/1.35 inference(symmetry,[status(thm)],[2513])).
% 1.14/1.35 tff(2515,plain,
% 1.14/1.35 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(z))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[2514])).
% 1.14/1.35 tff(2516,plain,
% 1.14/1.35 (~(s(s(s(elem!1))) = s(s(z)))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[231, 2515])).
% 1.14/1.35 tff(2517,plain,
% 1.14/1.35 ((s(s(elem!1)) = s(s(z))) <=> (s(s(z)) = s(s(elem!1)))),
% 1.14/1.35 inference(commutativity,[status(thm)],[])).
% 1.14/1.35 tff(2518,assumption,(s(s(elem!1)) = s(s(z))), introduced(assumption)).
% 1.14/1.35 tff(2519,plain,
% 1.14/1.35 (s(s(z)) = s(s(elem!1))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[2518, 2517])).
% 1.14/1.35 tff(2520,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[772, 2519])).
% 1.14/1.35 tff(2521,plain,((~(s(s(elem!1)) = s(s(z)))) | (s(s(z)) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(2522,plain,
% 1.14/1.35 (~(s(s(elem!1)) = s(s(z)))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2521, 772])).
% 1.14/1.35 tff(2523,assumption,(~(s(elem!1) = s(s(z)))), introduced(assumption)).
% 1.14/1.35 tff(2524,assumption,(~r(s(elem!1), s(s(z)))), introduced(assumption)).
% 1.14/1.35 tff(2525,plain,
% 1.14/1.35 (((~![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))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(2526,plain,
% 1.14/1.35 ((~![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))))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(2527,plain,
% 1.14/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z)))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[2526, 2525])).
% 1.14/1.35 tff(2528,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2527, 51, 2512, 2523, 2524])).
% 1.14/1.35 tff(2529,plain,(b(s(elem!1), s(s(z))) | (s(elem!1) = s(s(z))) | r(s(elem!1), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(2530,plain,
% 1.14/1.35 (r(s(elem!1), s(s(z)))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2529, 2523, 2512])).
% 1.14/1.35 tff(2531,plain,
% 1.14/1.35 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(z))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(2532,plain,
% 1.14/1.35 (((~r(s(s(z)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(z))))) <=> ((~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(z))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(2533,plain,
% 1.14/1.35 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(z)))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[2532])).
% 1.14/1.35 tff(2534,plain,
% 1.14/1.35 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(z))))),
% 1.14/1.35 inference(transitivity,[status(thm)],[2533, 2531])).
% 1.14/1.35 tff(2535,plain,
% 1.14/1.35 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(z)))))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(2536,plain,
% 1.14/1.35 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(z)))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[2535, 2534])).
% 1.14/1.35 tff(2537,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2536, 297, 203, 800, 2511])).
% 1.14/1.35 tff(2538,plain,((~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(2539,plain,
% 1.14/1.35 (~r(s(elem!1), s(z))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2538, 2530, 2511])).
% 1.14/1.35 tff(2540,plain,
% 1.14/1.35 (b(s(elem!1), s(z))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[783, 2539, 2498])).
% 1.14/1.35 tff(2541,assumption,(b(s(elem!1), s(z))), introduced(assumption)).
% 1.14/1.35 tff(2542,assumption,(~(s(s(elem!1)) = s(s(z)))), introduced(assumption)).
% 1.14/1.35 tff(2543,assumption,(b(s(s(elem!1)), s(s(z)))), introduced(assumption)).
% 1.14/1.35 tff(2544,plain,
% 1.14/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(2545,plain,
% 1.14/1.35 (((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(2546,plain,
% 1.14/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1))))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[2545])).
% 1.14/1.35 tff(2547,plain,
% 1.14/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.14/1.35 inference(transitivity,[status(thm)],[2546, 2544])).
% 1.14/1.35 tff(2548,plain,
% 1.14/1.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(2549,plain,
% 1.14/1.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1))))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[2548, 2547])).
% 1.14/1.35 tff(2550,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2549, 319, 2541, 2543, 785, 817])).
% 1.14/1.35 tff(2551,plain,((~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(2552,plain,
% 1.14/1.35 (~b(s(s(elem!1)), s(s(z)))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2551, 817, 785, 2541])).
% 1.14/1.35 tff(2553,plain,
% 1.14/1.35 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(z))) | b(s(s(elem!1)), s(s(z))) | r(s(s(elem!1)), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(z))) | b(s(s(elem!1)), s(s(z))) | r(s(s(elem!1)), s(s(z))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(2554,plain,
% 1.14/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(z))) | b(s(s(elem!1)), s(s(z))) | r(s(s(elem!1)), s(s(z))))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(2555,plain,
% 1.14/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(z))) | b(s(s(elem!1)), s(s(z))) | r(s(s(elem!1)), s(s(z)))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[2554, 2553])).
% 1.14/1.35 tff(2556,plain,
% 1.14/1.35 (r(s(s(elem!1)), s(s(z)))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2555, 51, 2552, 2542])).
% 1.14/1.35 tff(2557,assumption,(r(s(s(elem!1)), s(s(z)))), introduced(assumption)).
% 1.14/1.35 tff(2558,plain,
% 1.14/1.35 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(2559,plain,
% 1.14/1.35 (((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(2560,plain,
% 1.14/1.35 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z))))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[2559])).
% 1.14/1.36 tff(2561,plain,
% 1.14/1.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.14/1.36 inference(transitivity,[status(thm)],[2560, 2558])).
% 1.14/1.36 tff(2562,plain,
% 1.14/1.36 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(2563,plain,
% 1.14/1.36 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z))))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[2562, 2561])).
% 1.14/1.36 tff(2564,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2563, 297, 2169, 2511, 2557])).
% 1.14/1.36 tff(2565,plain,((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(2566,plain,
% 1.14/1.36 (~r(s(s(elem!1)), s(z))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2565, 2556, 2511])).
% 1.14/1.36 tff(2567,plain,
% 1.14/1.36 (b(s(s(elem!1)), s(z))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[871, 2566])).
% 1.14/1.36 tff(2568,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(2569,plain,
% 1.14/1.36 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(2570,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1))))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[2569])).
% 1.14/1.36 tff(2571,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.14/1.36 inference(transitivity,[status(thm)],[2570, 2568])).
% 1.14/1.36 tff(2572,plain,
% 1.14/1.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(2573,plain,
% 1.14/1.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1))))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[2572, 2571])).
% 1.14/1.36 tff(2574,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2573, 319, 2567, 2541, 785, 817])).
% 1.14/1.36 tff(2575,plain,((~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (s(s(elem!1)) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(2576,plain,
% 1.14/1.36 (~b(s(z), s(s(elem!1)))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2575, 2540, 785, 2511, 2522])).
% 1.14/1.36 tff(2577,plain,
% 1.14/1.36 (r(s(z), s(s(elem!1)))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1047, 2576])).
% 1.14/1.36 tff(2578,assumption,(r(s(s(z)), s(s(elem!1)))), introduced(assumption)).
% 1.14/1.36 tff(2579,plain,
% 1.14/1.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(2580,plain,
% 1.14/1.36 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(2581,plain,
% 1.14/1.36 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z)))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[2580, 2579])).
% 1.14/1.36 tff(2582,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2581, 297, 444, 2578, 2511])).
% 1.14/1.36 tff(2583,plain,((~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(2584,plain,
% 1.14/1.36 (~r(s(s(z)), s(s(elem!1)))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2583, 2577, 2511])).
% 1.14/1.36 tff(2585,plain,
% 1.14/1.36 (b(s(s(z)), s(s(elem!1)))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[122, 2584, 772])).
% 1.14/1.36 tff(2586,plain,
% 1.14/1.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(2587,plain,
% 1.14/1.36 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(2588,plain,
% 1.14/1.36 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z)))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[2587, 2586])).
% 1.14/1.36 tff(2589,plain,
% 1.14/1.36 (~r(z, s(z))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2588, 297, 2577, 70])).
% 1.14/1.36 tff(2590,plain,
% 1.14/1.36 (b(z, s(z))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1099, 2589])).
% 1.14/1.36 tff(2591,plain,
% 1.14/1.36 (~r(s(z), z)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[865, 2577, 70])).
% 1.14/1.36 tff(2592,plain,
% 1.14/1.36 (b(s(z), z)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[65, 51, 62, 2591])).
% 1.14/1.36 tff(2593,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)) | (~b(z, s(z))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(2594,plain,
% 1.14/1.36 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(elem!1), z))) <=> ((~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)) | (~b(z, s(z))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(2595,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)) | (~b(z, s(z)))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[2594])).
% 1.14/1.36 tff(2596,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)) | (~b(z, s(z))))),
% 1.14/1.36 inference(transitivity,[status(thm)],[2595, 2593])).
% 1.14/1.36 tff(2597,plain,
% 1.14/1.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(elem!1), z)))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(2598,plain,
% 1.14/1.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)) | (~b(z, s(z)))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[2597, 2596])).
% 1.14/1.36 tff(2599,plain,
% 1.14/1.36 (~b(s(elem!1), z)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2598, 319, 2540, 2590, 2592])).
% 1.14/1.36 tff(2600,assumption,(~r(s(elem!1), z)), introduced(assumption)).
% 1.14/1.36 tff(2601,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[744, 51, 193, 1174, 2600])).
% 1.14/1.36 tff(2602,plain,(b(s(elem!1), z) | r(s(elem!1), z)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(2603,plain,
% 1.14/1.36 (r(s(elem!1), z)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2602, 2599])).
% 1.14/1.36 tff(2604,assumption,(~b(s(s(z)), z)), introduced(assumption)).
% 1.14/1.36 tff(2605,plain,
% 1.14/1.36 (r(s(s(z)), z)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[663, 51, 28, 2604])).
% 1.14/1.36 tff(2606,plain,
% 1.14/1.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), z)))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(2607,plain,
% 1.14/1.36 (((~r(s(s(z)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z))))) <=> ((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), z)))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(2608,plain,
% 1.14/1.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), z))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[2607])).
% 1.14/1.36 tff(2609,plain,
% 1.14/1.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), z)))),
% 1.14/1.36 inference(transitivity,[status(thm)],[2608, 2606])).
% 1.14/1.36 tff(2610,plain,
% 1.14/1.36 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z)))))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(2611,plain,
% 1.14/1.36 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), z))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[2610, 2609])).
% 1.14/1.36 tff(2612,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2611, 297, 203, 731, 2605])).
% 1.14/1.36 tff(2613,plain,((~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), z)) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(2614,plain,
% 1.14/1.36 (b(s(s(z)), z)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2613, 731, 203])).
% 1.14/1.36 tff(2615,plain,
% 1.14/1.36 (~r(z, s(s(z)))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[740, 731, 203])).
% 1.14/1.36 tff(2616,plain,
% 1.14/1.36 (b(z, s(s(z)))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[729, 2615])).
% 1.14/1.36 tff(2617,plain,
% 1.14/1.36 (~r(s(z), z)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[865, 444, 70])).
% 1.14/1.36 tff(2618,plain,
% 1.14/1.36 (b(s(z), z)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[65, 51, 62, 2617])).
% 1.14/1.36 tff(2619,plain,
% 1.14/1.36 (~r(s(s(z)), s(s(elem!1)))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2583, 444, 2511])).
% 1.14/1.36 tff(2620,plain,
% 1.14/1.36 (b(s(s(z)), s(s(elem!1)))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[122, 2619, 772])).
% 1.14/1.36 tff(2621,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(2622,plain,
% 1.14/1.36 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z))))) <=> ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(2623,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1))))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[2622])).
% 1.14/1.36 tff(2624,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.14/1.36 inference(transitivity,[status(thm)],[2623, 2621])).
% 1.14/1.36 tff(2625,plain,
% 1.14/1.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(2626,plain,
% 1.14/1.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1))))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[2625, 2624])).
% 1.14/1.36 tff(2627,plain,
% 1.14/1.36 (~b(s(elem!1), s(s(z)))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2626, 319, 1, 785, 687])).
% 1.14/1.36 tff(2628,plain,
% 1.14/1.36 (r(s(elem!1), s(s(z)))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2527, 51, 2627, 2523])).
% 1.14/1.36 tff(2629,plain,
% 1.14/1.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(z), s(elem!1))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(2630,plain,
% 1.14/1.36 (((~r(s(elem!1), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(elem!1)))) <=> ((~r(s(z), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(z), s(elem!1))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(2631,plain,
% 1.14/1.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(z), s(elem!1)))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[2630])).
% 1.14/1.36 tff(2632,plain,
% 1.14/1.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(z), s(elem!1))))),
% 1.14/1.36 inference(transitivity,[status(thm)],[2631, 2629])).
% 1.14/1.36 tff(2633,plain,
% 1.14/1.36 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(elem!1))))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(2634,plain,
% 1.14/1.36 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(z), s(elem!1)))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[2633, 2632])).
% 1.14/1.36 tff(2635,plain,
% 1.14/1.36 (~r(s(z), s(elem!1))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2634, 297, 903, 2628])).
% 1.14/1.36 tff(2636,plain,
% 1.14/1.36 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1)))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(2637,plain,
% 1.14/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1)))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(2638,plain,
% 1.14/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[2637, 2636])).
% 1.14/1.36 tff(2639,plain,
% 1.14/1.36 (b(s(z), s(elem!1))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2638, 51, 2635, 136])).
% 1.14/1.36 tff(2640,plain,
% 1.14/1.36 (s(z) = s(elem!1)),
% 1.14/1.36 inference(symmetry,[status(thm)],[769])).
% 1.14/1.36 tff(2641,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[136, 2640])).
% 1.14/1.36 tff(2642,plain,((~(s(elem!1) = s(z))) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(2643,plain,
% 1.14/1.36 (~(s(elem!1) = s(z))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2642, 136])).
% 1.14/1.36 tff(2644,plain,
% 1.14/1.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(z))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(2645,plain,
% 1.14/1.36 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(z))))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(2646,plain,
% 1.14/1.36 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(z)))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[2645, 2644])).
% 1.14/1.36 tff(2647,plain,
% 1.14/1.36 (~r(s(elem!1), s(z))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2646, 297, 903, 2628])).
% 1.14/1.36 tff(2648,plain,
% 1.14/1.36 (b(s(elem!1), s(z))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[781, 51, 2647, 2643])).
% 1.14/1.36 tff(2649,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(2650,plain,
% 1.14/1.36 (((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(2651,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1))))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[2650])).
% 1.14/1.36 tff(2652,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.14/1.36 inference(transitivity,[status(thm)],[2651, 2649])).
% 1.14/1.36 tff(2653,plain,
% 1.14/1.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(2654,plain,
% 1.14/1.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1))))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[2653, 2652])).
% 1.14/1.36 tff(2655,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2654, 319, 1, 2648, 785, 2639])).
% 1.14/1.36 tff(2656,plain,((~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (s(z) = s(elem!1)) | (~r(s(z), s(s(z)))) | (s(elem!1) = s(s(z))) | (~b(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(2657,plain,
% 1.14/1.36 (~r(s(z), s(s(z)))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2656, 2620, 2504, 785, 2523, 1])).
% 1.14/1.36 tff(2658,plain,
% 1.14/1.36 (b(s(z), s(s(z)))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[685, 2657])).
% 1.14/1.36 tff(2659,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(2660,plain,
% 1.14/1.37 (((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z))) <=> ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(2661,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z))))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[2660])).
% 1.14/1.37 tff(2662,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))))),
% 1.14/1.37 inference(transitivity,[status(thm)],[2661, 2659])).
% 1.14/1.37 tff(2663,plain,
% 1.14/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(2664,plain,
% 1.14/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z))))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[2663, 2662])).
% 1.14/1.37 tff(2665,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2664, 319, 711, 2620, 2658, 2618])).
% 1.14/1.37 tff(2666,plain,((~r(s(z), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (s(elem!1) = s(s(z))) | (~b(s(s(elem!1)), s(z))) | (s(s(z)) = s(s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(2667,plain,
% 1.14/1.37 (~r(s(z), s(s(elem!1)))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2666, 2616, 785, 2523, 1, 772, 70, 2511])).
% 1.14/1.37 tff(2668,plain,
% 1.14/1.37 (b(s(z), s(s(elem!1)))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[1047, 2667])).
% 1.14/1.37 tff(2669,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(2670,plain,
% 1.14/1.37 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), 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(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(2671,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[2670])).
% 1.14/1.37 tff(2672,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.14/1.37 inference(transitivity,[status(thm)],[2671, 2669])).
% 1.14/1.37 tff(2673,plain,
% 1.14/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(2674,plain,
% 1.14/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[2673, 2672])).
% 1.14/1.37 tff(2675,plain,
% 1.14/1.37 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2674, 319, 1, 687, 116])).
% 1.14/1.37 tff(2676,plain,
% 1.14/1.37 (r(s(s(z)), s(s(s(elem!1))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[1571, 2675])).
% 1.14/1.37 tff(2677,plain,
% 1.14/1.37 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(2678,plain,
% 1.14/1.37 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))) <=> ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(2679,plain,
% 1.14/1.37 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z)))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[2678])).
% 1.14/1.37 tff(2680,plain,
% 1.14/1.37 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.14/1.37 inference(transitivity,[status(thm)],[2679, 2677])).
% 1.14/1.37 tff(2681,plain,
% 1.14/1.37 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(2682,plain,
% 1.14/1.37 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z)))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[2681, 2680])).
% 1.14/1.37 tff(2683,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2682, 297, 2676, 2511, 1089])).
% 1.14/1.37 tff(2684,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(2685,plain,
% 1.14/1.37 (~b(s(s(z)), s(s(elem!1)))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2684, 2668, 1, 116, 2511])).
% 1.14/1.37 tff(2686,plain,
% 1.14/1.37 (r(s(s(z)), s(s(elem!1)))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[122, 2685, 772])).
% 1.14/1.37 tff(2687,plain,
% 1.14/1.37 (~r(s(z), s(elem!1))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2634, 297, 903, 203])).
% 1.14/1.37 tff(2688,plain,
% 1.14/1.37 (b(s(z), s(elem!1))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2638, 51, 2687, 136])).
% 1.14/1.37 tff(2689,plain,
% 1.14/1.37 ((~(s(z) = s(elem!1))) <=> (~(s(elem!1) = s(z)))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[2500])).
% 1.14/1.37 tff(2690,plain,
% 1.14/1.37 (~(s(elem!1) = s(z))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[136, 2689])).
% 1.14/1.37 tff(2691,plain,
% 1.14/1.37 (~r(s(elem!1), s(z))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2646, 297, 903, 203])).
% 1.14/1.37 tff(2692,plain,
% 1.14/1.37 ((s(elem!1) = s(z)) | b(s(elem!1), s(z))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[781, 51, 2691])).
% 1.14/1.37 tff(2693,plain,
% 1.14/1.37 (b(s(elem!1), s(z))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2692, 2690])).
% 1.14/1.37 tff(2694,plain,
% 1.14/1.37 (~b(s(elem!1), s(s(elem!1)))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2654, 319, 1, 2693, 2688])).
% 1.14/1.37 tff(2695,plain,
% 1.14/1.37 (r(s(elem!1), s(s(elem!1)))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[807, 2694, 2142])).
% 1.14/1.37 tff(2696,plain,
% 1.14/1.37 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(2697,plain,
% 1.14/1.37 (((~r(s(s(z)), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(z))))) <=> ((~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(2698,plain,
% 1.14/1.37 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[2697])).
% 1.14/1.37 tff(2699,plain,
% 1.14/1.37 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.14/1.37 inference(transitivity,[status(thm)],[2698, 2696])).
% 1.14/1.37 tff(2700,plain,
% 1.14/1.37 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(z)))))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(2701,plain,
% 1.14/1.37 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1))))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[2700, 2699])).
% 1.14/1.37 tff(2702,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2701, 297, 2695, 2578, 203])).
% 1.14/1.37 tff(2703,plain,((~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (s(z) = s(elem!1)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(2704,plain,
% 1.14/1.37 (~r(s(z), s(s(z)))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2703, 2686, 203, 1, 2504, 2142])).
% 1.14/1.37 tff(2705,plain,
% 1.14/1.37 (b(s(z), s(s(z)))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[685, 2704])).
% 1.14/1.37 tff(2706,assumption,(b(z, s(z))), introduced(assumption)).
% 1.14/1.37 tff(2707,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(2708,plain,
% 1.14/1.37 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z)))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(2709,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(z)))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[2708])).
% 1.14/1.37 tff(2710,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))),
% 1.14/1.37 inference(transitivity,[status(thm)],[2709, 2707])).
% 1.14/1.37 tff(2711,plain,
% 1.14/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(2712,plain,
% 1.14/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(z)))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[2711, 2710])).
% 1.14/1.37 tff(2713,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2712, 319, 2616, 2706, 2705, 2614])).
% 1.14/1.37 tff(2714,plain,((~r(s(elem!1), z)) | (~b(z, s(z))) | (~r(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (s(elem!1) = s(s(elem!1))) | (s(s(z)) = s(s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (s(elem!1) = s(s(z))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(2715,plain,
% 1.14/1.37 (~b(s(s(elem!1)), s(z))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2714, 2603, 2530, 2590, 2142, 772, 116, 2511, 785, 2523, 70])).
% 1.14/1.37 tff(2716,plain,
% 1.14/1.37 (r(s(s(elem!1)), s(z))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[871, 2715])).
% 1.14/1.37 tff(2717,plain,
% 1.14/1.37 (~r(s(s(elem!1)), s(s(z)))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2565, 2716, 2511])).
% 1.14/1.37 tff(2718,plain,
% 1.14/1.37 (b(s(s(elem!1)), s(s(z)))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2555, 51, 2522, 2717])).
% 1.14/1.37 tff(2719,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(2720,plain,
% 1.14/1.37 (((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(2721,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[2720])).
% 1.14/1.37 tff(2722,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.14/1.37 inference(transitivity,[status(thm)],[2721, 2719])).
% 1.14/1.37 tff(2723,plain,
% 1.14/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(2724,plain,
% 1.14/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[2723, 2722])).
% 1.14/1.37 tff(2725,plain,
% 1.14/1.37 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2724, 319, 2718, 2585, 116])).
% 1.14/1.37 tff(2726,plain,
% 1.14/1.37 (((~![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))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(2727,plain,
% 1.14/1.37 ((~![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))))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(2728,plain,
% 1.14/1.37 ((~![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)))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[2727, 2726])).
% 1.14/1.37 tff(2729,plain,
% 1.14/1.37 ((s(s(s(elem!1))) = s(s(z))) | r(s(s(s(elem!1))), s(s(z)))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2728, 51, 2725])).
% 1.14/1.37 tff(2730,plain,
% 1.14/1.37 (r(s(s(s(elem!1))), s(s(z)))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2729, 2516])).
% 1.14/1.37 tff(2731,plain,
% 1.14/1.37 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(2732,plain,
% 1.14/1.37 (((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(2733,plain,
% 1.14/1.37 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[2732])).
% 1.14/1.37 tff(2734,plain,
% 1.14/1.37 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.14/1.37 inference(transitivity,[status(thm)],[2733, 2731])).
% 1.14/1.37 tff(2735,plain,
% 1.14/1.37 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(2736,plain,
% 1.14/1.37 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[2735, 2734])).
% 1.14/1.37 tff(2737,plain,
% 1.14/1.37 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2736, 297, 2530, 2730])).
% 1.14/1.37 tff(2738,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(2739,plain,
% 1.14/1.37 (((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(2740,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[2739])).
% 1.14/1.37 tff(2741,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.14/1.37 inference(transitivity,[status(thm)],[2740, 2738])).
% 1.14/1.37 tff(2742,plain,
% 1.14/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(2743,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[2742, 2741])).
% 1.14/1.38 tff(2744,plain,
% 1.14/1.38 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[2743, 319, 2718, 785, 116])).
% 1.14/1.38 tff(2745,plain,
% 1.14/1.38 ((s(s(s(elem!1))) = s(elem!1)) | r(s(s(s(elem!1))), s(elem!1))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[521, 51, 2744])).
% 1.14/1.38 tff(2746,plain,
% 1.14/1.38 (s(s(s(elem!1))) = s(elem!1)),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[2745, 2737])).
% 1.14/1.38 tff(2747,plain,
% 1.14/1.38 (inj_0(s(s(s(elem!1)))) = inj_0(s(elem!1))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[2746])).
% 1.14/1.38 tff(2748,plain,
% 1.14/1.38 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.14/1.38 inference(symmetry,[status(thm)],[2747])).
% 1.14/1.38 tff(2749,plain,
% 1.14/1.38 (elem!1 = s(s(elem!1))),
% 1.14/1.38 inference(transitivity,[status(thm)],[258, 2748, 83])).
% 1.14/1.38 tff(2750,plain,
% 1.14/1.38 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(elem!1)))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[2749])).
% 1.14/1.38 tff(2751,plain,
% 1.14/1.38 ((s(s(z)) = s(s(elem!1))) <=> (s(s(z)) = elem!1)),
% 1.14/1.38 inference(symmetry,[status(thm)],[2750])).
% 1.14/1.38 tff(2752,plain,
% 1.14/1.38 ((~(s(s(z)) = s(s(elem!1)))) <=> (~(s(s(z)) = elem!1))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[2751])).
% 1.14/1.38 tff(2753,plain,
% 1.14/1.38 (~(s(s(z)) = elem!1)),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[772, 2752])).
% 1.14/1.38 tff(2754,assumption,(s(s(s(z))) = s(elem!1)), introduced(assumption)).
% 1.14/1.38 tff(2755,plain,
% 1.14/1.38 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[2754])).
% 1.14/1.38 tff(2756,plain,
% 1.14/1.38 (s(s(z)) = elem!1),
% 1.14/1.38 inference(transitivity,[status(thm)],[18, 2755, 141])).
% 1.14/1.38 tff(2757,assumption,(~(s(s(z)) = elem!1)), introduced(assumption)).
% 1.14/1.38 tff(2758,plain,
% 1.14/1.38 ($false),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[2757, 2756])).
% 1.14/1.38 tff(2759,plain,((~(s(s(s(z))) = s(elem!1))) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.38 tff(2760,plain,
% 1.14/1.38 (~(s(s(s(z))) = s(elem!1))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[2759, 2753])).
% 1.14/1.38 tff(2761,plain,
% 1.14/1.38 (s(s(elem!1)) = elem!1),
% 1.14/1.38 inference(transitivity,[status(thm)],[168, 2747, 141])).
% 1.14/1.38 tff(2762,plain,
% 1.14/1.38 (b(s(s(elem!1)), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[2761])).
% 1.14/1.38 tff(2763,plain,
% 1.14/1.38 (~(s(s(elem!1)) = s(elem!1))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[2142, 2496])).
% 1.14/1.38 tff(2764,plain,
% 1.14/1.38 (~r(z, s(s(z)))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[740, 2603, 2530])).
% 1.14/1.38 tff(2765,plain,
% 1.14/1.38 (b(z, s(s(z)))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[729, 2764])).
% 1.14/1.38 tff(2766,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(2767,plain,
% 1.14/1.38 (((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(2768,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z))))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[2767])).
% 1.14/1.38 tff(2769,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.14/1.38 inference(transitivity,[status(thm)],[2768, 2766])).
% 1.14/1.38 tff(2770,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(2771,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z))))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[2770, 2769])).
% 1.14/1.38 tff(2772,plain,
% 1.14/1.38 (~b(s(s(elem!1)), z)),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[2771, 319, 2765, 2718, 2585])).
% 1.14/1.38 tff(2773,plain,
% 1.14/1.38 (r(s(s(elem!1)), z)),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[75, 2772])).
% 1.14/1.38 tff(2774,plain,
% 1.14/1.38 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(2775,plain,
% 1.14/1.38 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(2776,plain,
% 1.14/1.38 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[2775, 2774])).
% 1.14/1.38 tff(2777,plain,
% 1.14/1.38 (~r(s(s(elem!1)), s(elem!1))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[2776, 297, 2773, 2603])).
% 1.14/1.38 tff(2778,plain,
% 1.14/1.38 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1)))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(2779,plain,
% 1.14/1.38 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1)))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(2780,plain,
% 1.14/1.38 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[2779, 2778])).
% 1.14/1.38 tff(2781,plain,
% 1.14/1.38 ((s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[2780, 51, 2777])).
% 1.14/1.38 tff(2782,plain,
% 1.14/1.38 (b(s(s(elem!1)), s(elem!1))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[2781, 2763])).
% 1.14/1.38 tff(2783,plain,
% 1.14/1.38 (b(elem!1, s(elem!1))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[2782, 2762])).
% 1.14/1.38 tff(2784,plain,
% 1.14/1.38 (b(s(s(z)), z)),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[2613, 2603, 2530])).
% 1.14/1.38 tff(2785,plain,
% 1.14/1.38 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(z)), elem!1)),
% 1.14/1.38 inference(monotonicity,[status(thm)],[2761])).
% 1.14/1.38 tff(2786,plain,
% 1.14/1.38 (b(s(s(z)), elem!1)),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[2585, 2785])).
% 1.14/1.38 tff(2787,plain,
% 1.14/1.38 (elem!1 = s(s(elem!1))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[262, 2746])).
% 1.14/1.38 tff(2788,assumption,(elem!1 = s(s(elem!1))), introduced(assumption)).
% 1.14/1.38 tff(2789,plain,
% 1.14/1.38 (b(elem!1, s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[2788])).
% 1.14/1.38 tff(2790,plain,
% 1.14/1.38 (b(s(s(elem!1)), s(s(z))) <=> b(elem!1, s(s(z)))),
% 1.14/1.38 inference(symmetry,[status(thm)],[2789])).
% 1.14/1.38 tff(2791,plain,
% 1.14/1.38 (b(elem!1, s(s(z)))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[2543, 2790])).
% 1.14/1.38 tff(2792,assumption,(~b(elem!1, s(s(z)))), introduced(assumption)).
% 1.14/1.38 tff(2793,plain,
% 1.14/1.38 ($false),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[2792, 2791])).
% 1.14/1.38 tff(2794,plain,((~(elem!1 = s(s(elem!1)))) | b(elem!1, s(s(z))) | (~b(s(s(elem!1)), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.38 tff(2795,plain,
% 1.14/1.38 (b(elem!1, s(s(z)))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[2794, 2787, 2718])).
% 1.14/1.38 tff(2796,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(2797,plain,
% 1.14/1.38 (((~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z))))) <=> ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(2798,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[2797])).
% 1.14/1.38 tff(2799,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.14/1.38 inference(transitivity,[status(thm)],[2798, 2796])).
% 1.14/1.38 tff(2800,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(2801,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[2800, 2799])).
% 1.14/1.38 tff(2802,plain,
% 1.14/1.38 (~b(s(z), s(s(z)))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[2801, 319, 2795, 2765, 2786, 2784, 2592])).
% 1.14/1.38 tff(2803,plain,
% 1.14/1.38 (r(s(z), s(s(z)))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[685, 2802])).
% 1.14/1.38 tff(2804,plain,
% 1.14/1.38 (~r(s(z), s(elem!1))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[2634, 297, 2803, 2530])).
% 1.14/1.38 tff(2805,plain,
% 1.14/1.38 (b(s(z), s(elem!1))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[2638, 51, 2804, 2504])).
% 1.14/1.38 tff(2806,plain,
% 1.14/1.38 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), elem!1)),
% 1.14/1.38 inference(monotonicity,[status(thm)],[2761])).
% 1.14/1.38 tff(2807,plain,
% 1.14/1.38 (b(s(elem!1), elem!1)),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[785, 2806])).
% 1.14/1.38 tff(2808,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(2809,plain,
% 1.14/1.38 (((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(2810,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[2809])).
% 1.14/1.38 tff(2811,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.14/1.38 inference(transitivity,[status(thm)],[2810, 2808])).
% 1.14/1.38 tff(2812,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(2813,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[2812, 2811])).
% 1.14/1.38 tff(2814,plain,
% 1.14/1.38 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[2813, 319, 2718, 785, 116])).
% 1.14/1.38 tff(2815,plain,
% 1.14/1.38 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(2816,plain,
% 1.14/1.38 (((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(s(s(elem!1)))))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(2817,plain,
% 1.14/1.38 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[2816])).
% 1.14/1.38 tff(2818,plain,
% 1.14/1.38 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.14/1.38 inference(transitivity,[status(thm)],[2817, 2815])).
% 1.14/1.38 tff(2819,plain,
% 1.14/1.38 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(2820,plain,
% 1.14/1.38 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[2819, 2818])).
% 1.14/1.38 tff(2821,plain,
% 1.14/1.38 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[2820, 297, 2530, 2730])).
% 1.14/1.38 tff(2822,plain,
% 1.14/1.38 (s(elem!1) = s(s(s(elem!1)))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[434, 2821, 2814])).
% 1.14/1.38 tff(2823,assumption,(s(s(s(z))) = s(s(elem!1))), introduced(assumption)).
% 1.14/1.38 tff(2824,plain,
% 1.14/1.38 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[2823])).
% 1.14/1.38 tff(2825,plain,
% 1.14/1.38 (s(s(z)) = s(s(s(elem!1)))),
% 1.14/1.38 inference(transitivity,[status(thm)],[18, 2824, 118, 266])).
% 1.14/1.38 tff(2826,plain,
% 1.14/1.38 ($false),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[231, 2825])).
% 1.14/1.38 tff(2827,plain,((~(s(s(s(z))) = s(s(elem!1)))) | (~(s(elem!1) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.38 tff(2828,plain,
% 1.14/1.38 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[2827, 2822])).
% 1.14/1.38 tff(2829,plain,
% 1.14/1.38 (r(elem!1, s(z)) <=> r(s(s(elem!1)), s(z))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[259])).
% 1.14/1.38 tff(2830,plain,
% 1.14/1.38 (r(s(s(elem!1)), s(z)) <=> r(elem!1, s(z))),
% 1.14/1.38 inference(symmetry,[status(thm)],[2829])).
% 1.14/1.38 tff(2831,plain,
% 1.14/1.38 (r(elem!1, s(z))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[2169, 2830])).
% 1.14/1.38 tff(2832,assumption,(~r(elem!1, s(z))), introduced(assumption)).
% 1.14/1.38 tff(2833,plain,
% 1.14/1.38 ($false),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[2832, 2831])).
% 1.14/1.38 tff(2834,plain,(r(elem!1, s(z)) | (~r(s(s(elem!1)), s(z))) | (~(s(s(s(elem!1))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.38 tff(2835,plain,
% 1.14/1.38 (r(elem!1, s(z))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[2834, 2716, 2746])).
% 1.14/1.38 tff(2836,plain,
% 1.14/1.38 ((s(s(s(z))) = elem!1) <=> (s(s(s(z))) = s(s(elem!1)))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[259])).
% 1.14/1.38 tff(2837,plain,
% 1.14/1.38 ((s(s(s(z))) = s(s(elem!1))) <=> (s(s(s(z))) = elem!1)),
% 1.14/1.38 inference(symmetry,[status(thm)],[2836])).
% 1.14/1.38 tff(2838,plain,
% 1.14/1.38 ((~(s(s(s(z))) = s(s(elem!1)))) <=> (~(s(s(s(z))) = elem!1))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[2837])).
% 1.14/1.38 tff(2839,assumption,(~(s(s(s(z))) = s(s(elem!1)))), introduced(assumption)).
% 1.14/1.38 tff(2840,plain,
% 1.14/1.38 (~(s(s(s(z))) = elem!1)),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[2839, 2838])).
% 1.14/1.38 tff(2841,assumption,(b(s(s(s(z))), s(elem!1))), introduced(assumption)).
% 1.14/1.38 tff(2842,assumption,(b(s(z), s(elem!1))), introduced(assumption)).
% 1.14/1.38 tff(2843,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(2844,plain,
% 1.14/1.38 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(2845,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1)))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[2844])).
% 1.14/1.38 tff(2846,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.14/1.38 inference(transitivity,[status(thm)],[2845, 2843])).
% 1.14/1.38 tff(2847,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(2848,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1)))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[2847, 2846])).
% 1.14/1.38 tff(2849,plain,
% 1.14/1.38 (~b(s(s(s(z))), s(z))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[2848, 319, 449, 2842, 2841])).
% 1.14/1.38 tff(2850,plain,
% 1.14/1.38 (r(s(s(s(z))), s(z))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[910, 51, 30, 2849])).
% 1.14/1.38 tff(2851,assumption,(r(elem!1, s(z))), introduced(assumption)).
% 1.14/1.38 tff(2852,plain,
% 1.14/1.38 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(2853,plain,
% 1.14/1.38 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(2854,plain,
% 1.14/1.38 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[2853, 2852])).
% 1.14/1.38 tff(2855,plain,
% 1.14/1.38 (~r(s(s(s(z))), elem!1)),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[2854, 297, 2851, 2850])).
% 1.14/1.38 tff(2856,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(2857,plain,
% 1.14/1.39 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(2858,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1)))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[2857])).
% 1.14/1.39 tff(2859,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.14/1.39 inference(transitivity,[status(thm)],[2858, 2856])).
% 1.14/1.39 tff(2860,plain,
% 1.14/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(2861,plain,
% 1.14/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1)))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[2860, 2859])).
% 1.14/1.39 tff(2862,plain,
% 1.14/1.39 (~b(s(s(s(z))), elem!1)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[2861, 319, 275, 449, 2841])).
% 1.14/1.39 tff(2863,plain,
% 1.14/1.39 (((~![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))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(2864,plain,
% 1.14/1.39 ((~![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))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(2865,plain,
% 1.14/1.39 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1)),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[2864, 2863])).
% 1.14/1.39 tff(2866,plain,
% 1.14/1.39 ((s(s(s(z))) = elem!1) | r(s(s(s(z))), elem!1)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[2865, 51, 2862])).
% 1.14/1.39 tff(2867,plain,
% 1.14/1.39 ($false),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[2866, 2855, 2840])).
% 1.14/1.39 tff(2868,plain,((~b(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(z))) | (s(s(s(z))) = s(s(elem!1))) | (~(s(s(s(elem!1))) = s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.39 tff(2869,plain,
% 1.14/1.39 (~b(s(s(s(z))), s(elem!1))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[2868, 2835, 2828, 2746, 2807, 2805, 2783])).
% 1.14/1.39 tff(2870,plain,
% 1.14/1.39 (((~![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)))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(2871,plain,
% 1.14/1.39 ((~![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)))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(2872,plain,
% 1.14/1.39 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1)) | r(s(s(s(z))), s(elem!1))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[2871, 2870])).
% 1.14/1.39 tff(2873,plain,
% 1.14/1.39 ((s(s(s(z))) = s(elem!1)) | r(s(s(s(z))), s(elem!1))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[2872, 51, 2869])).
% 1.14/1.39 tff(2874,plain,
% 1.14/1.39 (r(s(s(s(z))), s(elem!1))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[2873, 2760])).
% 1.14/1.39 tff(2875,assumption,(z = s(elem!1)), introduced(assumption)).
% 1.14/1.39 tff(2876,plain,
% 1.14/1.39 (s(elem!1) = z),
% 1.14/1.39 inference(symmetry,[status(thm)],[2875])).
% 1.14/1.39 tff(2877,plain,
% 1.14/1.39 ($false),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[193, 2876])).
% 1.14/1.39 tff(2878,plain,(~(z = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.39 tff(2879,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(z, s(z))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(2880,plain,
% 1.14/1.39 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1)))) <=> ((~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(z, s(z))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(2881,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(z, s(z)))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[2880])).
% 1.14/1.39 tff(2882,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(z, s(z))))),
% 1.14/1.39 inference(transitivity,[status(thm)],[2881, 2879])).
% 1.14/1.39 tff(2883,plain,
% 1.14/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(2884,plain,
% 1.14/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(z, s(z)))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[2883, 2882])).
% 1.14/1.39 tff(2885,plain,
% 1.14/1.39 (~b(z, s(elem!1))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[2884, 319, 2540, 2590, 2592])).
% 1.14/1.39 tff(2886,plain,
% 1.14/1.39 (r(z, s(elem!1))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[759, 51, 2885, 2878])).
% 1.14/1.39 tff(2887,plain,
% 1.14/1.39 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(2888,plain,
% 1.14/1.39 (((~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(2889,plain,
% 1.14/1.39 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1)))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[2888])).
% 1.14/1.39 tff(2890,plain,
% 1.14/1.39 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.14/1.39 inference(transitivity,[status(thm)],[2889, 2887])).
% 1.14/1.39 tff(2891,plain,
% 1.14/1.39 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), z)))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(2892,plain,
% 1.14/1.39 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1)))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[2891, 2890])).
% 1.14/1.39 tff(2893,plain,
% 1.14/1.39 (~r(s(s(s(z))), z)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[2892, 297, 2886, 2874])).
% 1.14/1.39 tff(2894,plain,
% 1.14/1.39 (b(s(s(s(z))), z)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[901, 51, 898, 2893])).
% 1.14/1.39 tff(2895,plain,
% 1.14/1.39 ((s(s(z)) = s(elem!1)) <=> (s(elem!1) = s(s(z)))),
% 1.14/1.39 inference(commutativity,[status(thm)],[])).
% 1.14/1.39 tff(2896,plain,
% 1.14/1.39 ((s(elem!1) = s(s(z))) <=> (s(s(z)) = s(elem!1))),
% 1.14/1.39 inference(symmetry,[status(thm)],[2895])).
% 1.14/1.39 tff(2897,plain,
% 1.14/1.39 ((~(s(elem!1) = s(s(z)))) <=> (~(s(s(z)) = s(elem!1)))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[2896])).
% 1.14/1.39 tff(2898,plain,
% 1.14/1.39 (~(s(s(z)) = s(elem!1))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[2523, 2897])).
% 1.14/1.39 tff(2899,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(2900,plain,
% 1.14/1.39 (((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(2901,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1)))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[2900])).
% 1.14/1.39 tff(2902,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))))),
% 1.14/1.39 inference(transitivity,[status(thm)],[2901, 2899])).
% 1.14/1.39 tff(2903,plain,
% 1.14/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(2904,plain,
% 1.14/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1)))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[2903, 2902])).
% 1.14/1.39 tff(2905,plain,
% 1.14/1.39 (~b(s(s(z)), s(elem!1))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[2904, 319, 2718, 785, 2585])).
% 1.14/1.39 tff(2906,plain,
% 1.14/1.39 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1)))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(2907,plain,
% 1.14/1.39 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1)))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(2908,plain,
% 1.14/1.39 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[2907, 2906])).
% 1.14/1.39 tff(2909,plain,
% 1.14/1.39 ((s(s(z)) = s(elem!1)) | r(s(s(z)), s(elem!1))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[2908, 51, 2905])).
% 1.14/1.39 tff(2910,plain,
% 1.14/1.39 (r(s(s(z)), s(elem!1))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[2909, 2898])).
% 1.14/1.39 tff(2911,plain,
% 1.14/1.39 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(2912,plain,
% 1.14/1.39 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(2913,plain,
% 1.14/1.39 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(z))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[2912, 2911])).
% 1.14/1.39 tff(2914,plain,
% 1.14/1.39 (~r(s(s(s(z))), s(s(z)))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[2913, 297, 2910, 2874])).
% 1.14/1.39 tff(2915,assumption,(~b(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 1.14/1.39 tff(2916,plain,
% 1.14/1.39 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(2917,plain,
% 1.14/1.39 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z))))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(2918,plain,
% 1.14/1.39 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[2917, 2916])).
% 1.14/1.39 tff(2919,plain,
% 1.14/1.39 ($false),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[2918, 51, 2248, 2915, 941])).
% 1.14/1.39 tff(2920,plain,(r(s(s(s(z))), s(s(z))) | b(s(s(s(z))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.39 tff(2921,plain,
% 1.14/1.39 (b(s(s(s(z))), s(s(z)))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[2920, 2914])).
% 1.14/1.39 tff(2922,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(2923,plain,
% 1.14/1.39 (((~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(2924,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[2923])).
% 1.14/1.39 tff(2925,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)))),
% 1.14/1.39 inference(transitivity,[status(thm)],[2924, 2922])).
% 1.14/1.39 tff(2926,plain,
% 1.14/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(2927,plain,
% 1.14/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[2926, 2925])).
% 1.14/1.39 tff(2928,plain,
% 1.14/1.39 ($false),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[2927, 319, 2795, 2765, 2786, 2921, 2784, 2894])).
% 1.14/1.39 tff(2929,plain,((s(elem!1) = s(s(z))) | (s(s(z)) = s(s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(elem!1)))) | b(s(elem!1), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.39 tff(2930,plain,
% 1.14/1.39 (s(elem!1) = s(s(z))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[2929, 785, 772, 2142, 116, 2511, 70, 2512])).
% 1.14/1.39 tff(2931,plain,
% 1.14/1.39 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[2930])).
% 1.14/1.39 tff(2932,plain,
% 1.14/1.39 (elem!1 = s(z)),
% 1.14/1.39 inference(transitivity,[status(thm)],[258, 2931, 126])).
% 1.14/1.39 tff(2933,plain,
% 1.14/1.39 (b(elem!1, s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[2932])).
% 1.14/1.39 tff(2934,plain,
% 1.14/1.39 (b(s(z), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 1.14/1.39 inference(symmetry,[status(thm)],[2933])).
% 1.14/1.39 tff(2935,plain,
% 1.14/1.39 (s(s(elem!1)) = s(s(s(z)))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[2930])).
% 1.14/1.39 tff(2936,plain,
% 1.14/1.39 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[2935])).
% 1.14/1.39 tff(2937,plain,
% 1.14/1.39 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[2936, 2932])).
% 1.14/1.39 tff(2938,plain,
% 1.14/1.39 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(elem!1))) = s(z))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[2932])).
% 1.14/1.39 tff(2939,plain,
% 1.14/1.39 ((s(s(s(elem!1))) = s(z)) <=> (s(s(s(elem!1))) = elem!1)),
% 1.14/1.39 inference(symmetry,[status(thm)],[2938])).
% 1.14/1.39 tff(2940,plain,
% 1.14/1.39 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[2939])).
% 1.14/1.39 tff(2941,plain,
% 1.14/1.39 (~(s(s(s(elem!1))) = elem!1)),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[171, 2940])).
% 1.14/1.39 tff(2942,plain,
% 1.14/1.39 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.14/1.39 inference(symmetry,[status(thm)],[2936])).
% 1.14/1.39 tff(2943,plain,
% 1.14/1.39 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[2942])).
% 1.14/1.39 tff(2944,plain,
% 1.14/1.39 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(z)) = s(s(s(elem!1))))),
% 1.14/1.39 inference(transitivity,[status(thm)],[2943, 2513])).
% 1.14/1.39 tff(2945,plain,
% 1.14/1.39 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 1.14/1.39 inference(symmetry,[status(thm)],[2944])).
% 1.14/1.39 tff(2946,plain,
% 1.14/1.39 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(s(z)))) = s(s(z))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[2945])).
% 1.14/1.39 tff(2947,plain,
% 1.14/1.39 (~(s(s(s(s(z)))) = s(s(z)))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[231, 2946])).
% 1.14/1.39 tff(2948,plain,
% 1.14/1.39 (s(s(s(z))) = s(s(elem!1))),
% 1.14/1.39 inference(symmetry,[status(thm)],[2935])).
% 1.14/1.39 tff(2949,plain,
% 1.14/1.39 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), s(s(elem!1)))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[2948])).
% 1.14/1.39 tff(2950,plain,
% 1.14/1.39 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(z)), s(s(s(z))))),
% 1.14/1.39 inference(symmetry,[status(thm)],[2949])).
% 1.14/1.39 tff(2951,plain,
% 1.14/1.39 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(z)), s(s(elem!1)))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[2930])).
% 1.14/1.39 tff(2952,plain,
% 1.14/1.39 (b(s(s(z)), s(s(elem!1)))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[785, 2951])).
% 1.14/1.39 tff(2953,plain,
% 1.14/1.39 (b(s(s(z)), s(s(s(z))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[2952, 2950])).
% 1.14/1.39 tff(2954,plain,
% 1.14/1.39 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[2942])).
% 1.14/1.39 tff(2955,plain,
% 1.14/1.39 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.14/1.39 inference(symmetry,[status(thm)],[2954])).
% 1.14/1.39 tff(2956,plain,
% 1.14/1.39 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[2935])).
% 1.14/1.39 tff(2957,plain,
% 1.14/1.39 (b(s(s(s(elem!1))), s(s(s(z))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[116, 2956])).
% 1.14/1.39 tff(2958,plain,
% 1.14/1.39 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[2957, 2955])).
% 1.14/1.39 tff(2959,plain,
% 1.14/1.39 (r(s(elem!1), s(z)) <=> r(s(s(z)), s(z))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[2930])).
% 1.14/1.39 tff(2960,plain,
% 1.14/1.39 (r(s(s(z)), s(z)) <=> r(s(elem!1), s(z))),
% 1.14/1.39 inference(symmetry,[status(thm)],[2959])).
% 1.14/1.39 tff(2961,plain,
% 1.14/1.39 (r(s(elem!1), s(z))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[2511, 2960])).
% 1.14/1.39 tff(2962,plain,
% 1.14/1.39 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(z))), s(z))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[2935])).
% 1.14/1.39 tff(2963,plain,
% 1.14/1.39 (b(s(s(s(z))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.14/1.39 inference(symmetry,[status(thm)],[2962])).
% 1.14/1.39 tff(2964,plain,
% 1.14/1.39 ((~b(s(s(s(z))), s(z))) <=> (~b(s(s(elem!1)), s(z)))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[2963])).
% 1.14/1.39 tff(2965,assumption,(b(s(s(s(z))), s(z))), introduced(assumption)).
% 1.14/1.39 tff(2966,assumption,(b(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 1.14/1.39 tff(2967,assumption,(s(elem!1) = s(s(z))), introduced(assumption)).
% 1.14/1.40 tff(2968,plain,
% 1.14/1.40 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 1.14/1.40 inference(monotonicity,[status(thm)],[2967])).
% 1.14/1.40 tff(2969,plain,
% 1.14/1.40 (elem!1 = s(z)),
% 1.14/1.40 inference(transitivity,[status(thm)],[258, 2968, 126])).
% 1.14/1.40 tff(2970,plain,
% 1.14/1.40 (s(s(elem!1)) = s(s(s(z)))),
% 1.14/1.40 inference(monotonicity,[status(thm)],[2967])).
% 1.14/1.40 tff(2971,plain,
% 1.14/1.40 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.14/1.40 inference(monotonicity,[status(thm)],[2970])).
% 1.14/1.40 tff(2972,plain,
% 1.14/1.40 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 1.14/1.40 inference(monotonicity,[status(thm)],[2971, 2969])).
% 1.14/1.40 tff(2973,plain,
% 1.14/1.40 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(elem!1))) = s(z))),
% 1.14/1.40 inference(monotonicity,[status(thm)],[2969])).
% 1.14/1.40 tff(2974,plain,
% 1.14/1.40 ((s(s(s(elem!1))) = s(z)) <=> (s(s(s(elem!1))) = elem!1)),
% 1.14/1.40 inference(symmetry,[status(thm)],[2973])).
% 1.14/1.40 tff(2975,plain,
% 1.14/1.40 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.14/1.40 inference(monotonicity,[status(thm)],[2974])).
% 1.14/1.40 tff(2976,plain,
% 1.14/1.40 (~(s(s(s(elem!1))) = elem!1)),
% 1.14/1.40 inference(modus_ponens,[status(thm)],[171, 2975])).
% 1.14/1.40 tff(2977,plain,
% 1.14/1.40 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 1.14/1.40 inference(symmetry,[status(thm)],[2968])).
% 1.14/1.40 tff(2978,plain,
% 1.14/1.40 (s(z) = elem!1),
% 1.14/1.40 inference(transitivity,[status(thm)],[127, 2977, 141])).
% 1.14/1.40 tff(2979,plain,
% 1.14/1.40 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.14/1.40 inference(symmetry,[status(thm)],[2971])).
% 1.14/1.40 tff(2980,plain,
% 1.14/1.40 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 1.14/1.40 inference(monotonicity,[status(thm)],[2979, 2978])).
% 1.14/1.40 tff(2981,plain,
% 1.14/1.40 ((~r(s(s(s(s(z)))), s(z))) <=> (~r(s(s(s(elem!1))), elem!1))),
% 1.14/1.40 inference(monotonicity,[status(thm)],[2980])).
% 1.14/1.40 tff(2982,plain,
% 1.14/1.40 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 1.14/1.40 inference(monotonicity,[status(thm)],[2979])).
% 1.14/1.40 tff(2983,plain,
% 1.14/1.40 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(z)) = s(s(s(elem!1))))),
% 1.14/1.40 inference(transitivity,[status(thm)],[2982, 2513])).
% 1.14/1.40 tff(2984,plain,
% 1.14/1.40 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 1.14/1.40 inference(symmetry,[status(thm)],[2983])).
% 1.14/1.40 tff(2985,plain,
% 1.14/1.40 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(s(z)))) = s(s(z))))),
% 1.14/1.40 inference(monotonicity,[status(thm)],[2984])).
% 1.14/1.40 tff(2986,plain,
% 1.14/1.40 (~(s(s(s(s(z)))) = s(s(z)))),
% 1.14/1.40 inference(modus_ponens,[status(thm)],[231, 2985])).
% 1.14/1.40 tff(2987,plain,
% 1.14/1.40 (s(s(s(z))) = s(s(elem!1))),
% 1.14/1.40 inference(symmetry,[status(thm)],[2970])).
% 1.14/1.40 tff(2988,plain,
% 1.14/1.40 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), s(s(elem!1)))),
% 1.14/1.40 inference(monotonicity,[status(thm)],[2987])).
% 1.14/1.40 tff(2989,plain,
% 1.14/1.40 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(z)), s(s(s(z))))),
% 1.14/1.40 inference(symmetry,[status(thm)],[2988])).
% 1.14/1.40 tff(2990,plain,
% 1.14/1.40 (b(s(s(z)), s(s(s(z))))),
% 1.14/1.40 inference(modus_ponens,[status(thm)],[687, 2989])).
% 1.14/1.40 tff(2991,plain,
% 1.14/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.14/1.40 inference(rewrite,[status(thm)],[])).
% 1.14/1.40 tff(2992,plain,
% 1.14/1.40 (((~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(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.14/1.40 inference(rewrite,[status(thm)],[])).
% 1.14/1.40 tff(2993,plain,
% 1.14/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[2992])).
% 1.24/1.40 tff(2994,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.24/1.40 inference(transitivity,[status(thm)],[2993, 2991])).
% 1.24/1.40 tff(2995,plain,
% 1.24/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(2996,plain,
% 1.24/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[2995, 2994])).
% 1.24/1.40 tff(2997,plain,
% 1.24/1.40 ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[2996, 319, 2966, 2965])).
% 1.24/1.40 tff(2998,plain,
% 1.24/1.40 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[2997, 2990])).
% 1.24/1.40 tff(2999,plain,
% 1.24/1.40 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(3000,plain,
% 1.24/1.40 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(3001,plain,
% 1.24/1.40 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[3000, 2999])).
% 1.24/1.40 tff(3002,plain,
% 1.24/1.40 ((s(s(s(s(z)))) = s(s(z))) | r(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[3001, 51, 2998])).
% 1.24/1.40 tff(3003,plain,
% 1.24/1.40 (r(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[3002, 2986])).
% 1.24/1.40 tff(3004,assumption,(r(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 1.24/1.40 tff(3005,plain,
% 1.24/1.40 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(3006,plain,
% 1.24/1.40 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(3007,plain,
% 1.24/1.40 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[3006, 3005])).
% 1.24/1.40 tff(3008,plain,
% 1.24/1.40 ($false),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[3007, 297, 2511, 3004, 2444])).
% 1.24/1.40 tff(3009,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.40 tff(3010,plain,
% 1.24/1.40 (~r(s(s(s(s(z)))), s(z))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[3009, 3003, 2511])).
% 1.24/1.40 tff(3011,plain,
% 1.24/1.40 (~r(s(s(s(elem!1))), elem!1)),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[3010, 2981])).
% 1.24/1.40 tff(3012,plain,
% 1.24/1.40 (b(s(s(s(elem!1))), elem!1)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[361, 3011, 2976])).
% 1.24/1.40 tff(3013,plain,
% 1.24/1.40 (b(s(s(s(s(z)))), s(z))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[3012, 2972])).
% 1.24/1.40 tff(3014,plain,
% 1.24/1.40 (b(s(z), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[2978])).
% 1.24/1.40 tff(3015,plain,
% 1.24/1.40 (b(elem!1, s(s(s(s(z))))) <=> b(s(z), s(s(s(s(z)))))),
% 1.24/1.40 inference(symmetry,[status(thm)],[3014])).
% 1.24/1.40 tff(3016,plain,
% 1.24/1.40 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(z))),
% 1.24/1.40 inference(commutativity,[status(thm)],[])).
% 1.24/1.40 tff(3017,plain,
% 1.24/1.40 ((elem!1 = s(s(s(s(z))))) <=> (s(z) = s(s(s(elem!1))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[2969, 2979])).
% 1.24/1.40 tff(3018,plain,
% 1.24/1.40 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(z))),
% 1.24/1.40 inference(transitivity,[status(thm)],[3017, 3016])).
% 1.24/1.40 tff(3019,plain,
% 1.24/1.40 ((s(s(s(elem!1))) = s(z)) <=> (elem!1 = s(s(s(s(z)))))),
% 1.24/1.40 inference(symmetry,[status(thm)],[3018])).
% 1.24/1.40 tff(3020,plain,
% 1.24/1.40 ((~(s(s(s(elem!1))) = s(z))) <=> (~(elem!1 = s(s(s(s(z))))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[3019])).
% 1.24/1.40 tff(3021,plain,
% 1.24/1.40 (~(elem!1 = s(s(s(s(z)))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[171, 3020])).
% 1.24/1.40 tff(3022,plain,
% 1.24/1.40 (r(elem!1, s(s(s(s(z))))) <=> r(s(z), s(s(s(s(z)))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[2969])).
% 1.24/1.40 tff(3023,plain,
% 1.24/1.40 (r(s(z), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 1.24/1.40 inference(symmetry,[status(thm)],[3022])).
% 1.24/1.40 tff(3024,plain,
% 1.24/1.40 ((~r(s(z), s(s(s(s(z)))))) <=> (~r(elem!1, s(s(s(s(z))))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[3023])).
% 1.24/1.40 tff(3025,plain,
% 1.24/1.40 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(3026,plain,
% 1.24/1.40 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(3027,plain,
% 1.24/1.40 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[3026])).
% 1.24/1.40 tff(3028,plain,
% 1.24/1.40 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.24/1.40 inference(transitivity,[status(thm)],[3027, 3025])).
% 1.24/1.40 tff(3029,plain,
% 1.24/1.40 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(3030,plain,
% 1.24/1.40 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[3029, 3028])).
% 1.24/1.40 tff(3031,plain,
% 1.24/1.40 (~r(s(z), s(s(s(s(z)))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[3030, 297, 903, 3004])).
% 1.24/1.40 tff(3032,plain,
% 1.24/1.40 (~r(elem!1, s(s(s(s(z)))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[3031, 3024])).
% 1.24/1.40 tff(3033,plain,
% 1.24/1.40 (((~![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))))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(3034,plain,
% 1.24/1.40 ((~![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))))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(3035,plain,
% 1.24/1.40 ((~![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)))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[3034, 3033])).
% 1.24/1.40 tff(3036,plain,
% 1.24/1.40 ((elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z)))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[3035, 51])).
% 1.24/1.40 tff(3037,plain,
% 1.24/1.40 (b(elem!1, s(s(s(s(z)))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[3036, 3032, 3021])).
% 1.24/1.40 tff(3038,plain,
% 1.24/1.40 (b(s(z), s(s(s(s(z)))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[3037, 3015])).
% 1.24/1.40 tff(3039,plain,
% 1.24/1.40 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(3040,plain,
% 1.24/1.40 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(3041,plain,
% 1.24/1.40 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[3040])).
% 1.24/1.40 tff(3042,plain,
% 1.24/1.40 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.24/1.40 inference(transitivity,[status(thm)],[3041, 3039])).
% 1.24/1.40 tff(3043,plain,
% 1.24/1.40 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(3044,plain,
% 1.24/1.40 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[3043, 3042])).
% 1.24/1.40 tff(3045,plain,
% 1.24/1.40 (~r(s(s(s(s(z)))), s(z))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[3044, 297, 903, 3004])).
% 1.24/1.40 tff(3046,plain,
% 1.24/1.40 (~r(s(s(s(elem!1))), elem!1)),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[3045, 2981])).
% 1.24/1.40 tff(3047,plain,
% 1.24/1.40 (b(s(s(s(elem!1))), elem!1)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[361, 3046, 2976])).
% 1.24/1.40 tff(3048,plain,
% 1.24/1.40 (b(s(s(s(s(z)))), s(z))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[3047, 2972])).
% 1.24/1.40 tff(3049,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(3050,plain,
% 1.24/1.40 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(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(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(3051,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[3050])).
% 1.24/1.40 tff(3052,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.40 inference(transitivity,[status(thm)],[3051, 3049])).
% 1.24/1.40 tff(3053,plain,
% 1.24/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(3054,plain,
% 1.24/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[3053, 3052])).
% 1.24/1.40 tff(3055,plain,
% 1.24/1.40 ($false),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[3054, 319, 3048, 2966, 2965, 3038])).
% 1.24/1.40 tff(3056,plain,((~r(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~(s(elem!1) = s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.40 tff(3057,plain,
% 1.24/1.40 (~r(s(z), s(s(z)))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[3056, 2965, 2966, 2967, 3003])).
% 1.24/1.40 tff(3058,plain,
% 1.24/1.40 (b(s(z), s(s(z)))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[685, 3057])).
% 1.24/1.40 tff(3059,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(3060,plain,
% 1.24/1.40 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(3061,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[3060])).
% 1.24/1.40 tff(3062,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.40 inference(transitivity,[status(thm)],[3061, 3059])).
% 1.24/1.40 tff(3063,plain,
% 1.24/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(3064,plain,
% 1.24/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[3063, 3062])).
% 1.24/1.40 tff(3065,plain,
% 1.24/1.40 ($false),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[3064, 319, 3058, 3013, 2966, 2965])).
% 1.24/1.40 tff(3066,plain,((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~(s(elem!1) = s(s(z)))) | (~r(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.40 tff(3067,plain,
% 1.24/1.40 (~b(s(s(s(z))), s(z))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[3066, 2958, 2930, 2511, 2952])).
% 1.24/1.40 tff(3068,plain,
% 1.24/1.40 (~b(s(s(elem!1)), s(z))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[3067, 2964])).
% 1.24/1.40 tff(3069,plain,
% 1.24/1.40 (r(s(s(elem!1)), s(z))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[871, 3068])).
% 1.24/1.40 tff(3070,plain,
% 1.24/1.40 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(z))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(3071,plain,
% 1.24/1.40 (((~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(z))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(3072,plain,
% 1.24/1.40 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(z)))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[3071])).
% 1.24/1.40 tff(3073,plain,
% 1.24/1.40 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(z))))),
% 1.24/1.40 inference(transitivity,[status(thm)],[3072, 3070])).
% 1.24/1.40 tff(3074,plain,
% 1.24/1.40 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(3075,plain,
% 1.24/1.40 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(z)))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[3074, 3073])).
% 1.24/1.40 tff(3076,plain,
% 1.24/1.40 ($false),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[3075, 297, 2169, 2390, 800])).
% 1.24/1.40 tff(3077,plain,((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(3078,plain,
% 1.24/1.41 (~r(s(s(elem!1)), s(elem!1))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[3077, 3069, 2961])).
% 1.24/1.41 tff(3079,plain,
% 1.24/1.41 (s(s(z)) = s(elem!1)),
% 1.24/1.41 inference(symmetry,[status(thm)],[2967])).
% 1.24/1.41 tff(3080,plain,
% 1.24/1.41 (r(s(s(s(z))), s(s(z))) <=> r(s(s(elem!1)), s(elem!1))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[2987, 3079])).
% 1.24/1.41 tff(3081,plain,
% 1.24/1.41 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(z))), s(s(z)))),
% 1.24/1.41 inference(symmetry,[status(thm)],[3080])).
% 1.24/1.41 tff(3082,plain,
% 1.24/1.41 ((~r(s(s(elem!1)), s(elem!1))) <=> (~r(s(s(s(z))), s(s(z))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[3081])).
% 1.24/1.41 tff(3083,assumption,(~r(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 1.24/1.41 tff(3084,plain,
% 1.24/1.41 (~r(s(s(s(z))), s(s(z)))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[3083, 3082])).
% 1.24/1.41 tff(3085,assumption,(~(s(s(s(z))) = s(s(z)))), introduced(assumption)).
% 1.24/1.41 tff(3086,plain,
% 1.24/1.41 (r(s(s(s(z))), s(s(z)))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[2918, 51, 3085, 2915])).
% 1.24/1.41 tff(3087,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[3086, 3084])).
% 1.24/1.41 tff(3088,plain,(r(s(s(elem!1)), s(elem!1)) | (~(s(elem!1) = s(s(z)))) | (s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(3089,plain,
% 1.24/1.41 (r(s(s(elem!1)), s(elem!1)) | (~(s(elem!1) = s(s(z)))) | b(s(s(s(z))), s(s(z)))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[3088, 2248])).
% 1.24/1.41 tff(3090,plain,
% 1.24/1.41 (b(s(s(s(z))), s(s(z)))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[3089, 3078, 2930])).
% 1.24/1.41 tff(3091,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(3092,plain,
% 1.24/1.41 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(3093,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[3092])).
% 1.24/1.41 tff(3094,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[3093, 3091])).
% 1.24/1.41 tff(3095,plain,
% 1.24/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(3096,plain,
% 1.24/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[3095, 3094])).
% 1.24/1.41 tff(3097,plain,
% 1.24/1.41 ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[3096, 319, 3090, 2958])).
% 1.24/1.41 tff(3098,plain,
% 1.24/1.41 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[3097, 2953])).
% 1.24/1.41 tff(3099,plain,
% 1.24/1.41 ((s(s(s(s(z)))) = s(s(z))) | r(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[3001, 51, 3098])).
% 1.24/1.41 tff(3100,plain,
% 1.24/1.41 (r(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[3099, 2947])).
% 1.24/1.41 tff(3101,plain,
% 1.24/1.41 (~r(s(s(s(s(z)))), s(z))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[3009, 3100, 2511])).
% 1.24/1.41 tff(3102,plain,
% 1.24/1.41 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(z)))), s(z))),
% 1.24/1.41 inference(symmetry,[status(thm)],[2980])).
% 1.24/1.41 tff(3103,plain,
% 1.24/1.41 (r(s(s(s(s(z)))), s(z))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[461, 3102])).
% 1.24/1.41 tff(3104,assumption,(~r(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.24/1.41 tff(3105,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[3104, 3103])).
% 1.24/1.41 tff(3106,plain,((~r(s(s(s(elem!1))), elem!1)) | r(s(s(s(s(z)))), s(z)) | (~(s(elem!1) = s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(3107,plain,
% 1.24/1.41 (~r(s(s(s(elem!1))), elem!1)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[3106, 3101, 2930])).
% 1.24/1.41 tff(3108,plain,
% 1.24/1.41 (b(s(s(s(elem!1))), elem!1)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[361, 3107, 2941])).
% 1.24/1.41 tff(3109,plain,
% 1.24/1.41 (b(s(s(s(s(z)))), s(z))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[3108, 2937])).
% 1.24/1.41 tff(3110,plain,
% 1.24/1.41 (~r(z, s(z))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[2177, 3069, 70])).
% 1.24/1.41 tff(3111,plain,
% 1.24/1.41 (b(z, s(z))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[1099, 3110])).
% 1.24/1.41 tff(3112,plain,
% 1.24/1.41 (b(s(z), s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[2978])).
% 1.24/1.41 tff(3113,plain,
% 1.24/1.41 (b(elem!1, s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(elem!1)))))),
% 1.24/1.41 inference(symmetry,[status(thm)],[3112])).
% 1.24/1.41 tff(3114,assumption,(elem!1 = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.24/1.41 tff(3115,plain,
% 1.24/1.41 (s(z) = s(s(s(s(elem!1))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[127, 2977, 141, 3114])).
% 1.24/1.41 tff(3116,plain,
% 1.24/1.41 (inj_0(s(z)) = inj_0(s(s(s(s(elem!1)))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[3115])).
% 1.24/1.41 tff(3117,plain,
% 1.24/1.41 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(z))),
% 1.24/1.41 inference(symmetry,[status(thm)],[3116])).
% 1.24/1.41 tff(3118,plain,
% 1.24/1.41 (s(s(s(elem!1))) = z),
% 1.24/1.41 inference(transitivity,[status(thm)],[89, 3117, 13])).
% 1.24/1.41 tff(3119,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[160, 3118])).
% 1.24/1.41 tff(3120,plain,((~(elem!1 = s(s(s(s(elem!1)))))) | (~(s(elem!1) = s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(3121,plain,
% 1.24/1.41 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[3120, 2967])).
% 1.24/1.41 tff(3122,plain,
% 1.24/1.41 (r(s(z), s(s(s(s(elem!1))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[2978])).
% 1.24/1.41 tff(3123,plain,
% 1.24/1.41 ((~r(s(z), s(s(s(s(elem!1)))))) <=> (~r(elem!1, s(s(s(s(elem!1))))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[3122])).
% 1.24/1.41 tff(3124,plain,
% 1.24/1.41 (r(s(z), s(s(s(z)))) <=> r(s(z), s(s(elem!1)))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[2987])).
% 1.24/1.41 tff(3125,plain,
% 1.24/1.41 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(z))))),
% 1.24/1.41 inference(symmetry,[status(thm)],[3124])).
% 1.24/1.41 tff(3126,plain,
% 1.24/1.41 (r(s(z), s(s(s(z))))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[444, 3125])).
% 1.24/1.41 tff(3127,plain,
% 1.24/1.41 (r(s(s(s(s(elem!1)))), s(s(elem!1))) <=> r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[2970])).
% 1.24/1.41 tff(3128,plain,
% 1.24/1.41 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[3079])).
% 1.24/1.41 tff(3129,plain,
% 1.24/1.41 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.24/1.41 inference(transitivity,[status(thm)],[3128, 276])).
% 1.24/1.41 tff(3130,plain,
% 1.24/1.41 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[3129])).
% 1.24/1.41 tff(3131,plain,
% 1.24/1.41 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[231, 3130])).
% 1.24/1.41 tff(3132,plain,
% 1.24/1.41 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[178, 3131])).
% 1.24/1.41 tff(3133,assumption,(b(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 1.24/1.41 tff(3134,plain,
% 1.24/1.41 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[2979])).
% 1.24/1.41 tff(3135,plain,
% 1.24/1.41 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 1.24/1.41 inference(symmetry,[status(thm)],[3134])).
% 1.24/1.41 tff(3136,plain,
% 1.24/1.41 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[2979])).
% 1.24/1.41 tff(3137,plain,
% 1.24/1.41 ((~b(s(s(z)), s(s(s(s(z)))))) <=> (~b(s(s(z)), s(s(s(elem!1)))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[3136])).
% 1.24/1.41 tff(3138,assumption,(b(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 1.24/1.41 tff(3139,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(3140,plain,
% 1.24/1.41 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(3141,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[3140])).
% 1.24/1.41 tff(3142,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[3141, 3139])).
% 1.24/1.41 tff(3143,plain,
% 1.24/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(3144,plain,
% 1.24/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[3143, 3142])).
% 1.24/1.41 tff(3145,plain,
% 1.24/1.41 ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[3144, 319, 3138, 2966])).
% 1.24/1.41 tff(3146,plain,
% 1.24/1.41 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[3145, 3133])).
% 1.24/1.41 tff(3147,plain,
% 1.24/1.41 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[3146, 3137])).
% 1.24/1.41 tff(3148,plain,
% 1.24/1.41 (r(s(s(z)), s(s(s(elem!1))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[1571, 3147])).
% 1.24/1.41 tff(3149,plain,
% 1.24/1.41 (r(s(s(z)), s(s(s(s(z)))))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[3148, 3135])).
% 1.24/1.41 tff(3150,plain,
% 1.24/1.41 (r(z, s(s(s(s(z))))) <=> r(z, s(s(s(elem!1))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[2979])).
% 1.24/1.41 tff(3151,plain,
% 1.24/1.41 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(s(z)))))),
% 1.24/1.41 inference(symmetry,[status(thm)],[3150])).
% 1.24/1.41 tff(3152,plain,
% 1.24/1.41 (b(z, s(s(s(s(z))))) <=> b(z, s(s(s(elem!1))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[2979])).
% 1.24/1.41 tff(3153,plain,
% 1.24/1.41 ((~b(z, s(s(s(s(z)))))) <=> (~b(z, s(s(s(elem!1)))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[3152])).
% 1.24/1.41 tff(3154,assumption,(b(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.24/1.41 tff(3155,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(3156,plain,
% 1.24/1.41 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(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)))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(3157,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))))))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[3156])).
% 1.24/1.41 tff(3158,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)))))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[3157, 3155])).
% 1.24/1.41 tff(3159,plain,
% 1.24/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(3160,plain,
% 1.24/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))))))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[3159, 3158])).
% 1.24/1.41 tff(3161,plain,
% 1.24/1.41 (~b(z, s(s(s(s(z)))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[3160, 319, 2706, 2618, 3154])).
% 1.24/1.41 tff(3162,plain,
% 1.24/1.41 (~b(z, s(s(s(elem!1))))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[3161, 3153])).
% 1.24/1.41 tff(3163,plain,
% 1.24/1.41 (r(z, s(s(s(elem!1))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[416, 3162])).
% 1.24/1.41 tff(3164,plain,
% 1.24/1.41 (r(z, s(s(s(s(z)))))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[3163, 3151])).
% 1.24/1.41 tff(3165,plain,
% 1.24/1.41 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(3166,plain,
% 1.24/1.41 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(3167,plain,
% 1.24/1.41 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[3166])).
% 1.24/1.41 tff(3168,plain,
% 1.24/1.41 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[3167, 3165])).
% 1.24/1.41 tff(3169,plain,
% 1.24/1.41 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(3170,plain,
% 1.24/1.41 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[3169, 3168])).
% 1.24/1.41 tff(3171,plain,
% 1.24/1.41 ((~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[3170, 297])).
% 1.24/1.41 tff(3172,plain,
% 1.24/1.41 (~r(s(s(z)), z)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[3171, 3164, 3149])).
% 1.24/1.41 tff(3173,plain,
% 1.24/1.41 (r(s(elem!1), z) <=> r(s(s(z)), z)),
% 1.24/1.41 inference(monotonicity,[status(thm)],[2967])).
% 1.24/1.41 tff(3174,plain,
% 1.24/1.41 (r(s(s(z)), z) <=> r(s(elem!1), z)),
% 1.24/1.41 inference(symmetry,[status(thm)],[3173])).
% 1.24/1.41 tff(3175,plain,
% 1.24/1.41 ((~r(s(s(z)), z)) <=> (~r(s(elem!1), z))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[3174])).
% 1.24/1.41 tff(3176,assumption,(~r(s(s(z)), z)), introduced(assumption)).
% 1.24/1.41 tff(3177,plain,
% 1.24/1.41 (~r(s(elem!1), z)),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[3176, 3175])).
% 1.24/1.41 tff(3178,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[731, 3177])).
% 1.24/1.41 tff(3179,plain,(r(s(s(z)), z) | (~r(s(elem!1), z)) | (~(s(elem!1) = s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(3180,plain,
% 1.24/1.41 (~r(s(elem!1), z)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[3179, 3172, 2967])).
% 1.24/1.41 tff(3181,plain,
% 1.24/1.41 (b(s(elem!1), z)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[2602, 3180])).
% 1.24/1.41 tff(3182,plain,
% 1.24/1.41 (b(s(elem!1), z) <=> b(s(s(z)), z)),
% 1.24/1.41 inference(monotonicity,[status(thm)],[2967])).
% 1.24/1.41 tff(3183,plain,
% 1.24/1.41 (b(s(s(z)), z) <=> b(s(elem!1), z)),
% 1.24/1.41 inference(symmetry,[status(thm)],[3182])).
% 1.24/1.41 tff(3184,plain,
% 1.24/1.41 ((~b(s(s(z)), z)) <=> (~b(s(elem!1), z))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[3183])).
% 1.24/1.41 tff(3185,plain,
% 1.24/1.41 (~b(s(elem!1), z)),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[2604, 3184])).
% 1.24/1.41 tff(3186,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[786, 3185])).
% 1.24/1.41 tff(3187,plain,((~(s(elem!1) = s(s(z)))) | (~b(s(elem!1), z)) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(3188,plain,
% 1.24/1.41 (b(s(s(z)), z)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[3187, 3181, 2967])).
% 1.24/1.41 tff(3189,plain,
% 1.24/1.41 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(3190,plain,
% 1.24/1.42 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(3191,plain,
% 1.24/1.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[3190])).
% 1.24/1.42 tff(3192,plain,
% 1.24/1.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[3191, 3189])).
% 1.24/1.42 tff(3193,plain,
% 1.24/1.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(3194,plain,
% 1.24/1.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[3193, 3192])).
% 1.24/1.42 tff(3195,plain,
% 1.24/1.42 ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[3194, 297])).
% 1.24/1.42 tff(3196,plain,
% 1.24/1.42 (~r(z, s(s(z)))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[3195, 3164, 3149])).
% 1.24/1.42 tff(3197,plain,
% 1.24/1.42 (b(z, s(s(z)))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[729, 3196])).
% 1.24/1.42 tff(3198,plain,
% 1.24/1.42 (r(s(s(s(s(elem!1)))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[3079])).
% 1.24/1.42 tff(3199,plain,
% 1.24/1.42 (r(s(s(s(s(elem!1)))), s(elem!1)) <=> r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.24/1.42 inference(symmetry,[status(thm)],[3198])).
% 1.24/1.42 tff(3200,plain,
% 1.24/1.42 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[586, 2976])).
% 1.24/1.42 tff(3201,plain,
% 1.24/1.42 (b(s(s(s(s(elem!1)))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[3079])).
% 1.24/1.42 tff(3202,plain,
% 1.24/1.42 ((~b(s(s(s(s(elem!1)))), s(s(z)))) <=> (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[3201])).
% 1.24/1.42 tff(3203,assumption,(b(s(s(s(s(elem!1)))), s(s(s(z))))), introduced(assumption)).
% 1.24/1.42 tff(3204,assumption,(b(s(s(z)), z)), introduced(assumption)).
% 1.24/1.42 tff(3205,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(3206,plain,
% 1.24/1.42 (((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(3207,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(z))))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[3206])).
% 1.24/1.42 tff(3208,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[3207, 3205])).
% 1.24/1.42 tff(3209,plain,
% 1.24/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(3210,plain,
% 1.24/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[3209, 3208])).
% 1.24/1.42 tff(3211,plain,
% 1.24/1.42 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[3210, 319, 711, 3138, 3204, 3203, 3133])).
% 1.24/1.42 tff(3212,plain,
% 1.24/1.42 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[3211, 3202])).
% 1.24/1.42 tff(3213,plain,
% 1.24/1.42 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[595, 3212, 3200])).
% 1.24/1.42 tff(3214,plain,
% 1.24/1.42 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[3213, 3199])).
% 1.24/1.42 tff(3215,plain,
% 1.24/1.42 ((s(s(s(s(elem!1)))) = s(s(s(s(z))))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[2979])).
% 1.24/1.42 tff(3216,plain,
% 1.24/1.42 ((s(s(s(s(elem!1)))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[3215, 1324])).
% 1.24/1.42 tff(3217,plain,
% 1.24/1.42 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(s(z)))))),
% 1.24/1.42 inference(symmetry,[status(thm)],[3216])).
% 1.24/1.42 tff(3218,plain,
% 1.24/1.42 ((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(s(z))))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[3217])).
% 1.24/1.42 tff(3219,plain,
% 1.24/1.42 (~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[99, 3218])).
% 1.24/1.42 tff(3220,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(3221,plain,
% 1.24/1.42 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(3222,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[3221])).
% 1.24/1.42 tff(3223,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[3222, 3220])).
% 1.24/1.42 tff(3224,plain,
% 1.24/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(3225,plain,
% 1.24/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[3224, 3223])).
% 1.24/1.42 tff(3226,plain,
% 1.24/1.42 (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[3225, 319, 3138, 3203, 2966])).
% 1.24/1.42 tff(3227,plain,
% 1.24/1.42 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(s(z))))) | b(s(s(s(s(elem!1)))), s(s(s(s(z))))) | r(s(s(s(s(elem!1)))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(s(z))))) | b(s(s(s(s(elem!1)))), s(s(s(s(z))))) | r(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(3228,plain,
% 1.24/1.42 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(s(z))))) | b(s(s(s(s(elem!1)))), s(s(s(s(z))))) | r(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(3229,plain,
% 1.24/1.42 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(s(z))))) | b(s(s(s(s(elem!1)))), s(s(s(s(z))))) | r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[3228, 3227])).
% 1.24/1.42 tff(3230,plain,
% 1.24/1.42 ((s(s(s(s(elem!1)))) = s(s(s(s(z))))) | r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[3229, 51, 3226])).
% 1.24/1.42 tff(3231,plain,
% 1.24/1.42 (r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[3230, 3219])).
% 1.24/1.42 tff(3232,plain,
% 1.24/1.42 ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[3096, 319, 3138, 2966])).
% 1.24/1.42 tff(3233,plain,
% 1.24/1.42 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[3232, 3133])).
% 1.24/1.42 tff(3234,plain,
% 1.24/1.42 ((s(s(s(s(z)))) = s(s(z))) | r(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[3001, 51, 3233])).
% 1.24/1.42 tff(3235,plain,
% 1.24/1.42 (r(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[3234, 2986])).
% 1.24/1.42 tff(3236,plain,
% 1.24/1.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(3237,plain,
% 1.24/1.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(3238,plain,
% 1.24/1.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[3237, 3236])).
% 1.24/1.42 tff(3239,plain,
% 1.24/1.42 ($false),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[3238, 297, 3235, 3231, 3214])).
% 1.24/1.42 tff(3240,plain,((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~(s(elem!1) = s(s(z)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.42 tff(3241,plain,
% 1.24/1.42 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[3240, 3197, 99, 3138, 2966, 2967, 3188, 3133])).
% 1.24/1.42 tff(3242,plain,
% 1.24/1.42 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[2970])).
% 1.24/1.42 tff(3243,plain,
% 1.24/1.42 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[1021, 3242])).
% 1.24/1.42 tff(3244,assumption,(~b(s(s(s(s(elem!1)))), s(s(s(z))))), introduced(assumption)).
% 1.24/1.42 tff(3245,plain,
% 1.24/1.42 ($false),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[3244, 3243])).
% 1.24/1.42 tff(3246,plain,((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(z)))) | (~(s(elem!1) = s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.42 tff(3247,plain,
% 1.24/1.42 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[3246, 3241, 2967])).
% 1.24/1.42 tff(3248,plain,
% 1.24/1.42 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[571, 3247, 3132])).
% 1.24/1.42 tff(3249,plain,
% 1.24/1.42 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[3248, 3127])).
% 1.24/1.42 tff(3250,plain,
% 1.24/1.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(3251,plain,
% 1.24/1.42 (((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1))))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(3252,plain,
% 1.24/1.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1))))))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[3251])).
% 1.24/1.42 tff(3253,plain,
% 1.24/1.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[3252, 3250])).
% 1.24/1.42 tff(3254,plain,
% 1.24/1.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(3255,plain,
% 1.24/1.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1))))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[3254, 3253])).
% 1.24/1.42 tff(3256,plain,
% 1.24/1.42 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[3255, 297, 3249, 3126])).
% 1.24/1.42 tff(3257,plain,
% 1.24/1.42 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[3256, 3123])).
% 1.24/1.42 tff(3258,plain,
% 1.24/1.42 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[634, 3257, 3121])).
% 1.24/1.42 tff(3259,plain,
% 1.24/1.42 (b(s(z), s(s(s(s(elem!1)))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[3258, 3113])).
% 1.24/1.42 tff(3260,plain,
% 1.24/1.42 (r(z, s(s(elem!1))) <=> r(z, s(s(s(z))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[2970])).
% 1.24/1.42 tff(3261,plain,
% 1.24/1.42 (r(z, s(s(s(z))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[70, 3260])).
% 1.24/1.42 tff(3262,plain,
% 1.24/1.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(3263,plain,
% 1.24/1.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(3264,plain,
% 1.24/1.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[3263, 3262])).
% 1.24/1.42 tff(3265,plain,
% 1.24/1.42 (~r(s(s(s(s(elem!1)))), z)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[3264, 297, 3249, 3261])).
% 1.24/1.42 tff(3266,plain,
% 1.24/1.42 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(3267,plain,
% 1.24/1.42 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(3268,plain,
% 1.24/1.42 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z)),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[3267, 3266])).
% 1.24/1.42 tff(3269,plain,
% 1.24/1.42 (b(s(s(s(s(elem!1)))), z)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[3268, 51, 604, 3265])).
% 1.24/1.42 tff(3270,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(3271,plain,
% 1.24/1.42 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1))))))) <=> ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(3272,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[3271])).
% 1.24/1.42 tff(3273,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.24/1.42 inference(transitivity,[status(thm)],[3272, 3270])).
% 1.24/1.42 tff(3274,plain,
% 1.24/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(3275,plain,
% 1.24/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[3274, 3273])).
% 1.24/1.42 tff(3276,plain,
% 1.24/1.42 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[3275, 319, 3197, 2618, 3269])).
% 1.24/1.42 tff(3277,plain,
% 1.24/1.42 ($false),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[3276, 3259])).
% 1.24/1.42 tff(3278,plain,((~r(s(z), s(s(elem!1)))) | (~(s(elem!1) = s(s(z)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.42 tff(3279,plain,
% 1.24/1.42 (~r(s(z), s(s(elem!1)))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[3278, 2930, 99, 3090, 2958, 2953, 3111, 3109, 70])).
% 1.24/1.42 tff(3280,plain,
% 1.24/1.42 (b(s(z), s(s(elem!1)))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[1047, 3279])).
% 1.24/1.42 tff(3281,plain,
% 1.24/1.42 (b(elem!1, s(s(elem!1)))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[3280, 2934])).
% 1.24/1.42 tff(3282,plain,
% 1.24/1.42 (s(s(z)) = s(elem!1)),
% 1.24/1.42 inference(symmetry,[status(thm)],[2930])).
% 1.24/1.42 tff(3283,plain,
% 1.24/1.42 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[3282])).
% 1.24/1.42 tff(3284,plain,
% 1.24/1.42 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.24/1.42 inference(transitivity,[status(thm)],[3283, 276])).
% 1.24/1.42 tff(3285,plain,
% 1.24/1.42 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[3284])).
% 1.24/1.42 tff(3286,plain,
% 1.24/1.42 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[231, 3285])).
% 1.24/1.42 tff(3287,plain,
% 1.24/1.42 (r(s(elem!1), elem!1) <=> r(s(s(z)), elem!1)),
% 1.24/1.42 inference(monotonicity,[status(thm)],[2930])).
% 1.24/1.42 tff(3288,plain,
% 1.24/1.42 (r(s(s(z)), elem!1) <=> r(s(elem!1), elem!1)),
% 1.24/1.42 inference(symmetry,[status(thm)],[3287])).
% 1.24/1.42 tff(3289,plain,
% 1.24/1.42 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(z))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[2932])).
% 1.24/1.42 tff(3290,plain,
% 1.24/1.42 (r(s(s(z)), s(z)) <=> r(s(s(z)), elem!1)),
% 1.24/1.42 inference(symmetry,[status(thm)],[3289])).
% 1.24/1.42 tff(3291,plain,
% 1.24/1.42 (r(s(s(z)), s(z)) <=> r(s(elem!1), elem!1)),
% 1.24/1.42 inference(transitivity,[status(thm)],[3290, 3288])).
% 1.24/1.42 tff(3292,plain,
% 1.24/1.42 (r(s(elem!1), elem!1)),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[2511, 3291])).
% 1.24/1.42 tff(3293,plain,
% 1.24/1.42 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(s(z)))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[2930])).
% 1.24/1.42 tff(3294,plain,
% 1.24/1.42 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(elem!1)), s(elem!1))),
% 1.24/1.43 inference(symmetry,[status(thm)],[3293])).
% 1.24/1.43 tff(3295,plain,
% 1.24/1.43 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(s(z))), s(s(z)))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[2935])).
% 1.24/1.43 tff(3296,plain,
% 1.24/1.43 (b(s(s(s(z))), s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 1.24/1.43 inference(symmetry,[status(thm)],[3295])).
% 1.24/1.43 tff(3297,plain,
% 1.24/1.43 (b(s(s(s(z))), s(s(z))) <=> b(s(s(elem!1)), s(elem!1))),
% 1.24/1.43 inference(transitivity,[status(thm)],[3296, 3294])).
% 1.24/1.43 tff(3298,plain,
% 1.24/1.43 (b(s(s(elem!1)), s(elem!1))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[3090, 3297])).
% 1.24/1.43 tff(3299,plain,
% 1.24/1.43 (~b(elem!1, s(s(elem!1)))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[534, 3298, 116, 2941, 3292, 3286])).
% 1.24/1.43 tff(3300,plain,
% 1.24/1.43 ($false),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[3299, 3281])).
% 1.24/1.43 tff(3301,plain,((~b(s(elem!1), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.43 tff(3302,plain,
% 1.24/1.43 (~b(s(elem!1), s(s(elem!1)))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[3301, 2512, 70, 2511, 116, 772, 114, 93])).
% 1.24/1.43 tff(3303,plain,
% 1.24/1.43 (r(s(elem!1), s(s(elem!1)))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[807, 3302, 114])).
% 1.24/1.43 tff(3304,plain,
% 1.24/1.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(3305,plain,
% 1.24/1.43 (((~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1)))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(3306,plain,
% 1.24/1.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[3305])).
% 1.24/1.43 tff(3307,plain,
% 1.24/1.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[3306, 3304])).
% 1.24/1.43 tff(3308,plain,
% 1.24/1.43 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(3309,plain,
% 1.24/1.43 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(elem!1))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[3308, 3307])).
% 1.24/1.43 tff(3310,plain,
% 1.24/1.43 (~r(s(z), s(elem!1))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[3309, 297, 444, 197])).
% 1.24/1.43 tff(3311,plain,
% 1.24/1.43 (b(s(z), s(elem!1))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[2638, 51, 3310, 136])).
% 1.24/1.43 tff(3312,plain,
% 1.24/1.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(3313,plain,
% 1.24/1.43 (((~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(3314,plain,
% 1.24/1.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[3313])).
% 1.24/1.43 tff(3315,plain,
% 1.24/1.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[3314, 3312])).
% 1.24/1.43 tff(3316,plain,
% 1.24/1.43 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(3317,plain,
% 1.24/1.43 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[3316, 3315])).
% 1.24/1.43 tff(3318,plain,
% 1.24/1.43 (~r(s(elem!1), z)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[3317, 297, 197, 70])).
% 1.24/1.43 tff(3319,plain,
% 1.24/1.43 (b(s(elem!1), z)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[744, 51, 193, 3318])).
% 1.24/1.43 tff(3320,plain,
% 1.24/1.43 (~r(s(elem!1), s(z))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[853, 297, 444, 197])).
% 1.24/1.43 tff(3321,plain,
% 1.24/1.43 (b(s(elem!1), s(z))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[783, 3320, 2643])).
% 1.24/1.43 tff(3322,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)) | (~b(z, s(z))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(3323,plain,
% 1.24/1.43 (((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(elem!1), z))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)) | (~b(z, s(z))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(3324,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)) | (~b(z, s(z)))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[3323])).
% 1.24/1.43 tff(3325,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)) | (~b(z, s(z))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[3324, 3322])).
% 1.24/1.43 tff(3326,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(elem!1), z)))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(3327,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)) | (~b(z, s(z)))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[3326, 3325])).
% 1.24/1.43 tff(3328,plain,
% 1.24/1.43 ($false),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[3327, 319, 3321, 3319, 2706, 3311])).
% 1.24/1.43 tff(3329,plain,((~r(s(elem!1), s(s(elem!1)))) | (~b(z, s(z))) | (s(z) = s(elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.43 tff(3330,plain,
% 1.24/1.43 (~b(z, s(z))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[3329, 444, 70, 197, 136])).
% 1.24/1.43 tff(3331,plain,
% 1.24/1.43 (r(z, s(z))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1099, 3330])).
% 1.24/1.43 tff(3332,plain,
% 1.24/1.43 ($false),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[2588, 297, 444, 70, 3331])).
% 1.24/1.43 tff(3333,plain,((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.43 tff(3334,plain,
% 1.24/1.43 (~r(s(z), s(s(elem!1)))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[3333, 3303, 70, 2504])).
% 1.24/1.43 tff(3335,plain,
% 1.24/1.43 (b(s(z), s(s(elem!1)))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1047, 3334])).
% 1.24/1.43 tff(3336,plain,
% 1.24/1.43 (~b(s(s(elem!1)), s(z))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[2684, 687, 817, 116, 2511])).
% 1.24/1.43 tff(3337,plain,
% 1.24/1.43 (r(s(s(elem!1)), s(z))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[871, 3336])).
% 1.24/1.43 tff(3338,plain,
% 1.24/1.43 (~r(s(s(elem!1)), s(s(z)))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[2565, 3337, 2511])).
% 1.24/1.43 tff(3339,plain,
% 1.24/1.43 (b(s(s(elem!1)), s(s(z)))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[2555, 51, 2542, 3338])).
% 1.24/1.43 tff(3340,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(3341,plain,
% 1.24/1.43 (((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(3342,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[3341])).
% 1.24/1.43 tff(3343,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[3342, 3340])).
% 1.24/1.43 tff(3344,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(3345,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[3344, 3343])).
% 1.24/1.43 tff(3346,plain,
% 1.24/1.43 (~b(s(s(s(elem!1))), s(z))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[3345, 319, 3339, 817, 116])).
% 1.24/1.43 tff(3347,plain,
% 1.24/1.43 (r(s(s(s(elem!1))), s(z))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1088, 51, 171, 3346])).
% 1.24/1.43 tff(3348,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(3349,plain,
% 1.24/1.43 (((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), 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(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(3350,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[3349])).
% 1.24/1.43 tff(3351,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[3350, 3348])).
% 1.24/1.43 tff(3352,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(3353,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[3352, 3351])).
% 1.24/1.43 tff(3354,plain,
% 1.24/1.43 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[3353, 319, 3339, 687, 116])).
% 1.24/1.43 tff(3355,plain,
% 1.24/1.43 (r(s(s(z)), s(s(s(elem!1))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1571, 3354])).
% 1.24/1.43 tff(3356,plain,
% 1.24/1.43 ($false),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[2682, 297, 3355, 2511, 3347])).
% 1.24/1.43 tff(3357,plain,((~b(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (s(s(elem!1)) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.43 tff(3358,plain,
% 1.24/1.43 (~b(s(s(z)), s(s(elem!1)))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[3357, 3335, 116, 2511, 2522])).
% 1.24/1.43 tff(3359,plain,
% 1.24/1.43 (r(s(s(z)), s(s(elem!1)))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[122, 3358, 772])).
% 1.24/1.43 tff(3360,plain,
% 1.24/1.43 ($false),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[2701, 297, 197, 2578, 203])).
% 1.24/1.43 tff(3361,plain,((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(elem!1), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.43 tff(3362,plain,
% 1.24/1.43 (~r(s(elem!1), s(s(z)))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[3361, 3359, 3303])).
% 1.24/1.43 tff(3363,plain,
% 1.24/1.43 (s(elem!1) = s(s(z))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[2529, 3362, 2512])).
% 1.24/1.43 tff(3364,plain,
% 1.24/1.43 (s(s(z)) = s(elem!1)),
% 1.24/1.43 inference(symmetry,[status(thm)],[3363])).
% 1.24/1.43 tff(3365,plain,
% 1.24/1.43 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[3364])).
% 1.24/1.43 tff(3366,plain,
% 1.24/1.43 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.24/1.43 inference(transitivity,[status(thm)],[3365, 276])).
% 1.24/1.43 tff(3367,plain,
% 1.24/1.43 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[3366])).
% 1.24/1.43 tff(3368,plain,
% 1.24/1.43 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[231, 3367])).
% 1.24/1.43 tff(3369,plain,
% 1.24/1.43 (r(s(elem!1), elem!1) <=> r(s(s(z)), elem!1)),
% 1.24/1.43 inference(monotonicity,[status(thm)],[3363])).
% 1.24/1.43 tff(3370,plain,
% 1.24/1.43 (r(s(s(z)), elem!1) <=> r(s(elem!1), elem!1)),
% 1.24/1.43 inference(symmetry,[status(thm)],[3369])).
% 1.24/1.43 tff(3371,plain,
% 1.24/1.43 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[3363])).
% 1.24/1.43 tff(3372,plain,
% 1.24/1.43 (elem!1 = s(z)),
% 1.24/1.43 inference(transitivity,[status(thm)],[258, 3371, 126])).
% 1.24/1.43 tff(3373,plain,
% 1.24/1.43 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(z))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[3372])).
% 1.24/1.43 tff(3374,plain,
% 1.24/1.43 (r(s(s(z)), s(z)) <=> r(s(s(z)), elem!1)),
% 1.24/1.43 inference(symmetry,[status(thm)],[3373])).
% 1.24/1.43 tff(3375,plain,
% 1.24/1.43 (r(s(s(z)), s(z)) <=> r(s(elem!1), elem!1)),
% 1.24/1.43 inference(transitivity,[status(thm)],[3374, 3370])).
% 1.24/1.43 tff(3376,plain,
% 1.24/1.43 (r(s(elem!1), elem!1)),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[2511, 3375])).
% 1.24/1.43 tff(3377,plain,
% 1.24/1.43 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(elem!1))) = s(z))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[3372])).
% 1.24/1.43 tff(3378,plain,
% 1.24/1.43 ((s(s(s(elem!1))) = s(z)) <=> (s(s(s(elem!1))) = elem!1)),
% 1.24/1.43 inference(symmetry,[status(thm)],[3377])).
% 1.24/1.43 tff(3379,plain,
% 1.24/1.43 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[3378])).
% 1.24/1.43 tff(3380,plain,
% 1.24/1.43 (~(s(s(s(elem!1))) = elem!1)),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[171, 3379])).
% 1.24/1.43 tff(3381,plain,
% 1.24/1.43 (b(elem!1, s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[3372])).
% 1.24/1.43 tff(3382,plain,
% 1.24/1.43 (b(s(z), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 1.24/1.43 inference(symmetry,[status(thm)],[3381])).
% 1.24/1.43 tff(3383,plain,
% 1.24/1.43 (b(elem!1, s(s(elem!1)))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[3335, 3382])).
% 1.24/1.43 tff(3384,plain,
% 1.24/1.43 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(s(z)))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[3363])).
% 1.24/1.43 tff(3385,plain,
% 1.24/1.43 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(elem!1)), s(elem!1))),
% 1.24/1.43 inference(symmetry,[status(thm)],[3384])).
% 1.24/1.43 tff(3386,plain,
% 1.24/1.43 (s(s(elem!1)) = s(s(s(z)))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[3363])).
% 1.24/1.43 tff(3387,plain,
% 1.24/1.43 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(s(z))), s(s(z)))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[3386])).
% 1.24/1.43 tff(3388,plain,
% 1.24/1.43 (b(s(s(s(z))), s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 1.24/1.43 inference(symmetry,[status(thm)],[3387])).
% 1.24/1.43 tff(3389,plain,
% 1.24/1.43 (b(s(s(s(z))), s(s(z))) <=> b(s(s(elem!1)), s(elem!1))),
% 1.24/1.43 inference(transitivity,[status(thm)],[3388, 3385])).
% 1.24/1.43 tff(3390,assumption,(b(s(s(z)), s(z))), introduced(assumption)).
% 1.24/1.43 tff(3391,plain,
% 1.24/1.43 (b(z, s(s(s(z)))) <=> b(z, s(s(elem!1)))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[2987])).
% 1.24/1.43 tff(3392,plain,
% 1.24/1.43 (b(z, s(s(elem!1))) <=> b(z, s(s(s(z))))),
% 1.24/1.43 inference(symmetry,[status(thm)],[3391])).
% 1.24/1.43 tff(3393,plain,
% 1.24/1.43 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[2970])).
% 1.24/1.43 tff(3394,plain,
% 1.24/1.43 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.24/1.43 inference(symmetry,[status(thm)],[3393])).
% 1.24/1.43 tff(3395,plain,
% 1.24/1.43 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 1.24/1.43 inference(commutativity,[status(thm)],[])).
% 1.24/1.43 tff(3396,plain,
% 1.24/1.43 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 1.24/1.43 inference(symmetry,[status(thm)],[3395])).
% 1.24/1.43 tff(3397,plain,
% 1.24/1.43 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[2970])).
% 1.24/1.43 tff(3398,plain,
% 1.24/1.43 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[3397, 3395])).
% 1.24/1.43 tff(3399,plain,
% 1.24/1.43 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[3398, 3396])).
% 1.24/1.43 tff(3400,plain,
% 1.24/1.43 ((~(s(s(s(elem!1))) = s(s(elem!1)))) <=> (~(s(s(s(elem!1))) = s(s(s(z)))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[3399])).
% 1.24/1.43 tff(3401,plain,
% 1.24/1.43 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[58, 3400])).
% 1.24/1.43 tff(3402,plain,
% 1.24/1.43 (r(s(s(s(z))), s(s(z))) <=> r(s(s(elem!1)), s(s(z)))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[2987])).
% 1.24/1.43 tff(3403,plain,
% 1.24/1.43 (r(s(s(elem!1)), s(s(z))) <=> r(s(s(s(z))), s(s(z)))),
% 1.24/1.43 inference(symmetry,[status(thm)],[3402])).
% 1.24/1.43 tff(3404,plain,
% 1.24/1.43 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(s(z)))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[2967])).
% 1.24/1.43 tff(3405,plain,
% 1.24/1.43 (r(s(s(elem!1)), s(elem!1))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[3089, 2967, 2915])).
% 1.24/1.43 tff(3406,plain,
% 1.24/1.43 (r(s(s(elem!1)), s(s(z)))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[3405, 3404])).
% 1.24/1.43 tff(3407,plain,
% 1.24/1.43 (r(s(s(s(z))), s(s(z)))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[3406, 3403])).
% 1.24/1.43 tff(3408,plain,
% 1.24/1.43 (r(z, elem!1) <=> r(z, s(z))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[2969])).
% 1.24/1.43 tff(3409,plain,
% 1.24/1.43 ((z = s(z)) <=> (s(z) = z)),
% 1.24/1.43 inference(commutativity,[status(thm)],[])).
% 1.24/1.43 tff(3410,plain,
% 1.24/1.43 ((z = elem!1) <=> (z = s(z))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[2969])).
% 1.24/1.43 tff(3411,plain,
% 1.24/1.43 ((z = elem!1) <=> (s(z) = z)),
% 1.24/1.43 inference(transitivity,[status(thm)],[3410, 3409])).
% 1.24/1.43 tff(3412,plain,
% 1.24/1.43 ((s(z) = z) <=> (z = elem!1)),
% 1.24/1.43 inference(symmetry,[status(thm)],[3411])).
% 1.24/1.43 tff(3413,plain,
% 1.24/1.43 ((~(s(z) = z)) <=> (~(z = elem!1))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[3412])).
% 1.24/1.43 tff(3414,plain,
% 1.24/1.43 (~(z = elem!1)),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[62, 3413])).
% 1.24/1.43 tff(3415,plain,
% 1.24/1.43 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[3079])).
% 1.24/1.43 tff(3416,plain,
% 1.24/1.43 (s(z) = elem!1),
% 1.24/1.43 inference(transitivity,[status(thm)],[127, 3415, 141])).
% 1.24/1.43 tff(3417,assumption,(~(s(z) = elem!1)), introduced(assumption)).
% 1.24/1.43 tff(3418,plain,
% 1.24/1.43 ($false),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[3417, 3416])).
% 1.24/1.43 tff(3419,plain,((~(s(elem!1) = s(s(z)))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.43 tff(3420,plain,
% 1.24/1.43 (s(z) = elem!1),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[3419, 2967])).
% 1.24/1.43 tff(3421,plain,
% 1.24/1.43 (b(s(s(s(z))), z) <=> b(s(s(elem!1)), z)),
% 1.24/1.43 inference(monotonicity,[status(thm)],[2987])).
% 1.24/1.43 tff(3422,plain,
% 1.24/1.43 (b(s(s(elem!1)), z) <=> b(s(s(s(z))), z)),
% 1.24/1.43 inference(symmetry,[status(thm)],[3421])).
% 1.24/1.43 tff(3423,plain,
% 1.24/1.43 (r(s(s(s(z))), z) <=> r(s(s(elem!1)), z)),
% 1.24/1.43 inference(monotonicity,[status(thm)],[2987])).
% 1.24/1.43 tff(3424,plain,
% 1.24/1.43 ((~r(s(s(s(z))), z)) <=> (~r(s(s(elem!1)), z))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[3423])).
% 1.24/1.43 tff(3425,plain,
% 1.24/1.43 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(elem!1)))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[2987])).
% 1.24/1.44 tff(3426,plain,
% 1.24/1.44 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(z))))),
% 1.24/1.44 inference(symmetry,[status(thm)],[3425])).
% 1.24/1.44 tff(3427,plain,
% 1.24/1.44 (b(s(z), s(s(s(z))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[817, 3426])).
% 1.24/1.44 tff(3428,plain,
% 1.24/1.44 (r(z, s(z)) <=> r(z, elem!1)),
% 1.24/1.44 inference(symmetry,[status(thm)],[3408])).
% 1.24/1.44 tff(3429,plain,
% 1.24/1.44 ((~r(z, s(z))) <=> (~r(z, elem!1))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[3428])).
% 1.24/1.44 tff(3430,plain,
% 1.24/1.44 (~r(z, elem!1)),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[976, 3429])).
% 1.24/1.44 tff(3431,plain,
% 1.24/1.44 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = elem!1) | b(z, elem!1) | r(z, elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = elem!1) | b(z, elem!1) | r(z, elem!1))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(3432,plain,
% 1.24/1.44 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = elem!1) | b(z, elem!1) | r(z, elem!1))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(3433,plain,
% 1.24/1.44 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[3432, 3431])).
% 1.24/1.44 tff(3434,plain,
% 1.24/1.44 ((z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[3433, 51])).
% 1.24/1.44 tff(3435,plain,
% 1.24/1.44 (b(z, elem!1)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[3434, 3430, 3414])).
% 1.24/1.44 tff(3436,assumption,(s(z) = elem!1), introduced(assumption)).
% 1.24/1.44 tff(3437,plain,
% 1.24/1.44 (b(z, s(z)) <=> b(z, elem!1)),
% 1.24/1.44 inference(monotonicity,[status(thm)],[3436])).
% 1.24/1.44 tff(3438,plain,
% 1.24/1.44 (b(z, elem!1) <=> b(z, s(z))),
% 1.24/1.44 inference(symmetry,[status(thm)],[3437])).
% 1.24/1.44 tff(3439,assumption,(b(z, elem!1)), introduced(assumption)).
% 1.24/1.44 tff(3440,plain,
% 1.24/1.44 (b(z, s(z))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[3439, 3438])).
% 1.24/1.44 tff(3441,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1097, 3440])).
% 1.24/1.44 tff(3442,plain,((~(s(z) = elem!1)) | b(z, s(z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(3443,plain,
% 1.24/1.44 (b(z, s(z))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[3442, 3435, 3420])).
% 1.24/1.44 tff(3444,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(z, s(z))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(3445,plain,
% 1.24/1.44 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(z, s(z))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(3446,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(z, s(z)))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[3445])).
% 1.24/1.44 tff(3447,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(z, s(z))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[3446, 3444])).
% 1.24/1.44 tff(3448,plain,
% 1.24/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(3449,plain,
% 1.24/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(z, s(z)))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[3448, 3447])).
% 1.24/1.44 tff(3450,plain,
% 1.24/1.44 (~b(s(z), s(s(s(z))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[3449, 319, 3390, 711, 3443])).
% 1.24/1.44 tff(3451,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[3450, 3427])).
% 1.24/1.44 tff(3452,plain,((~(s(elem!1) = s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | r(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(3453,plain,
% 1.24/1.44 (~b(z, s(s(z)))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[3452, 976, 817, 3390, 2967])).
% 1.24/1.44 tff(3454,plain,
% 1.24/1.44 (r(z, s(s(z)))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[729, 3453])).
% 1.24/1.44 tff(3455,plain,
% 1.24/1.44 (~r(s(s(s(z))), z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[895, 297, 3454, 889])).
% 1.24/1.44 tff(3456,plain,
% 1.24/1.44 (~r(s(s(elem!1)), z)),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[3455, 3424])).
% 1.24/1.44 tff(3457,plain,
% 1.24/1.44 (b(s(s(elem!1)), z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[75, 3456])).
% 1.24/1.44 tff(3458,plain,
% 1.24/1.44 (b(s(s(s(z))), z)),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[3457, 3422])).
% 1.24/1.44 tff(3459,plain,
% 1.24/1.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(z)))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(3460,plain,
% 1.24/1.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(z)))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(3461,plain,
% 1.24/1.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(z))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[3460, 3459])).
% 1.24/1.44 tff(3462,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[3461, 297, 2578, 70, 732])).
% 1.24/1.44 tff(3463,plain,((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(3464,plain,
% 1.24/1.44 (~r(z, s(s(elem!1)))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[3463, 3454, 2578])).
% 1.24/1.44 tff(3465,plain,
% 1.24/1.44 (b(z, s(s(elem!1)))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[56, 3464])).
% 1.24/1.44 tff(3466,plain,
% 1.24/1.44 (b(z, s(s(s(z))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[3465, 3392])).
% 1.24/1.44 tff(3467,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(3468,plain,
% 1.24/1.44 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(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))))) | (~b(z, s(z))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(3469,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z)))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[3468])).
% 1.24/1.44 tff(3470,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[3469, 3467])).
% 1.24/1.44 tff(3471,plain,
% 1.24/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(3472,plain,
% 1.24/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z)))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[3471, 3470])).
% 1.24/1.44 tff(3473,plain,
% 1.24/1.44 ((~b(s(s(s(z))), z)) | (~b(z, s(z)))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[3472, 319, 3427, 3466])).
% 1.24/1.44 tff(3474,plain,
% 1.24/1.44 (~b(z, s(z))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[3473, 3458])).
% 1.24/1.44 tff(3475,plain,
% 1.24/1.44 (~b(z, elem!1)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[3442, 3474, 3420])).
% 1.24/1.44 tff(3476,plain,
% 1.24/1.44 (r(z, elem!1)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[3434, 3475, 3414])).
% 1.24/1.44 tff(3477,plain,
% 1.24/1.44 (r(z, s(z))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[3476, 3408])).
% 1.24/1.44 tff(3478,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[976, 3477])).
% 1.24/1.44 tff(3479,plain,(r(z, s(z)) | (~(s(elem!1) = s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(3480,plain,
% 1.24/1.44 (r(z, s(z))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[3479, 2967, 3407, 2578, 817, 3390])).
% 1.24/1.44 tff(3481,plain,
% 1.24/1.44 ((~(s(s(s(elem!1))) = s(s(elem!1)))) <=> (~(s(s(s(z))) = s(s(s(elem!1)))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[3398])).
% 1.24/1.44 tff(3482,plain,
% 1.24/1.44 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[58, 3481])).
% 1.24/1.44 tff(3483,plain,
% 1.24/1.44 (b(s(elem!1), elem!1) <=> b(s(s(z)), elem!1)),
% 1.24/1.44 inference(monotonicity,[status(thm)],[2967])).
% 1.24/1.44 tff(3484,plain,
% 1.24/1.44 (b(s(s(z)), elem!1) <=> b(s(elem!1), elem!1)),
% 1.24/1.44 inference(symmetry,[status(thm)],[3483])).
% 1.24/1.44 tff(3485,plain,
% 1.24/1.44 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(z))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[2969])).
% 1.24/1.44 tff(3486,plain,
% 1.24/1.44 (b(s(s(z)), s(z)) <=> b(s(s(z)), elem!1)),
% 1.24/1.44 inference(symmetry,[status(thm)],[3485])).
% 1.24/1.44 tff(3487,plain,
% 1.24/1.44 (b(s(s(z)), s(z)) <=> b(s(elem!1), elem!1)),
% 1.24/1.44 inference(transitivity,[status(thm)],[3486, 3484])).
% 1.24/1.44 tff(3488,plain,
% 1.24/1.44 (b(s(elem!1), elem!1)),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[3390, 3487])).
% 1.24/1.44 tff(3489,plain,
% 1.24/1.44 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.24/1.44 inference(symmetry,[status(thm)],[3201])).
% 1.24/1.44 tff(3490,plain,
% 1.24/1.44 ((~r(s(s(s(s(elem!1)))), s(s(z)))) <=> (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[3198])).
% 1.24/1.44 tff(3491,plain,
% 1.24/1.44 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(z)), s(s(elem!1)))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[2987])).
% 1.24/1.44 tff(3492,plain,
% 1.24/1.44 (r(s(s(z)), s(s(elem!1))) <=> r(s(s(z)), s(s(s(z))))),
% 1.24/1.44 inference(symmetry,[status(thm)],[3491])).
% 1.24/1.44 tff(3493,plain,
% 1.24/1.44 (r(s(s(z)), s(s(s(z))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[2578, 3492])).
% 1.24/1.44 tff(3494,assumption,(~r(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 1.24/1.44 tff(3495,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[3494, 3493])).
% 1.24/1.44 tff(3496,plain,(r(s(s(z)), s(s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~(s(elem!1) = s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(3497,plain,
% 1.24/1.44 (r(s(s(z)), s(s(s(z))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[3496, 2967, 2578])).
% 1.24/1.44 tff(3498,plain,
% 1.24/1.44 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.24/1.44 inference(symmetry,[status(thm)],[3242])).
% 1.24/1.44 tff(3499,plain,
% 1.24/1.44 ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) <=> (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[3498])).
% 1.24/1.44 tff(3500,plain,
% 1.24/1.44 (r(z, s(s(s(z)))) <=> r(z, s(s(elem!1)))),
% 1.24/1.44 inference(symmetry,[status(thm)],[3260])).
% 1.24/1.44 tff(3501,plain,
% 1.24/1.44 ((~r(z, s(s(s(z))))) <=> (~r(z, s(s(elem!1))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[3500])).
% 1.24/1.44 tff(3502,assumption,(r(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 1.24/1.44 tff(3503,assumption,(r(z, s(s(s(z))))), introduced(assumption)).
% 1.24/1.44 tff(3504,plain,
% 1.24/1.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(3505,plain,
% 1.24/1.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(3506,plain,
% 1.24/1.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[3505, 3504])).
% 1.24/1.44 tff(3507,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[3506, 297, 665, 3503, 3502])).
% 1.24/1.44 tff(3508,plain,((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(3509,plain,
% 1.24/1.44 (~r(z, s(s(s(z))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[3508, 665, 3497])).
% 1.24/1.44 tff(3510,plain,
% 1.24/1.44 (~r(z, s(s(elem!1)))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[3509, 3501])).
% 1.24/1.44 tff(3511,plain,
% 1.24/1.44 (b(z, s(s(elem!1)))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[56, 3510])).
% 1.24/1.44 tff(3512,plain,
% 1.24/1.44 (b(z, s(s(s(z))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[3511, 3392])).
% 1.24/1.44 tff(3513,plain,
% 1.24/1.44 (b(s(s(s(z))), s(z)) <=> b(s(s(s(z))), elem!1)),
% 1.24/1.44 inference(monotonicity,[status(thm)],[2978])).
% 1.24/1.44 tff(3514,plain,
% 1.24/1.44 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(z))),
% 1.24/1.44 inference(symmetry,[status(thm)],[3513])).
% 1.24/1.44 tff(3515,plain,
% 1.24/1.44 (b(s(s(s(z))), elem!1) <=> b(s(s(elem!1)), s(z))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[2987, 2969])).
% 1.24/1.44 tff(3516,plain,
% 1.24/1.44 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(z))), elem!1)),
% 1.24/1.44 inference(symmetry,[status(thm)],[3515])).
% 1.24/1.44 tff(3517,plain,
% 1.24/1.44 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(z))), s(z))),
% 1.24/1.44 inference(transitivity,[status(thm)],[3516, 3514])).
% 1.24/1.44 tff(3518,plain,
% 1.24/1.44 (b(elem!1, s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[2969])).
% 1.24/1.44 tff(3519,plain,
% 1.24/1.44 (b(s(z), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 1.24/1.44 inference(symmetry,[status(thm)],[3518])).
% 1.24/1.44 tff(3520,plain,
% 1.24/1.44 (b(elem!1, s(s(elem!1)))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[817, 3519])).
% 1.24/1.44 tff(3521,assumption,(~(s(s(s(elem!1))) = s(s(s(z))))), introduced(assumption)).
% 1.24/1.44 tff(3522,plain,
% 1.24/1.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(3523,plain,
% 1.24/1.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(3524,plain,
% 1.24/1.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[3523, 3522])).
% 1.24/1.44 tff(3525,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[3524, 297, 115, 2578, 665])).
% 1.24/1.44 tff(3526,plain,((~r(s(s(z)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(3527,plain,
% 1.24/1.44 (~r(s(s(elem!1)), z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[3526, 665, 2578])).
% 1.24/1.44 tff(3528,plain,
% 1.24/1.44 (b(s(s(elem!1)), z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[75, 3527])).
% 1.24/1.44 tff(3529,plain,
% 1.24/1.44 (b(s(s(s(z))), z)),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[3528, 3422])).
% 1.24/1.44 tff(3530,assumption,(b(s(s(s(elem!1))), s(s(s(z))))), introduced(assumption)).
% 1.24/1.44 tff(3531,plain,
% 1.24/1.44 ((~b(s(s(s(z))), elem!1)) <=> (~b(s(s(elem!1)), s(z)))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[3515])).
% 1.24/1.44 tff(3532,plain,
% 1.24/1.44 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[2979])).
% 1.24/1.44 tff(3533,plain,
% 1.24/1.44 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.44 inference(symmetry,[status(thm)],[3532])).
% 1.24/1.44 tff(3534,plain,
% 1.24/1.44 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[3530, 3533])).
% 1.24/1.44 tff(3535,plain,
% 1.24/1.44 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 1.24/1.44 inference(monotonicity,[status(thm)],[2979, 2978])).
% 1.24/1.44 tff(3536,plain,
% 1.24/1.44 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 1.24/1.44 inference(symmetry,[status(thm)],[3535])).
% 1.24/1.44 tff(3537,plain,
% 1.24/1.44 (b(s(s(s(s(z)))), s(z))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[448, 3536])).
% 1.24/1.44 tff(3538,assumption,(b(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.24/1.44 tff(3539,plain,
% 1.24/1.44 (b(s(s(s(z))), s(z))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[3538, 3514])).
% 1.24/1.44 tff(3540,assumption,(b(s(z), s(s(s(z))))), introduced(assumption)).
% 1.24/1.44 tff(3541,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(3542,plain,
% 1.24/1.44 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(3543,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)))))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[3542])).
% 1.24/1.44 tff(3544,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[3543, 3541])).
% 1.24/1.44 tff(3545,plain,
% 1.24/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(3546,plain,
% 1.24/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[3545, 3544])).
% 1.24/1.44 tff(3547,plain,
% 1.24/1.44 (~b(s(s(s(z))), s(z))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[3546, 319, 3540, 3154, 2966])).
% 1.24/1.44 tff(3548,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[3547, 3539])).
% 1.24/1.44 tff(3549,plain,((~b(s(s(s(z))), elem!1)) | (~(s(elem!1) = s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(3550,plain,
% 1.24/1.44 (~b(s(s(s(z))), elem!1)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[3549, 3427, 2967, 3537, 3534])).
% 1.24/1.44 tff(3551,plain,
% 1.24/1.44 (~b(s(s(elem!1)), s(z))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[3550, 3531])).
% 1.24/1.44 tff(3552,plain,
% 1.24/1.44 (r(s(s(elem!1)), s(z))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[871, 3551])).
% 1.24/1.44 tff(3553,plain,
% 1.24/1.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(3554,plain,
% 1.24/1.44 (((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(3555,plain,
% 1.24/1.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z)))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[3554])).
% 1.24/1.44 tff(3556,plain,
% 1.24/1.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[3555, 3553])).
% 1.24/1.44 tff(3557,plain,
% 1.24/1.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(3558,plain,
% 1.24/1.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z)))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[3557, 3556])).
% 1.24/1.44 tff(3559,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[3558, 297, 2169, 115, 917])).
% 1.24/1.44 tff(3560,plain,((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(3561,plain,
% 1.24/1.44 (~r(s(s(elem!1)), z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[3560, 3552, 917])).
% 1.24/1.44 tff(3562,plain,
% 1.24/1.44 (b(s(s(elem!1)), z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[75, 3561])).
% 1.24/1.44 tff(3563,plain,
% 1.24/1.44 (b(s(s(s(z))), z)),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[3562, 3422])).
% 1.24/1.44 tff(3564,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(3565,plain,
% 1.24/1.45 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(3566,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[3565])).
% 1.24/1.45 tff(3567,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.45 inference(transitivity,[status(thm)],[3566, 3564])).
% 1.24/1.45 tff(3568,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(3569,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[3568, 3567])).
% 1.24/1.45 tff(3570,plain,
% 1.24/1.45 (~b(s(s(s(z))), z)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[3569, 319, 3427, 3537, 3534])).
% 1.24/1.45 tff(3571,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[3570, 3563])).
% 1.24/1.45 tff(3572,plain,((~b(s(s(s(elem!1))), elem!1)) | (~(s(elem!1) = s(s(z)))) | (~r(z, s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(3573,plain,
% 1.24/1.45 (~b(s(s(s(elem!1))), elem!1)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[3572, 3530, 2967, 917, 817])).
% 1.24/1.45 tff(3574,plain,
% 1.24/1.45 (r(s(s(s(elem!1))), elem!1)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[361, 3573, 2976])).
% 1.24/1.45 tff(3575,plain,
% 1.24/1.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(3576,plain,
% 1.24/1.45 (((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(3577,plain,
% 1.24/1.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[3576])).
% 1.24/1.45 tff(3578,plain,
% 1.24/1.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.24/1.45 inference(transitivity,[status(thm)],[3577, 3575])).
% 1.24/1.45 tff(3579,plain,
% 1.24/1.45 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(3580,plain,
% 1.24/1.45 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z)))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[3579, 3578])).
% 1.24/1.45 tff(3581,plain,
% 1.24/1.45 (~r(s(s(s(s(z)))), s(z))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[3580, 297, 917, 2467])).
% 1.24/1.45 tff(3582,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[3581, 3103])).
% 1.24/1.45 tff(3583,plain,((~r(s(s(s(elem!1))), elem!1)) | (~(s(elem!1) = s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(3584,plain,
% 1.24/1.45 (~r(s(s(s(s(z)))), z)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[3583, 3574, 917, 2967])).
% 1.24/1.45 tff(3585,assumption,(b(s(s(s(z))), z)), introduced(assumption)).
% 1.24/1.45 tff(3586,assumption,(b(z, s(s(s(z))))), introduced(assumption)).
% 1.24/1.45 tff(3587,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(3588,plain,
% 1.24/1.45 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(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)))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(3589,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[3588])).
% 1.24/1.45 tff(3590,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)))),
% 1.24/1.45 inference(transitivity,[status(thm)],[3589, 3587])).
% 1.24/1.45 tff(3591,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(3592,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[3591, 3590])).
% 1.24/1.45 tff(3593,plain,
% 1.24/1.45 (~b(s(s(s(s(z)))), z)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[3592, 319, 3534, 3586, 3585])).
% 1.24/1.45 tff(3594,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[2481, 51, 2478, 3593, 3584])).
% 1.24/1.45 tff(3595,plain,((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~(s(elem!1) = s(s(z)))) | (~r(z, s(z))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(3596,plain,
% 1.24/1.45 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[3595, 3512, 3529, 2967, 917, 817])).
% 1.24/1.45 tff(3597,plain,
% 1.24/1.45 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z)))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(3598,plain,
% 1.24/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z)))))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(3599,plain,
% 1.24/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z))))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[3598, 3597])).
% 1.24/1.45 tff(3600,plain,
% 1.24/1.45 ((s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[3599, 51])).
% 1.24/1.45 tff(3601,plain,
% 1.24/1.45 (r(s(s(s(elem!1))), s(s(s(z))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[3600, 3596, 3521])).
% 1.24/1.45 tff(3602,plain,
% 1.24/1.45 (r(s(s(s(z))), s(z)) <=> r(s(s(elem!1)), s(z))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[2987])).
% 1.24/1.45 tff(3603,plain,
% 1.24/1.45 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(z))), s(z))),
% 1.24/1.45 inference(symmetry,[status(thm)],[3602])).
% 1.24/1.45 tff(3604,plain,
% 1.24/1.45 (r(s(s(s(z))), s(z))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[2169, 3603])).
% 1.24/1.45 tff(3605,plain,
% 1.24/1.45 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.24/1.45 inference(transitivity,[status(thm)],[3129, 277])).
% 1.24/1.45 tff(3606,plain,
% 1.24/1.45 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[3605])).
% 1.24/1.45 tff(3607,plain,
% 1.24/1.45 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[231, 3606])).
% 1.24/1.45 tff(3608,assumption,(r(s(s(s(elem!1))), s(s(s(z))))), introduced(assumption)).
% 1.24/1.45 tff(3609,plain,
% 1.24/1.45 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[3608, 3394])).
% 1.24/1.45 tff(3610,plain,
% 1.24/1.45 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[343, 3609, 197])).
% 1.24/1.45 tff(3611,plain,
% 1.24/1.45 (b(s(elem!1), s(s(s(elem!1))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[434, 3610, 3607])).
% 1.24/1.45 tff(3612,plain,
% 1.24/1.45 (~b(s(s(s(elem!1))), elem!1)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[457, 3611, 397, 449])).
% 1.24/1.45 tff(3613,plain,
% 1.24/1.45 (r(s(s(s(elem!1))), elem!1)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[361, 3612, 2976])).
% 1.24/1.45 tff(3614,plain,
% 1.24/1.45 (r(s(s(s(s(z)))), s(z))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[3613, 3102])).
% 1.24/1.45 tff(3615,plain,
% 1.24/1.45 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[2979])).
% 1.24/1.45 tff(3616,plain,
% 1.24/1.45 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.45 inference(symmetry,[status(thm)],[3615])).
% 1.24/1.45 tff(3617,plain,
% 1.24/1.45 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[3608, 3616])).
% 1.24/1.45 tff(3618,plain,
% 1.24/1.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(3619,plain,
% 1.24/1.45 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(3620,plain,
% 1.24/1.45 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[3619, 3618])).
% 1.24/1.45 tff(3621,plain,
% 1.24/1.45 ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z)))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[3620, 297, 3617])).
% 1.24/1.45 tff(3622,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[3621, 3614, 3604])).
% 1.24/1.45 tff(3623,plain,((~r(s(s(s(elem!1))), s(s(s(z))))) | (~(s(elem!1) = s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(3624,plain,
% 1.24/1.45 (~r(s(s(elem!1)), s(z))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[3623, 3601, 2967, 3520, 449, 197])).
% 1.24/1.45 tff(3625,plain,
% 1.24/1.45 (b(s(s(elem!1)), s(z))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[871, 3624])).
% 1.24/1.45 tff(3626,plain,
% 1.24/1.45 (b(s(s(s(z))), s(z))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[3625, 3517])).
% 1.24/1.45 tff(3627,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(3628,plain,
% 1.24/1.45 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(3629,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[3628])).
% 1.24/1.45 tff(3630,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 1.24/1.45 inference(transitivity,[status(thm)],[3629, 3627])).
% 1.24/1.45 tff(3631,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(3632,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[3631, 3630])).
% 1.24/1.45 tff(3633,plain,
% 1.24/1.45 ((~b(s(s(s(z))), z)) | (~b(s(z), z))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[3632, 319, 3427, 3512])).
% 1.24/1.45 tff(3634,plain,
% 1.24/1.45 (~b(s(z), z)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[3633, 3529])).
% 1.24/1.45 tff(3635,plain,
% 1.24/1.45 (r(s(z), z)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[65, 51, 62, 3634])).
% 1.24/1.45 tff(3636,plain,
% 1.24/1.45 (r(elem!1, s(s(s(s(elem!1))))) <=> r(s(z), s(s(s(s(elem!1)))))),
% 1.24/1.45 inference(symmetry,[status(thm)],[3122])).
% 1.24/1.45 tff(3637,plain,
% 1.24/1.45 ((~b(s(z), s(s(s(s(elem!1)))))) <=> (~b(elem!1, s(s(s(s(elem!1))))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[3112])).
% 1.24/1.45 tff(3638,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(3639,plain,
% 1.24/1.45 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1))))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(3640,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[3639])).
% 1.24/1.45 tff(3641,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.24/1.45 inference(transitivity,[status(thm)],[3640, 3638])).
% 1.24/1.45 tff(3642,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(3643,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[3642, 3641])).
% 1.24/1.45 tff(3644,plain,
% 1.24/1.45 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[3643, 319, 3203, 3540, 2965])).
% 1.24/1.45 tff(3645,plain,
% 1.24/1.45 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[3644, 3637])).
% 1.24/1.45 tff(3646,plain,
% 1.24/1.45 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[634, 3645, 3121])).
% 1.24/1.45 tff(3647,plain,
% 1.24/1.45 (r(s(z), s(s(s(s(elem!1)))))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[3646, 3636])).
% 1.24/1.45 tff(3648,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(3649,plain,
% 1.24/1.46 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(3650,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[3649])).
% 1.24/1.46 tff(3651,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.24/1.46 inference(transitivity,[status(thm)],[3650, 3648])).
% 1.24/1.46 tff(3652,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(3653,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[3652, 3651])).
% 1.24/1.46 tff(3654,plain,
% 1.24/1.46 (~b(s(s(s(s(elem!1)))), z)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[3653, 319, 3203, 3586, 2965])).
% 1.24/1.46 tff(3655,plain,
% 1.24/1.46 (r(s(s(s(s(elem!1)))), z)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[3268, 51, 604, 3654])).
% 1.24/1.46 tff(3656,plain,
% 1.24/1.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(3657,plain,
% 1.24/1.46 (((~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1))))))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(3658,plain,
% 1.24/1.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), s(s(s(s(elem!1))))))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[3657])).
% 1.24/1.46 tff(3659,plain,
% 1.24/1.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.24/1.46 inference(transitivity,[status(thm)],[3658, 3656])).
% 1.24/1.46 tff(3660,plain,
% 1.24/1.46 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(3661,plain,
% 1.24/1.46 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), s(s(s(s(elem!1))))))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[3660, 3659])).
% 1.24/1.46 tff(3662,plain,
% 1.24/1.46 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[3661, 297, 666, 3655])).
% 1.24/1.46 tff(3663,plain,
% 1.24/1.46 ($false),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[3662, 3647])).
% 1.24/1.46 tff(3664,plain,((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~(s(elem!1) = 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,[]))).
% 1.24/1.46 tff(3665,plain,
% 1.24/1.46 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[3664, 3635, 2967, 3427, 3626, 3512])).
% 1.24/1.46 tff(3666,plain,
% 1.24/1.46 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[3665, 3499])).
% 1.24/1.46 tff(3667,plain,
% 1.24/1.46 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[571, 3666, 3132])).
% 1.24/1.46 tff(3668,plain,
% 1.24/1.46 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[3667, 3127])).
% 1.24/1.46 tff(3669,plain,
% 1.24/1.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(3670,plain,
% 1.24/1.46 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(3671,plain,
% 1.24/1.46 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[3670, 3669])).
% 1.24/1.46 tff(3672,plain,
% 1.24/1.46 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[3671, 297, 3668, 3497])).
% 1.24/1.46 tff(3673,plain,
% 1.24/1.46 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[3672, 3490])).
% 1.24/1.46 tff(3674,plain,
% 1.24/1.46 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[595, 3673, 3200])).
% 1.24/1.46 tff(3675,plain,
% 1.24/1.46 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[3674, 3489])).
% 1.24/1.46 tff(3676,plain,
% 1.24/1.46 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[3601, 3616])).
% 1.24/1.46 tff(3677,plain,
% 1.24/1.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(3678,plain,
% 1.24/1.46 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))) <=> ((~r(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(elem!1)))), s(s(s(s(z)))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(3679,plain,
% 1.24/1.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[3678])).
% 1.24/1.46 tff(3680,plain,
% 1.24/1.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.24/1.46 inference(transitivity,[status(thm)],[3679, 3677])).
% 1.24/1.46 tff(3681,plain,
% 1.24/1.46 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(3682,plain,
% 1.24/1.46 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[3681, 3680])).
% 1.24/1.46 tff(3683,plain,
% 1.24/1.46 (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[3682, 297, 3668, 3676])).
% 1.24/1.46 tff(3684,plain,
% 1.24/1.46 ((s(s(s(s(elem!1)))) = s(s(s(s(z))))) | b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[3229, 51, 3683])).
% 1.24/1.46 tff(3685,plain,
% 1.24/1.46 (b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[3684, 3219])).
% 1.24/1.46 tff(3686,plain,
% 1.24/1.46 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.24/1.46 inference(symmetry,[status(thm)],[3136])).
% 1.24/1.46 tff(3687,plain,
% 1.24/1.46 ((~r(s(s(z)), s(s(s(s(z)))))) <=> (~r(s(s(z)), s(s(s(elem!1)))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[3134])).
% 1.24/1.46 tff(3688,plain,
% 1.24/1.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(3689,plain,
% 1.24/1.46 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(3690,plain,
% 1.24/1.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[3689])).
% 1.24/1.46 tff(3691,plain,
% 1.24/1.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.46 inference(transitivity,[status(thm)],[3690, 3688])).
% 1.24/1.46 tff(3692,plain,
% 1.24/1.46 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(3693,plain,
% 1.24/1.46 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[3692, 3691])).
% 1.24/1.46 tff(3694,plain,
% 1.24/1.46 ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[3693, 297, 3497])).
% 1.24/1.46 tff(3695,plain,
% 1.24/1.46 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[3694, 3676])).
% 1.24/1.46 tff(3696,plain,
% 1.24/1.46 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[3695, 3687])).
% 1.24/1.46 tff(3697,plain,
% 1.24/1.46 (b(s(s(z)), s(s(s(elem!1))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1571, 3696])).
% 1.24/1.46 tff(3698,plain,
% 1.24/1.46 (b(s(s(z)), s(s(s(s(z)))))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[3697, 3686])).
% 1.24/1.46 tff(3699,plain,
% 1.24/1.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(3700,plain,
% 1.24/1.46 (((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(3701,plain,
% 1.24/1.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[3700])).
% 1.24/1.46 tff(3702,plain,
% 1.24/1.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.46 inference(transitivity,[status(thm)],[3701, 3699])).
% 1.24/1.46 tff(3703,plain,
% 1.24/1.46 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(3704,plain,
% 1.24/1.46 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[3703, 3702])).
% 1.24/1.46 tff(3705,plain,
% 1.24/1.46 ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[3704, 297, 3497])).
% 1.24/1.46 tff(3706,plain,
% 1.24/1.46 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[3705, 3676])).
% 1.24/1.46 tff(3707,plain,
% 1.24/1.46 ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[3001, 51, 3706])).
% 1.24/1.46 tff(3708,plain,
% 1.24/1.46 (b(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[3707, 2986])).
% 1.24/1.46 tff(3709,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(3710,plain,
% 1.24/1.46 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(3711,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[3710])).
% 1.24/1.46 tff(3712,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.24/1.46 inference(transitivity,[status(thm)],[3711, 3709])).
% 1.24/1.46 tff(3713,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(3714,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[3713, 3712])).
% 1.24/1.46 tff(3715,plain,
% 1.24/1.46 ($false),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[3714, 319, 3708, 3698, 3685, 3675])).
% 1.24/1.46 tff(3716,plain,((~r(s(s(z)), z)) | (~(s(elem!1) = s(s(z)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(s(z)))) | (~r(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.46 tff(3717,plain,
% 1.24/1.46 (~r(s(s(z)), z)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[3716, 2967, 93, 3488, 197, 3401, 3480, 817, 2578])).
% 1.24/1.46 tff(3718,plain,
% 1.24/1.46 (~r(s(elem!1), z)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[3179, 3717, 2967])).
% 1.24/1.46 tff(3719,plain,
% 1.24/1.46 (b(s(elem!1), z)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[2602, 3718])).
% 1.24/1.46 tff(3720,plain,
% 1.24/1.46 (b(s(s(z)), z)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[3187, 3719, 2967])).
% 1.24/1.46 tff(3721,plain,
% 1.24/1.46 (b(s(s(s(z))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.24/1.46 inference(transitivity,[status(thm)],[3513, 3515])).
% 1.24/1.46 tff(3722,plain,
% 1.24/1.46 ((~b(s(s(s(z))), s(z))) <=> (~b(s(s(elem!1)), s(z)))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[3721])).
% 1.24/1.46 tff(3723,plain,
% 1.24/1.46 ((~r(z, s(s(s(s(z)))))) <=> (~r(z, s(s(s(elem!1)))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[3150])).
% 1.24/1.46 tff(3724,plain,
% 1.24/1.46 (~b(s(s(s(elem!1))), elem!1)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[3572, 917, 2967, 3530, 817])).
% 1.24/1.46 tff(3725,plain,
% 1.24/1.46 (r(s(s(s(elem!1))), elem!1)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[361, 3724, 2976])).
% 1.24/1.46 tff(3726,plain,
% 1.24/1.46 (r(s(s(s(s(z)))), s(z))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[3725, 3102])).
% 1.24/1.46 tff(3727,plain,
% 1.24/1.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(3728,plain,
% 1.24/1.46 (((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(3729,plain,
% 1.24/1.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[3728])).
% 1.24/1.46 tff(3730,plain,
% 1.24/1.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.24/1.46 inference(transitivity,[status(thm)],[3729, 3727])).
% 1.24/1.46 tff(3731,plain,
% 1.24/1.46 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(3732,plain,
% 1.24/1.46 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[3731, 3730])).
% 1.24/1.46 tff(3733,plain,
% 1.24/1.46 ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[3732, 297, 917])).
% 1.24/1.46 tff(3734,plain,
% 1.24/1.46 (~r(z, s(s(s(s(z)))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[3733, 3726])).
% 1.24/1.46 tff(3735,plain,
% 1.24/1.46 (~r(z, s(s(s(elem!1))))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[3734, 3723])).
% 1.24/1.46 tff(3736,plain,
% 1.24/1.46 (b(z, s(s(s(elem!1))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[416, 3735])).
% 1.24/1.46 tff(3737,plain,
% 1.24/1.46 (~r(s(s(s(s(z)))), z)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[3583, 3725, 917, 2967])).
% 1.24/1.46 tff(3738,plain,
% 1.24/1.46 (b(s(s(s(s(z)))), z)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[2481, 51, 2478, 3737])).
% 1.24/1.46 tff(3739,assumption,(~(s(s(s(z))) = s(s(s(elem!1))))), introduced(assumption)).
% 1.24/1.46 tff(3740,plain,
% 1.24/1.46 ((~b(z, s(s(s(z))))) <=> (~b(z, s(s(elem!1))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[3391])).
% 1.24/1.46 tff(3741,assumption,(b(z, s(s(s(elem!1))))), introduced(assumption)).
% 1.24/1.46 tff(3742,plain,
% 1.24/1.46 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(s(z)))))),
% 1.24/1.46 inference(symmetry,[status(thm)],[3152])).
% 1.24/1.46 tff(3743,plain,
% 1.24/1.46 (b(z, s(s(s(s(z)))))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[3741, 3742])).
% 1.24/1.46 tff(3744,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(3745,plain,
% 1.24/1.46 (((~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(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(3746,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(s(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z))))))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[3745])).
% 1.24/1.46 tff(3747,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(s(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[3746, 3744])).
% 1.24/1.47 tff(3748,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(3749,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z))))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[3748, 3747])).
% 1.24/1.47 tff(3750,plain,
% 1.24/1.47 ($false),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[3749, 319, 2966, 2965, 3586, 3743])).
% 1.24/1.47 tff(3751,plain,((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~(s(elem!1) = s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.47 tff(3752,plain,
% 1.24/1.47 (~b(z, s(s(s(z))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[3751, 2965, 2966, 3741, 2967])).
% 1.24/1.47 tff(3753,plain,
% 1.24/1.47 (~b(z, s(s(elem!1)))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[3752, 3740])).
% 1.24/1.47 tff(3754,plain,
% 1.24/1.47 (r(z, s(s(elem!1)))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[56, 3753])).
% 1.24/1.47 tff(3755,plain,
% 1.24/1.47 (r(z, s(s(s(z))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[3754, 3260])).
% 1.24/1.47 tff(3756,assumption,(b(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.24/1.47 tff(3757,plain,
% 1.24/1.47 ((~b(s(z), s(s(s(s(z)))))) <=> (~b(elem!1, s(s(s(s(z))))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[3014])).
% 1.24/1.47 tff(3758,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(3759,plain,
% 1.24/1.47 (((~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(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(3760,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z), s(s(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[3759])).
% 1.24/1.47 tff(3761,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z), s(s(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[3760, 3758])).
% 1.24/1.47 tff(3762,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(3763,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[3762, 3761])).
% 1.24/1.47 tff(3764,plain,
% 1.24/1.47 ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[3763, 319, 3540, 2966])).
% 1.24/1.47 tff(3765,plain,
% 1.24/1.47 (~b(s(z), s(s(s(s(z)))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[3764, 2965])).
% 1.24/1.47 tff(3766,plain,
% 1.24/1.47 (~b(elem!1, s(s(s(s(z)))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[3765, 3757])).
% 1.24/1.47 tff(3767,plain,
% 1.24/1.47 (r(elem!1, s(s(s(s(z)))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[3036, 3766, 3021])).
% 1.24/1.47 tff(3768,plain,
% 1.24/1.47 (~r(z, s(s(z)))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[3463, 3754, 2578])).
% 1.24/1.47 tff(3769,plain,
% 1.24/1.47 (b(z, s(s(z)))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[729, 3768])).
% 1.24/1.47 tff(3770,plain,
% 1.24/1.47 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[2979])).
% 1.24/1.47 tff(3771,plain,
% 1.24/1.47 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.47 inference(symmetry,[status(thm)],[3770])).
% 1.24/1.47 tff(3772,plain,
% 1.24/1.47 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[2979])).
% 1.24/1.47 tff(3773,plain,
% 1.24/1.47 ((~r(s(s(s(z))), s(s(s(s(z)))))) <=> (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[3772])).
% 1.24/1.47 tff(3774,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(3775,plain,
% 1.24/1.47 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(3776,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[3775])).
% 1.24/1.47 tff(3777,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 1.24/1.47 inference(transitivity,[status(thm)],[3776, 3774])).
% 1.24/1.47 tff(3778,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(3779,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[3778, 3777])).
% 1.24/1.47 tff(3780,plain,
% 1.24/1.47 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[3779, 319, 711, 3204, 3756])).
% 1.24/1.47 tff(3781,plain,
% 1.24/1.47 ((s(s(s(s(z)))) = s(s(z))) | r(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[3001, 51, 3780])).
% 1.24/1.47 tff(3782,plain,
% 1.24/1.47 (r(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[3781, 2986])).
% 1.24/1.47 tff(3783,plain,
% 1.24/1.47 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(3784,plain,
% 1.24/1.47 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(3785,plain,
% 1.24/1.47 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[3784])).
% 1.24/1.47 tff(3786,plain,
% 1.24/1.47 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[3785, 3783])).
% 1.24/1.47 tff(3787,plain,
% 1.24/1.47 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(3788,plain,
% 1.24/1.47 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[3787, 3786])).
% 1.24/1.47 tff(3789,plain,
% 1.24/1.47 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[3788, 297, 889, 3782])).
% 1.24/1.47 tff(3790,plain,
% 1.24/1.47 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[3789, 3773])).
% 1.24/1.47 tff(3791,plain,
% 1.24/1.47 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(elem!1)))) | b(s(s(s(z))), s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(elem!1)))) | b(s(s(s(z))), s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1)))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(3792,plain,
% 1.24/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(elem!1)))) | b(s(s(s(z))), s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1)))))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(3793,plain,
% 1.24/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(elem!1)))) | b(s(s(s(z))), s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[3792, 3791])).
% 1.24/1.47 tff(3794,plain,
% 1.24/1.47 ((s(s(s(z))) = s(s(s(elem!1)))) | b(s(s(s(z))), s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[3793, 51])).
% 1.24/1.47 tff(3795,plain,
% 1.24/1.47 (b(s(s(s(z))), s(s(s(elem!1))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[3794, 3790, 3739])).
% 1.24/1.47 tff(3796,plain,
% 1.24/1.47 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[3795, 3771])).
% 1.24/1.47 tff(3797,plain,
% 1.24/1.47 (r(s(z), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[2978])).
% 1.24/1.47 tff(3798,plain,
% 1.24/1.47 (r(elem!1, s(s(s(s(z))))) <=> r(s(z), s(s(s(s(z)))))),
% 1.24/1.47 inference(symmetry,[status(thm)],[3797])).
% 1.24/1.47 tff(3799,assumption,(r(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 1.24/1.47 tff(3800,plain,
% 1.24/1.47 (r(s(z), s(s(s(s(z)))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[3799, 3798])).
% 1.24/1.47 tff(3801,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(3802,plain,
% 1.24/1.47 (((~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(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1))))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(3803,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[3802])).
% 1.24/1.47 tff(3804,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[3803, 3801])).
% 1.24/1.47 tff(3805,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(3806,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[3805, 3804])).
% 1.24/1.47 tff(3807,plain,
% 1.24/1.47 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[3806, 319, 3203, 3540, 2023])).
% 1.24/1.47 tff(3808,plain,
% 1.24/1.47 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[3807, 3637])).
% 1.24/1.47 tff(3809,plain,
% 1.24/1.47 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[634, 3808, 3121])).
% 1.24/1.47 tff(3810,plain,
% 1.24/1.47 (r(s(z), s(s(s(s(elem!1)))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[3809, 3636])).
% 1.24/1.47 tff(3811,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(3812,plain,
% 1.24/1.47 (((~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(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(3813,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[3812])).
% 1.24/1.47 tff(3814,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[3813, 3811])).
% 1.24/1.47 tff(3815,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(3816,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[3815, 3814])).
% 1.24/1.47 tff(3817,plain,
% 1.24/1.47 (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[3816, 319, 3203, 2966, 2023])).
% 1.24/1.47 tff(3818,plain,
% 1.24/1.47 ((s(s(s(s(elem!1)))) = s(s(s(s(z))))) | r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[3229, 51, 3817])).
% 1.24/1.47 tff(3819,plain,
% 1.24/1.47 (r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[3818, 3219])).
% 1.24/1.47 tff(3820,plain,
% 1.24/1.47 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(3821,plain,
% 1.24/1.47 (((~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(elem!1))))))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(3822,plain,
% 1.24/1.47 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[3821])).
% 1.24/1.47 tff(3823,plain,
% 1.24/1.47 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[3822, 3820])).
% 1.24/1.47 tff(3824,plain,
% 1.24/1.47 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(3825,plain,
% 1.24/1.47 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[3824, 3823])).
% 1.24/1.47 tff(3826,plain,
% 1.24/1.47 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[3825, 297, 1588, 3819])).
% 1.24/1.47 tff(3827,plain,
% 1.24/1.47 ($false),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[3826, 3810])).
% 1.24/1.47 tff(3828,plain,((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~(s(elem!1) = s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.47 tff(3829,plain,
% 1.24/1.47 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[3828, 3800, 2967, 99, 3540, 3796, 2966])).
% 1.24/1.47 tff(3830,plain,
% 1.24/1.47 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[3829, 3499])).
% 1.24/1.47 tff(3831,plain,
% 1.24/1.47 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[571, 3830, 3132])).
% 1.24/1.47 tff(3832,plain,
% 1.24/1.47 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[3831, 3127])).
% 1.24/1.47 tff(3833,plain,
% 1.24/1.47 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[3671, 297, 3832, 3493])).
% 1.24/1.47 tff(3834,plain,
% 1.24/1.47 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[3833, 3490])).
% 1.24/1.47 tff(3835,plain,
% 1.24/1.47 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[595, 3834, 3200])).
% 1.24/1.47 tff(3836,plain,
% 1.24/1.47 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[3835, 3489])).
% 1.24/1.47 tff(3837,plain,
% 1.24/1.47 (~r(s(s(s(s(elem!1)))), z)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[3264, 297, 3832, 3503])).
% 1.24/1.47 tff(3838,plain,
% 1.24/1.47 (b(s(s(s(s(elem!1)))), z)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[3268, 51, 604, 3837])).
% 1.24/1.47 tff(3839,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(3840,plain,
% 1.24/1.48 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(3841,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z))))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[3840])).
% 1.24/1.48 tff(3842,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.24/1.48 inference(transitivity,[status(thm)],[3841, 3839])).
% 1.24/1.48 tff(3843,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(3844,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[3843, 3842])).
% 1.24/1.48 tff(3845,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[3844, 319, 711, 3204, 3838, 3836])).
% 1.24/1.48 tff(3846,plain,((~r(z, s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~(s(elem!1) = s(s(z)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(3847,plain,
% 1.24/1.48 (~r(z, s(s(s(z))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[3846, 3769, 3204, 2967, 99, 3540, 2966, 3739, 889, 3767, 3756, 2578])).
% 1.24/1.48 tff(3848,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[3847, 3755])).
% 1.24/1.48 tff(3849,plain,((~b(s(s(s(z))), s(z))) | (~(s(elem!1) = s(s(z)))) | (~b(s(s(z)), z)) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(3850,plain,
% 1.24/1.48 (~b(s(s(s(z))), s(z))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[3849, 3427, 3204, 99, 2967, 3534, 3739, 889, 3738, 2578, 3736])).
% 1.24/1.48 tff(3851,plain,
% 1.24/1.48 (~b(s(s(elem!1)), s(z))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[3850, 3722])).
% 1.24/1.48 tff(3852,plain,
% 1.24/1.48 (r(s(s(elem!1)), s(z))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[871, 3851])).
% 1.24/1.48 tff(3853,plain,
% 1.24/1.48 (~r(s(s(elem!1)), z)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[3560, 3852, 917])).
% 1.24/1.48 tff(3854,plain,
% 1.24/1.48 (b(s(s(elem!1)), z)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[75, 3853])).
% 1.24/1.48 tff(3855,plain,
% 1.24/1.48 (b(s(s(s(z))), z)),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[3854, 3422])).
% 1.24/1.48 tff(3856,plain,
% 1.24/1.48 (~r(z, s(s(elem!1)))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[2177, 3852, 917])).
% 1.24/1.48 tff(3857,plain,
% 1.24/1.48 (b(z, s(s(elem!1)))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[56, 3856])).
% 1.24/1.48 tff(3858,plain,
% 1.24/1.48 (b(z, s(s(s(z))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[3857, 3392])).
% 1.24/1.48 tff(3859,plain,
% 1.24/1.48 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(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)))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(3860,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[3859])).
% 1.24/1.48 tff(3861,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)))),
% 1.24/1.48 inference(transitivity,[status(thm)],[3860, 3587])).
% 1.24/1.48 tff(3862,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(3863,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[3862, 3861])).
% 1.24/1.48 tff(3864,plain,
% 1.24/1.48 (~b(s(s(s(z))), z)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[3863, 319, 3738, 3534, 3858])).
% 1.24/1.48 tff(3865,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[3864, 3855])).
% 1.24/1.48 tff(3866,plain,((~r(z, s(z))) | (~(s(elem!1) = s(s(z)))) | (~b(s(s(z)), z)) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(3867,plain,
% 1.24/1.48 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[3866, 3720, 2967, 93, 3482, 3407, 2578, 3480, 817])).
% 1.24/1.48 tff(3868,plain,
% 1.24/1.48 (r(s(s(s(elem!1))), s(s(s(z))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[3600, 3867, 3401])).
% 1.24/1.48 tff(3869,plain,
% 1.24/1.48 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[3868, 3394])).
% 1.24/1.48 tff(3870,plain,
% 1.24/1.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(3871,plain,
% 1.24/1.48 (((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(3872,plain,
% 1.24/1.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[3871])).
% 1.24/1.48 tff(3873,plain,
% 1.24/1.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)))),
% 1.24/1.48 inference(transitivity,[status(thm)],[3872, 3870])).
% 1.24/1.48 tff(3874,plain,
% 1.24/1.48 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(3875,plain,
% 1.24/1.48 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[3874, 3873])).
% 1.24/1.48 tff(3876,plain,
% 1.24/1.48 (~r(s(s(z)), z)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[3875, 297, 2578, 70])).
% 1.24/1.48 tff(3877,plain,
% 1.24/1.48 (b(s(s(z)), z)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[663, 51, 28, 3876])).
% 1.24/1.48 tff(3878,plain,
% 1.24/1.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(3879,plain,
% 1.24/1.48 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(3880,plain,
% 1.24/1.48 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[3879, 3878])).
% 1.24/1.48 tff(3881,plain,
% 1.24/1.48 (~r(s(s(s(elem!1))), z)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[3880, 297, 70, 335])).
% 1.24/1.48 tff(3882,plain,
% 1.24/1.48 (b(s(s(s(elem!1))), z)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1077, 51, 160, 3881])).
% 1.24/1.48 tff(3883,plain,
% 1.24/1.48 (~r(z, s(s(z)))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[3463, 2578, 70])).
% 1.24/1.48 tff(3884,plain,
% 1.24/1.48 (b(z, s(s(z)))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[729, 3883])).
% 1.24/1.48 tff(3885,plain,
% 1.24/1.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(3886,plain,
% 1.24/1.48 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1)))))) <=> ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(3887,plain,
% 1.24/1.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[3886])).
% 1.24/1.48 tff(3888,plain,
% 1.24/1.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.24/1.48 inference(transitivity,[status(thm)],[3887, 3885])).
% 1.24/1.48 tff(3889,plain,
% 1.24/1.48 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(3890,plain,
% 1.24/1.48 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[3889, 3888])).
% 1.24/1.48 tff(3891,plain,
% 1.24/1.48 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[3890, 297, 2578, 335])).
% 1.24/1.48 tff(3892,plain,
% 1.24/1.48 (b(s(s(z)), s(s(s(elem!1))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1571, 3891])).
% 1.24/1.48 tff(3893,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(3894,plain,
% 1.24/1.48 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(3895,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[3894])).
% 1.24/1.48 tff(3896,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.24/1.48 inference(transitivity,[status(thm)],[3895, 3893])).
% 1.24/1.48 tff(3897,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(3898,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[3897, 3896])).
% 1.24/1.48 tff(3899,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[3898, 319, 3892, 3884, 3882, 3877])).
% 1.24/1.48 tff(3900,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(3901,plain,
% 1.24/1.48 (~r(z, s(s(elem!1)))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[3900, 3869, 2578])).
% 1.24/1.48 tff(3902,plain,
% 1.24/1.48 (b(z, s(s(elem!1)))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[56, 3901])).
% 1.24/1.48 tff(3903,plain,
% 1.24/1.48 (b(z, s(s(s(z))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[3902, 3392])).
% 1.24/1.48 tff(3904,plain,
% 1.24/1.48 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[343, 3869, 197])).
% 1.24/1.48 tff(3905,plain,
% 1.24/1.48 (b(s(elem!1), s(s(s(elem!1))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[434, 3904, 3607])).
% 1.24/1.48 tff(3906,plain,
% 1.24/1.48 (~b(s(s(s(elem!1))), elem!1)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[457, 3905, 3520, 3488])).
% 1.24/1.48 tff(3907,plain,
% 1.24/1.48 (r(s(s(s(elem!1))), elem!1)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[361, 3906, 2976])).
% 1.24/1.48 tff(3908,plain,
% 1.24/1.48 (~r(s(s(s(s(z)))), z)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[3583, 3907, 3480, 2967])).
% 1.24/1.48 tff(3909,plain,
% 1.24/1.48 (b(s(s(s(s(z)))), z)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[2481, 51, 2478, 3908])).
% 1.24/1.48 tff(3910,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(3911,plain,
% 1.24/1.48 (((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(3912,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[3911])).
% 1.24/1.48 tff(3913,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 1.24/1.48 inference(transitivity,[status(thm)],[3912, 3910])).
% 1.24/1.48 tff(3914,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(3915,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[3914, 3913])).
% 1.24/1.48 tff(3916,plain,
% 1.24/1.48 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[3915, 319, 3390, 3720, 3909, 3427, 3903])).
% 1.24/1.49 tff(3917,plain,
% 1.24/1.49 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[3868, 3616])).
% 1.24/1.49 tff(3918,plain,
% 1.24/1.49 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3705, 3917])).
% 1.24/1.49 tff(3919,plain,
% 1.24/1.49 ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3001, 51, 3918])).
% 1.24/1.49 tff(3920,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3919, 3916, 2986])).
% 1.24/1.49 tff(3921,plain,((~(s(elem!1) = s(s(z)))) | (~b(s(s(z)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(z))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(3922,plain,
% 1.24/1.49 (~(s(elem!1) = s(s(z)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3921, 3390, 197, 2578, 817, 58, 2915])).
% 1.24/1.49 tff(3923,plain,
% 1.24/1.49 (b(s(elem!1), s(s(z)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[2529, 3922, 2524])).
% 1.24/1.49 tff(3924,plain,
% 1.24/1.49 (~r(z, s(s(z)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3463, 70, 2578])).
% 1.24/1.49 tff(3925,plain,
% 1.24/1.49 (b(z, s(s(z)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[729, 3924])).
% 1.24/1.49 tff(3926,assumption,(b(s(elem!1), s(s(z)))), introduced(assumption)).
% 1.24/1.49 tff(3927,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(3928,plain,
% 1.24/1.49 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z))) <=> ((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(3929,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[3928])).
% 1.24/1.49 tff(3930,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)))),
% 1.24/1.49 inference(transitivity,[status(thm)],[3929, 3927])).
% 1.24/1.49 tff(3931,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(3932,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[3931, 3930])).
% 1.24/1.49 tff(3933,plain,
% 1.24/1.49 (~b(s(elem!1), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3932, 319, 3390, 3926, 3925])).
% 1.24/1.49 tff(3934,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[2602, 3933, 3318])).
% 1.24/1.49 tff(3935,plain,((~r(z, s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(3936,plain,
% 1.24/1.49 (~r(z, s(s(elem!1)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3935, 3390, 3923, 197, 2578])).
% 1.24/1.49 tff(3937,plain,
% 1.24/1.49 (b(z, s(s(elem!1)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[56, 3936])).
% 1.24/1.49 tff(3938,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(z, s(z))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(3939,plain,
% 1.24/1.49 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(z, s(z))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(3940,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(z, s(z)))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[3939])).
% 1.24/1.49 tff(3941,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(z, s(z))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[3940, 3938])).
% 1.24/1.49 tff(3942,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(3943,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(z, s(z)))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[3942, 3941])).
% 1.24/1.49 tff(3944,plain,
% 1.24/1.49 (~b(s(s(z)), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3943, 319, 3390, 2706, 817])).
% 1.24/1.49 tff(3945,plain,
% 1.24/1.49 (r(s(s(z)), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[663, 51, 28, 3944])).
% 1.24/1.49 tff(3946,plain,
% 1.24/1.49 (~r(s(s(elem!1)), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3526, 3945, 2578])).
% 1.24/1.49 tff(3947,plain,
% 1.24/1.49 (b(s(s(elem!1)), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[75, 3946])).
% 1.24/1.49 tff(3948,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(3949,plain,
% 1.24/1.49 (((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z)))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(3950,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z)))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[3949])).
% 1.24/1.49 tff(3951,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[3950, 3948])).
% 1.24/1.49 tff(3952,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(3953,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z)))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[3952, 3951])).
% 1.24/1.49 tff(3954,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3953, 319, 2706, 817, 202, 3947])).
% 1.24/1.49 tff(3955,plain,((~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(3956,plain,
% 1.24/1.49 (~b(z, s(z))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3955, 3937, 817, 2578, 3390])).
% 1.24/1.49 tff(3957,plain,
% 1.24/1.49 (r(z, s(z))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1099, 3956])).
% 1.24/1.49 tff(3958,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(3959,plain,
% 1.24/1.49 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(3960,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1))))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[3959])).
% 1.24/1.49 tff(3961,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[3960, 3958])).
% 1.24/1.49 tff(3962,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(3963,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1))))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[3962, 3961])).
% 1.24/1.49 tff(3964,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3963, 319, 3390, 3926, 2541, 817])).
% 1.24/1.49 tff(3965,plain,((~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(3966,plain,
% 1.24/1.49 (~b(s(elem!1), s(z))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3965, 3390, 3923, 817])).
% 1.24/1.49 tff(3967,plain,
% 1.24/1.49 (r(s(elem!1), s(z))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[783, 3966, 776])).
% 1.24/1.49 tff(3968,plain,
% 1.24/1.49 (~r(s(s(elem!1)), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3558, 297, 2169, 917])).
% 1.24/1.49 tff(3969,plain,
% 1.24/1.49 (b(s(s(elem!1)), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[75, 3968])).
% 1.24/1.49 tff(3970,plain,
% 1.24/1.49 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(3971,plain,
% 1.24/1.49 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(3972,plain,
% 1.24/1.49 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1))))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[3971, 3970])).
% 1.24/1.49 tff(3973,plain,
% 1.24/1.49 (~r(s(elem!1), s(s(elem!1)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3972, 297, 2169, 800])).
% 1.24/1.49 tff(3974,plain,
% 1.24/1.49 (b(s(elem!1), s(s(elem!1)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[807, 3973, 2142])).
% 1.24/1.49 tff(3975,plain,
% 1.24/1.49 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(3976,plain,
% 1.24/1.49 (((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(3977,plain,
% 1.24/1.49 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(z)))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[3976])).
% 1.24/1.49 tff(3978,plain,
% 1.24/1.49 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[3977, 3975])).
% 1.24/1.49 tff(3979,plain,
% 1.24/1.49 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(3980,plain,
% 1.24/1.49 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(z)))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[3979, 3978])).
% 1.24/1.49 tff(3981,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3980, 297, 731, 917, 800])).
% 1.24/1.49 tff(3982,plain,((~r(s(elem!1), s(z))) | (~r(s(elem!1), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(3983,plain,
% 1.24/1.49 (~r(s(elem!1), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3982, 800, 917])).
% 1.24/1.49 tff(3984,plain,
% 1.24/1.49 (b(s(elem!1), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[744, 51, 193, 3983])).
% 1.24/1.49 tff(3985,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(3986,plain,
% 1.24/1.49 (((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(3987,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[3986])).
% 1.24/1.49 tff(3988,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))),
% 1.24/1.49 inference(transitivity,[status(thm)],[3987, 3985])).
% 1.24/1.49 tff(3989,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(3990,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[3989, 3988])).
% 1.24/1.49 tff(3991,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3990, 319, 3984, 3974, 202, 3969])).
% 1.24/1.49 tff(3992,plain,((~r(s(elem!1), s(z))) | (~b(z, s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(3993,plain,
% 1.24/1.49 (~r(s(s(elem!1)), s(z))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3992, 3967, 3957, 114, 3937])).
% 1.24/1.49 tff(3994,plain,
% 1.24/1.49 (b(s(s(elem!1)), s(z))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[871, 3993])).
% 1.24/1.49 tff(3995,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(3996,plain,
% 1.24/1.49 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(3997,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z))))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[3996])).
% 1.24/1.49 tff(3998,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[3997, 3995])).
% 1.24/1.49 tff(3999,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(4000,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z))))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[3999, 3998])).
% 1.24/1.49 tff(4001,plain,
% 1.24/1.49 (~b(s(s(elem!1)), s(s(z)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[4000, 319, 3994, 3390, 817])).
% 1.24/1.49 tff(4002,plain,
% 1.24/1.49 (r(s(s(elem!1)), s(s(z)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[2555, 51, 4001, 2542])).
% 1.24/1.49 tff(4003,plain,
% 1.24/1.49 (~r(s(s(elem!1)), s(z))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3560, 115, 917])).
% 1.24/1.49 tff(4004,plain,
% 1.24/1.49 (b(s(s(elem!1)), s(z))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[871, 4003])).
% 1.24/1.49 tff(4005,plain,
% 1.24/1.49 (~b(s(s(elem!1)), s(s(z)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[4000, 319, 4004, 3390, 817])).
% 1.24/1.49 tff(4006,plain,
% 1.24/1.49 (r(s(s(elem!1)), s(s(z)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[2555, 51, 4005, 2542])).
% 1.24/1.49 tff(4007,plain,
% 1.24/1.49 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(4008,plain,
% 1.24/1.50 (((~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), z))) <=> ((~r(s(s(elem!1)), z)) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.24/1.50 inference(rewrite,[status(thm)],[])).
% 1.24/1.50 tff(4009,plain,
% 1.24/1.50 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z))))))),
% 1.24/1.50 inference(monotonicity,[status(thm)],[4008])).
% 1.24/1.50 tff(4010,plain,
% 1.24/1.50 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.24/1.50 inference(transitivity,[status(thm)],[4009, 4007])).
% 1.24/1.50 tff(4011,plain,
% 1.24/1.50 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), z)))),
% 1.24/1.50 inference(quant_inst,[status(thm)],[])).
% 1.24/1.50 tff(4012,plain,
% 1.24/1.50 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z))))),
% 1.24/1.50 inference(modus_ponens,[status(thm)],[4011, 4010])).
% 1.24/1.50 tff(4013,plain,
% 1.24/1.50 ($false),
% 1.24/1.50 inference(unit_resolution,[status(thm)],[4012, 297, 115, 732, 2557])).
% 1.24/1.50 tff(4014,plain,((~r(z, s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.50 tff(4015,plain,
% 1.24/1.50 (~r(z, s(s(z)))),
% 1.24/1.50 inference(unit_resolution,[status(thm)],[4014, 115, 4006])).
% 1.24/1.50 tff(4016,plain,
% 1.24/1.50 (b(z, s(s(z)))),
% 1.24/1.50 inference(unit_resolution,[status(thm)],[729, 4015])).
% 1.24/1.50 tff(4017,plain,
% 1.24/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), z)))),
% 1.24/1.50 inference(rewrite,[status(thm)],[])).
% 1.24/1.50 tff(4018,plain,
% 1.24/1.50 (((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), z)))),
% 1.24/1.50 inference(rewrite,[status(thm)],[])).
% 1.24/1.50 tff(4019,plain,
% 1.24/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), z))))),
% 1.24/1.50 inference(monotonicity,[status(thm)],[4018])).
% 1.24/1.50 tff(4020,plain,
% 1.24/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), z)))),
% 1.24/1.50 inference(transitivity,[status(thm)],[4019, 4017])).
% 1.34/1.50 tff(4021,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(4022,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), z))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[4021, 4020])).
% 1.34/1.50 tff(4023,plain,
% 1.34/1.50 (~b(s(elem!1), z)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[4022, 319, 4004, 3390, 3926, 4016, 202])).
% 1.34/1.50 tff(4024,plain,
% 1.34/1.50 (r(s(elem!1), z)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[2602, 4023])).
% 1.34/1.50 tff(4025,plain,
% 1.34/1.50 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(4026,plain,
% 1.34/1.50 (((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(4027,plain,
% 1.34/1.50 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[4026])).
% 1.34/1.50 tff(4028,plain,
% 1.34/1.50 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.34/1.50 inference(transitivity,[status(thm)],[4027, 4025])).
% 1.34/1.50 tff(4029,plain,
% 1.34/1.50 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(4030,plain,
% 1.34/1.50 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1))))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[4029, 4028])).
% 1.34/1.50 tff(4031,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[4030, 297, 115, 197, 4024])).
% 1.34/1.50 tff(4032,plain,((~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(elem!1)))) | (s(s(elem!1)) = s(s(z))) | (~b(s(z), s(s(elem!1)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(4033,plain,
% 1.34/1.50 (~r(s(s(elem!1)), z)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[4032, 3390, 197, 3923, 3937, 2542, 817, 3957])).
% 1.34/1.50 tff(4034,plain,
% 1.34/1.50 (b(s(s(elem!1)), z)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[75, 4033])).
% 1.34/1.50 tff(4035,plain,
% 1.34/1.50 (~(s(s(z)) = s(elem!1))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[3922, 2897])).
% 1.34/1.50 tff(4036,plain,
% 1.34/1.50 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(4037,plain,
% 1.34/1.50 (((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(elem!1)))) <=> ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(4038,plain,
% 1.34/1.50 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[4037])).
% 1.34/1.50 tff(4039,plain,
% 1.34/1.50 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.34/1.50 inference(transitivity,[status(thm)],[4038, 4036])).
% 1.34/1.50 tff(4040,plain,
% 1.34/1.50 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(elem!1))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(4041,plain,
% 1.34/1.50 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1))))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[4040, 4039])).
% 1.34/1.50 tff(4042,plain,
% 1.34/1.50 (~r(s(s(z)), s(elem!1))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[4041, 297, 197, 2578])).
% 1.34/1.50 tff(4043,plain,
% 1.34/1.50 ((s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[2908, 51, 4042])).
% 1.34/1.50 tff(4044,plain,
% 1.34/1.50 (b(s(s(z)), s(elem!1))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[4043, 4035])).
% 1.34/1.50 tff(4045,plain,
% 1.34/1.50 (~r(s(elem!1), z)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[3982, 3967, 3957])).
% 1.34/1.50 tff(4046,plain,
% 1.34/1.50 (b(s(elem!1), z)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[2602, 4045])).
% 1.34/1.50 tff(4047,plain,
% 1.34/1.50 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(4048,plain,
% 1.34/1.50 (((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(4049,plain,
% 1.34/1.50 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(z, s(z)))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[4048])).
% 1.34/1.50 tff(4050,plain,
% 1.34/1.50 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))))),
% 1.34/1.50 inference(transitivity,[status(thm)],[4049, 4047])).
% 1.34/1.50 tff(4051,plain,
% 1.34/1.50 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(4052,plain,
% 1.34/1.50 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(z, s(z)))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[4051, 4050])).
% 1.34/1.50 tff(4053,plain,
% 1.34/1.50 (~r(z, s(elem!1))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[4052, 297, 3957, 3967])).
% 1.34/1.50 tff(4054,plain,
% 1.34/1.50 (b(z, s(elem!1))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[759, 51, 4053, 2878])).
% 1.34/1.50 tff(4055,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)) | (~b(s(s(z)), s(elem!1))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(4056,plain,
% 1.34/1.50 (((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(s(z))))) <=> ((~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)) | (~b(s(s(z)), s(elem!1))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(4057,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)) | (~b(s(s(z)), s(elem!1)))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[4056])).
% 1.34/1.50 tff(4058,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)) | (~b(s(s(z)), s(elem!1))))),
% 1.34/1.50 inference(transitivity,[status(thm)],[4057, 4055])).
% 1.34/1.50 tff(4059,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(s(z)))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(4060,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)) | (~b(s(s(z)), s(elem!1)))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[4059, 4058])).
% 1.34/1.50 tff(4061,plain,
% 1.34/1.50 (~b(z, s(s(z)))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[4060, 319, 4054, 4046, 4044])).
% 1.34/1.50 tff(4062,plain,
% 1.34/1.50 (r(z, s(s(z)))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[729, 4061])).
% 1.34/1.50 tff(4063,assumption,(~b(s(s(s(z))), s(s(elem!1)))), introduced(assumption)).
% 1.34/1.50 tff(4064,plain,
% 1.34/1.50 (((~![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))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(4065,plain,
% 1.34/1.50 ((~![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))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(4066,plain,
% 1.34/1.50 ((~![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)))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[4065, 4064])).
% 1.34/1.50 tff(4067,plain,
% 1.34/1.50 (r(s(s(s(z))), s(s(elem!1)))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[4066, 51, 2839, 4063])).
% 1.34/1.50 tff(4068,plain,
% 1.34/1.50 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(4069,plain,
% 1.34/1.50 (((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(4070,plain,
% 1.34/1.50 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1))))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[4069])).
% 1.34/1.50 tff(4071,plain,
% 1.34/1.50 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.34/1.50 inference(transitivity,[status(thm)],[4070, 4068])).
% 1.34/1.50 tff(4072,plain,
% 1.34/1.50 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(4073,plain,
% 1.34/1.50 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1))))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[4072, 4071])).
% 1.34/1.50 tff(4074,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[4073, 297, 2557, 3086, 4067])).
% 1.34/1.50 tff(4075,plain,(b(s(s(s(z))), s(s(elem!1))) | (~r(s(s(elem!1)), s(s(z)))) | (s(s(s(z))) = s(s(elem!1))) | (s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(4076,plain,
% 1.34/1.50 (b(s(s(s(z))), s(s(elem!1)))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[4075, 3085, 2839, 2557, 2915])).
% 1.34/1.50 tff(4077,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(4078,plain,
% 1.34/1.50 (((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~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(s(z))), s(s(elem!1)))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(4079,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[4078])).
% 1.34/1.50 tff(4080,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.34/1.50 inference(transitivity,[status(thm)],[4079, 4077])).
% 1.34/1.50 tff(4081,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(4082,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1))))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[4081, 4080])).
% 1.34/1.50 tff(4083,plain,
% 1.34/1.50 (~b(s(s(s(z))), z)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[4082, 319, 202, 496, 4076])).
% 1.34/1.50 tff(4084,plain,
% 1.34/1.50 (r(s(s(s(z))), z)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[901, 51, 898, 4083])).
% 1.34/1.50 tff(4085,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[895, 297, 732, 3086, 4084])).
% 1.34/1.50 tff(4086,plain,((s(s(s(z))) = s(s(z))) | (~r(z, s(s(z)))) | b(s(s(s(z))), s(s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(4087,plain,
% 1.34/1.51 ((~r(z, s(s(z)))) | b(s(s(s(z))), s(s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(s(z))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[4086, 2248])).
% 1.34/1.51 tff(4088,plain,
% 1.34/1.51 (s(s(s(z))) = s(s(elem!1))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[4087, 4062, 2915, 4034, 4002, 3937])).
% 1.34/1.51 tff(4089,plain,
% 1.34/1.51 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[4088])).
% 1.34/1.51 tff(4090,plain,
% 1.34/1.51 (inj_0(s(s(elem!1))) = inj_0(s(s(s(z))))),
% 1.34/1.51 inference(symmetry,[status(thm)],[4089])).
% 1.34/1.51 tff(4091,plain,
% 1.34/1.51 (s(elem!1) = s(s(z))),
% 1.34/1.51 inference(transitivity,[status(thm)],[206, 4090, 17])).
% 1.34/1.51 tff(4092,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[3922, 4091])).
% 1.34/1.51 tff(4093,plain,((~b(s(s(z)), s(z))) | b(s(s(s(z))), s(s(z))) | (s(s(elem!1)) = s(s(z))) | (~b(s(z), s(s(elem!1)))) | (s(elem!1) = s(z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | r(s(elem!1), s(s(z))) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(4094,plain,
% 1.34/1.51 (~b(s(s(z)), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[4093, 817, 2542, 2915, 776, 197, 2578, 2524, 58])).
% 1.34/1.51 tff(4095,assumption,(s(s(z)) = s(z)), introduced(assumption)).
% 1.34/1.51 tff(4096,plain,
% 1.34/1.51 (s(z) = s(s(z))),
% 1.34/1.51 inference(symmetry,[status(thm)],[4095])).
% 1.34/1.51 tff(4097,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[680, 4096])).
% 1.34/1.51 tff(4098,plain,(~(s(s(z)) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(4099,assumption,(~r(s(s(z)), s(z))), introduced(assumption)).
% 1.34/1.51 tff(4100,assumption,(~b(s(s(z)), s(z))), introduced(assumption)).
% 1.34/1.51 tff(4101,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[698, 51, 4100, 4099, 4098])).
% 1.34/1.51 tff(4102,plain,(b(s(s(z)), s(z)) | r(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(4103,plain,
% 1.34/1.51 (r(s(s(z)), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[4102, 4094])).
% 1.34/1.51 tff(4104,plain,
% 1.34/1.51 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(4105,plain,
% 1.34/1.51 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(4106,plain,
% 1.34/1.51 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1))))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[4105, 4104])).
% 1.34/1.51 tff(4107,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[4106, 297, 2169, 2578, 2511])).
% 1.34/1.51 tff(4108,plain,((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(4109,plain,
% 1.34/1.51 (~r(s(s(elem!1)), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[4108, 2511, 2578])).
% 1.34/1.51 tff(4110,plain,
% 1.34/1.51 (b(s(s(elem!1)), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[871, 4109])).
% 1.34/1.51 tff(4111,plain,
% 1.34/1.51 (b(s(elem!1), z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[2602, 3318])).
% 1.34/1.51 tff(4112,assumption,(r(z, s(elem!1))), introduced(assumption)).
% 1.34/1.51 tff(4113,plain,
% 1.34/1.51 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(4114,plain,
% 1.34/1.51 (((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(4115,plain,
% 1.34/1.51 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[4114])).
% 1.34/1.51 tff(4116,plain,
% 1.34/1.51 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.34/1.51 inference(transitivity,[status(thm)],[4115, 4113])).
% 1.34/1.51 tff(4117,plain,
% 1.34/1.51 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(4118,plain,
% 1.34/1.51 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1))))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[4117, 4116])).
% 1.34/1.51 tff(4119,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[4118, 297, 197, 70, 4112])).
% 1.34/1.51 tff(4120,plain,((~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(4121,plain,
% 1.34/1.51 (~r(z, s(elem!1))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[4120, 70, 197])).
% 1.34/1.51 tff(4122,plain,
% 1.34/1.51 (b(z, s(elem!1))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[759, 51, 4121, 2878])).
% 1.34/1.51 tff(4123,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(4124,plain,
% 1.34/1.51 (((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z))))) <=> ((~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(4125,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(elem!1), z))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[4124])).
% 1.34/1.51 tff(4126,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)))),
% 1.34/1.51 inference(transitivity,[status(thm)],[4125, 4123])).
% 1.34/1.51 tff(4127,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z)))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(4128,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(elem!1), z))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[4127, 4126])).
% 1.34/1.51 tff(4129,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[4128, 319, 3926, 2389, 786, 3204])).
% 1.34/1.51 tff(4130,plain,((~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(4131,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[4130, 3877, 4122, 3926, 4111])).
% 1.34/1.51 tff(4132,plain,((~r(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(4133,plain,
% 1.34/1.51 (~r(z, s(s(elem!1)))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[4132, 3926, 2578, 197])).
% 1.34/1.51 tff(4134,plain,
% 1.34/1.51 (b(z, s(s(elem!1)))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[56, 4133])).
% 1.34/1.51 tff(4135,plain,
% 1.34/1.51 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1105, 4134, 4110, 817])).
% 1.34/1.51 tff(4136,plain,
% 1.34/1.51 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[348, 4135, 58])).
% 1.34/1.51 tff(4137,plain,
% 1.34/1.51 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(4138,plain,
% 1.34/1.51 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(4139,plain,
% 1.34/1.51 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[4138, 4137])).
% 1.34/1.51 tff(4140,plain,
% 1.34/1.51 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[4139, 297, 2578, 4136])).
% 1.34/1.51 tff(4141,plain,
% 1.34/1.51 ((s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z)))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[2728, 51, 4140])).
% 1.34/1.51 tff(4142,plain,
% 1.34/1.51 (b(s(s(s(elem!1))), s(s(z)))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[4141, 2516])).
% 1.34/1.51 tff(4143,plain,
% 1.34/1.51 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[3890, 297, 2578, 4136])).
% 1.34/1.51 tff(4144,plain,
% 1.34/1.51 (b(s(s(z)), s(s(s(elem!1))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1571, 4143])).
% 1.34/1.51 tff(4145,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(4146,plain,
% 1.34/1.51 (((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(elem!1), s(s(z)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(4147,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(elem!1), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[4146])).
% 1.34/1.51 tff(4148,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(elem!1), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.34/1.51 inference(transitivity,[status(thm)],[4147, 4145])).
% 1.34/1.51 tff(4149,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(4150,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[4149, 4148])).
% 1.34/1.51 tff(4151,plain,
% 1.34/1.51 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[4150, 319, 4144, 3926, 4142])).
% 1.34/1.51 tff(4152,plain,
% 1.34/1.51 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[544, 297, 197, 4136])).
% 1.34/1.51 tff(4153,plain,
% 1.34/1.51 ((s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[521, 51, 4152])).
% 1.34/1.51 tff(4154,plain,
% 1.34/1.51 (s(s(s(elem!1))) = s(elem!1)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[4153, 4151])).
% 1.34/1.51 tff(4155,plain,
% 1.34/1.51 (~b(z, s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1095, 319, 4110, 817, 4134])).
% 1.34/1.51 tff(4156,plain,
% 1.34/1.51 (r(z, s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1099, 4155])).
% 1.34/1.51 tff(4157,plain,
% 1.34/1.51 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(z, s(z))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(4158,plain,
% 1.34/1.51 (((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(z, s(z))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(4159,plain,
% 1.34/1.51 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(z, s(z)))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[4158])).
% 1.34/1.51 tff(4160,plain,
% 1.34/1.51 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(z, s(z))))),
% 1.34/1.51 inference(transitivity,[status(thm)],[4159, 4157])).
% 1.34/1.51 tff(4161,plain,
% 1.34/1.51 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(4162,plain,
% 1.34/1.51 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(z, s(z)))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[4161, 4160])).
% 1.34/1.51 tff(4163,plain,
% 1.34/1.51 (~r(s(s(z)), z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[4162, 297, 4156, 2511])).
% 1.34/1.51 tff(4164,plain,
% 1.34/1.51 (b(s(s(z)), z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[663, 51, 28, 4163])).
% 1.34/1.51 tff(4165,plain,
% 1.34/1.51 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(z, s(z))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(4166,plain,
% 1.34/1.51 (((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(z, s(z))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(4167,plain,
% 1.34/1.51 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(z, s(z)))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[4166])).
% 1.34/1.51 tff(4168,plain,
% 1.34/1.51 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(z, s(z))))),
% 1.34/1.51 inference(transitivity,[status(thm)],[4167, 4165])).
% 1.34/1.51 tff(4169,plain,
% 1.34/1.51 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(4170,plain,
% 1.34/1.51 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(z, s(z)))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[4169, 4168])).
% 1.34/1.51 tff(4171,plain,
% 1.34/1.51 (~r(z, s(s(z)))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[4170, 297, 4156, 2511])).
% 1.34/1.51 tff(4172,plain,
% 1.34/1.51 (b(z, s(s(z)))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[729, 4171])).
% 1.34/1.51 tff(4173,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(4174,plain,
% 1.34/1.51 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1)))) <=> ((~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(4175,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[4174])).
% 1.34/1.51 tff(4176,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.34/1.51 inference(transitivity,[status(thm)],[4175, 4173])).
% 1.34/1.51 tff(4177,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(4178,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[4177, 4176])).
% 1.34/1.51 tff(4179,plain,
% 1.34/1.51 (~b(z, s(elem!1))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[4178, 319, 3926, 4172, 4164])).
% 1.34/1.51 tff(4180,plain,
% 1.34/1.51 (r(z, s(elem!1))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[759, 51, 4179, 2878])).
% 1.34/1.51 tff(4181,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(4182,plain,
% 1.34/1.51 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(4183,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(elem!1), z))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[4182])).
% 1.34/1.51 tff(4184,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)))),
% 1.34/1.51 inference(transitivity,[status(thm)],[4183, 4181])).
% 1.34/1.51 tff(4185,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(4186,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(elem!1), z))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[4185, 4184])).
% 1.34/1.52 tff(4187,plain,
% 1.34/1.52 (~b(s(elem!1), z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[4186, 319, 3926, 4172, 4164])).
% 1.34/1.52 tff(4188,plain,
% 1.34/1.52 (r(s(elem!1), z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2602, 4187])).
% 1.34/1.52 tff(4189,plain,
% 1.34/1.52 (~r(s(elem!1), s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[3982, 4188, 4156])).
% 1.34/1.52 tff(4190,plain,
% 1.34/1.52 (b(s(elem!1), s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[783, 4189, 776])).
% 1.34/1.52 tff(4191,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(4192,plain,
% 1.34/1.52 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(4193,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[4192])).
% 1.34/1.52 tff(4194,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.34/1.52 inference(transitivity,[status(thm)],[4193, 4191])).
% 1.34/1.52 tff(4195,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(4196,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[4195, 4194])).
% 1.34/1.52 tff(4197,plain,
% 1.34/1.52 (~b(s(s(elem!1)), s(elem!1))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[4196, 319, 4110, 4190, 817])).
% 1.34/1.52 tff(4198,plain,
% 1.34/1.52 ((s(s(elem!1)) = s(elem!1)) | r(s(s(elem!1)), s(elem!1))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2780, 51, 4197])).
% 1.34/1.52 tff(4199,plain,
% 1.34/1.52 (r(s(s(elem!1)), s(elem!1))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[4198, 2497])).
% 1.34/1.52 tff(4200,plain,
% 1.34/1.52 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(4201,plain,
% 1.34/1.52 (((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z))) <=> ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(4202,plain,
% 1.34/1.52 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1)))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[4201])).
% 1.34/1.52 tff(4203,plain,
% 1.34/1.52 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.34/1.52 inference(transitivity,[status(thm)],[4202, 4200])).
% 1.34/1.52 tff(4204,plain,
% 1.34/1.52 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(4205,plain,
% 1.34/1.52 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[4204, 4203])).
% 1.34/1.52 tff(4206,plain,
% 1.34/1.52 (~r(s(s(elem!1)), z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[4205, 297, 4199, 4180])).
% 1.34/1.52 tff(4207,plain,
% 1.34/1.52 (b(s(s(elem!1)), z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[75, 4206])).
% 1.34/1.52 tff(4208,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(4209,plain,
% 1.34/1.52 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(4210,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z))))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[4209])).
% 1.34/1.52 tff(4211,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.34/1.52 inference(transitivity,[status(thm)],[4210, 4208])).
% 1.34/1.52 tff(4212,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(4213,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[4212, 4211])).
% 1.34/1.52 tff(4214,plain,
% 1.34/1.52 (~b(s(s(elem!1)), s(s(z)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[4213, 319, 4172, 4207, 4164])).
% 1.34/1.52 tff(4215,plain,
% 1.34/1.52 (r(s(s(elem!1)), s(s(z)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2555, 51, 4214, 2542])).
% 1.34/1.52 tff(4216,plain,
% 1.34/1.52 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[343, 4136, 197])).
% 1.34/1.52 tff(4217,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(z)))) | (~b(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(4218,plain,
% 1.34/1.52 (((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(4219,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[4218])).
% 1.34/1.52 tff(4220,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.34/1.52 inference(transitivity,[status(thm)],[4219, 4217])).
% 1.34/1.52 tff(4221,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(4222,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[4221, 4220])).
% 1.34/1.52 tff(4223,plain,
% 1.34/1.52 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[4222, 319, 4144, 3926, 4142])).
% 1.34/1.52 tff(4224,plain,
% 1.34/1.52 (s(elem!1) = s(s(s(elem!1)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[434, 4223, 4216])).
% 1.34/1.52 tff(4225,plain,
% 1.34/1.52 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2827, 4224])).
% 1.34/1.52 tff(4226,plain,
% 1.34/1.52 (b(s(s(s(z))), s(s(elem!1))) | (~r(s(s(elem!1)), s(s(z)))) | (s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(z)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[4075, 2248])).
% 1.34/1.52 tff(4227,plain,
% 1.34/1.52 (b(s(s(s(z))), s(s(elem!1)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[4226, 4225, 2915, 4215])).
% 1.34/1.52 tff(4228,plain,
% 1.34/1.52 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[259])).
% 1.34/1.52 tff(4229,plain,
% 1.34/1.52 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), elem!1)),
% 1.34/1.52 inference(symmetry,[status(thm)],[4228])).
% 1.34/1.52 tff(4230,assumption,(b(s(s(s(z))), s(s(elem!1)))), introduced(assumption)).
% 1.34/1.52 tff(4231,plain,
% 1.34/1.52 (b(s(s(s(z))), elem!1)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[4230, 4229])).
% 1.34/1.52 tff(4232,assumption,(~b(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.34/1.52 tff(4233,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[4232, 4231])).
% 1.34/1.52 tff(4234,plain,(b(s(s(s(z))), elem!1) | (~b(s(s(s(z))), s(s(elem!1)))) | (~(s(s(s(elem!1))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(4235,plain,
% 1.34/1.52 (b(s(s(s(z))), elem!1)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[4234, 4227, 4154])).
% 1.34/1.52 tff(4236,plain,
% 1.34/1.52 (inj_0(s(s(s(elem!1)))) = inj_0(s(elem!1))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[4154])).
% 1.34/1.52 tff(4237,plain,
% 1.34/1.52 (s(s(elem!1)) = elem!1),
% 1.34/1.52 inference(transitivity,[status(thm)],[168, 4236, 141])).
% 1.34/1.52 tff(4238,plain,
% 1.34/1.52 (b(s(s(elem!1)), z) <=> b(elem!1, z)),
% 1.34/1.52 inference(monotonicity,[status(thm)],[4237])).
% 1.34/1.52 tff(4239,plain,
% 1.34/1.52 (b(elem!1, z)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[4207, 4238])).
% 1.34/1.52 tff(4240,plain,
% 1.34/1.52 (b(z, s(s(elem!1))) <=> b(z, elem!1)),
% 1.34/1.52 inference(monotonicity,[status(thm)],[4237])).
% 1.34/1.52 tff(4241,plain,
% 1.34/1.52 (b(z, elem!1)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[4134, 4240])).
% 1.34/1.52 tff(4242,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(4243,plain,
% 1.34/1.52 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z))) <=> ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(4244,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[4243])).
% 1.34/1.52 tff(4245,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)))),
% 1.34/1.52 inference(transitivity,[status(thm)],[4244, 4242])).
% 1.34/1.52 tff(4246,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(4247,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[4246, 4245])).
% 1.34/1.52 tff(4248,plain,
% 1.34/1.52 (~b(s(s(s(z))), z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[4247, 319, 4241, 4239, 4235])).
% 1.34/1.52 tff(4249,plain,
% 1.34/1.52 (r(s(s(s(z))), z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[901, 51, 898, 4248])).
% 1.34/1.52 tff(4250,plain,
% 1.34/1.52 (b(s(z), s(s(elem!1))) <=> b(s(z), elem!1)),
% 1.34/1.52 inference(monotonicity,[status(thm)],[4237])).
% 1.34/1.52 tff(4251,plain,
% 1.34/1.52 (b(s(z), elem!1)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[817, 4250])).
% 1.34/1.52 tff(4252,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(4253,plain,
% 1.34/1.52 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(4254,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[4253])).
% 1.34/1.52 tff(4255,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 1.34/1.52 inference(transitivity,[status(thm)],[4254, 4252])).
% 1.34/1.52 tff(4256,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(4257,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[4256, 4255])).
% 1.34/1.52 tff(4258,plain,
% 1.34/1.52 (~b(s(s(s(z))), s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[4257, 319, 4239, 4251, 4235])).
% 1.34/1.52 tff(4259,plain,
% 1.34/1.52 (r(s(s(s(z))), s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[910, 51, 30, 4258])).
% 1.34/1.52 tff(4260,plain,
% 1.34/1.52 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(4261,plain,
% 1.34/1.52 (((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(4262,plain,
% 1.34/1.52 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[4261])).
% 1.34/1.52 tff(4263,plain,
% 1.34/1.52 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))),
% 1.34/1.52 inference(transitivity,[status(thm)],[4262, 4260])).
% 1.34/1.52 tff(4264,plain,
% 1.34/1.52 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(4265,plain,
% 1.34/1.52 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[4264, 4263])).
% 1.34/1.52 tff(4266,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[4265, 297, 4156, 4259, 4249])).
% 1.34/1.52 tff(4267,plain,((~b(s(elem!1), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | b(s(s(s(z))), s(s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (s(s(elem!1)) = s(s(z))) | (s(elem!1) = s(z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(4268,plain,
% 1.34/1.52 (~b(s(elem!1), s(s(z)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[4267, 817, 2915, 2578, 197, 58, 2542, 776, 4103])).
% 1.34/1.52 tff(4269,plain,
% 1.34/1.52 (s(elem!1) = s(s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2529, 4268, 2524])).
% 1.34/1.52 tff(4270,plain,
% 1.34/1.52 (s(s(elem!1)) = s(s(s(z)))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[4269])).
% 1.34/1.52 tff(4271,plain,
% 1.34/1.52 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[4270])).
% 1.34/1.52 tff(4272,plain,
% 1.34/1.52 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.34/1.52 inference(symmetry,[status(thm)],[4271])).
% 1.34/1.52 tff(4273,plain,
% 1.34/1.52 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[4272])).
% 1.34/1.52 tff(4274,plain,
% 1.34/1.52 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.52 inference(symmetry,[status(thm)],[4273])).
% 1.34/1.52 tff(4275,plain,
% 1.34/1.52 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[4272])).
% 1.34/1.52 tff(4276,plain,
% 1.34/1.52 ((~r(s(s(z)), s(s(s(s(z)))))) <=> (~r(s(s(z)), s(s(s(elem!1)))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[4275])).
% 1.34/1.52 tff(4277,plain,
% 1.34/1.52 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[4272])).
% 1.34/1.52 tff(4278,plain,
% 1.34/1.52 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.52 inference(symmetry,[status(thm)],[4277])).
% 1.34/1.52 tff(4279,plain,
% 1.34/1.52 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[4270])).
% 1.34/1.52 tff(4280,plain,
% 1.34/1.52 (~r(s(s(elem!1)), s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[4108, 4103, 2578])).
% 1.34/1.52 tff(4281,plain,
% 1.34/1.52 (b(s(s(elem!1)), s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[871, 4280])).
% 1.34/1.52 tff(4282,plain,
% 1.34/1.52 (r(s(s(s(z))), s(s(z)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2918, 51, 2248, 2915])).
% 1.34/1.52 tff(4283,plain,
% 1.34/1.52 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(z))), s(z))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[2970])).
% 1.34/1.52 tff(4284,plain,
% 1.34/1.52 (b(s(s(s(z))), s(z))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[4110, 4283])).
% 1.34/1.52 tff(4285,plain,
% 1.34/1.52 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[2970])).
% 1.34/1.52 tff(4286,plain,
% 1.34/1.52 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[4285, 3533])).
% 1.34/1.53 tff(4287,plain,
% 1.34/1.53 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3900, 70, 2578])).
% 1.34/1.53 tff(4288,plain,
% 1.34/1.53 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[348, 4287, 58])).
% 1.34/1.53 tff(4289,plain,
% 1.34/1.53 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[4288, 4286])).
% 1.34/1.53 tff(4290,plain,
% 1.34/1.53 (~b(s(z), s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3763, 319, 3427, 4289, 4284])).
% 1.34/1.53 tff(4291,plain,
% 1.34/1.53 (~b(elem!1, s(s(s(s(z)))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[4290, 3757])).
% 1.34/1.53 tff(4292,plain,
% 1.34/1.53 (r(elem!1, s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3036, 4291, 3021])).
% 1.34/1.53 tff(4293,plain,
% 1.34/1.53 (r(s(z), s(s(s(s(z)))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[4292, 3022])).
% 1.34/1.53 tff(4294,plain,
% 1.34/1.53 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[2971])).
% 1.34/1.53 tff(4295,plain,
% 1.34/1.53 (b(s(s(s(elem!1))), s(s(s(z))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[4288, 4285])).
% 1.34/1.53 tff(4296,plain,
% 1.34/1.53 (~r(s(s(z)), z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3506, 297, 3261, 3497])).
% 1.34/1.53 tff(4297,plain,
% 1.34/1.53 (~r(s(elem!1), z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3179, 4296, 2967])).
% 1.34/1.53 tff(4298,plain,
% 1.34/1.53 (b(s(elem!1), z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2602, 4297])).
% 1.34/1.53 tff(4299,plain,
% 1.34/1.53 (b(s(s(z)), z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3187, 4298, 2967])).
% 1.34/1.53 tff(4300,plain,
% 1.34/1.53 (~r(z, s(z))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3866, 4299, 2967, 93, 3482, 889, 2578, 4295, 817])).
% 1.34/1.53 tff(4301,plain,
% 1.34/1.53 (b(z, s(z))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1099, 4300])).
% 1.34/1.53 tff(4302,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(4303,plain,
% 1.34/1.53 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(4304,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z)))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[4303])).
% 1.34/1.53 tff(4305,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[4304, 4302])).
% 1.34/1.53 tff(4306,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(4307,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z)))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[4306, 4305])).
% 1.34/1.53 tff(4308,plain,
% 1.34/1.53 (~b(s(s(s(z))), z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[4307, 319, 4301, 3427, 4284])).
% 1.34/1.53 tff(4309,plain,
% 1.34/1.53 (r(s(s(s(z))), z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[901, 51, 898, 4308])).
% 1.34/1.53 tff(4310,plain,
% 1.34/1.53 (~b(s(s(s(s(z)))), z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3846, 4292, 3261, 2967, 93, 3427, 4289, 3482, 889, 4299, 3925, 2578])).
% 1.34/1.53 tff(4311,plain,
% 1.34/1.53 (r(s(s(s(s(z)))), z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2481, 51, 2478, 4310])).
% 1.34/1.53 tff(4312,plain,
% 1.34/1.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(4313,plain,
% 1.34/1.53 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(4314,plain,
% 1.34/1.53 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[4313, 4312])).
% 1.34/1.53 tff(4315,plain,
% 1.34/1.53 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[4314, 297, 4311, 4309])).
% 1.34/1.53 tff(4316,plain,
% 1.34/1.53 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[4315, 3773])).
% 1.34/1.53 tff(4317,plain,
% 1.34/1.53 (b(s(s(s(z))), s(s(s(elem!1))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3794, 4316, 3482])).
% 1.34/1.53 tff(4318,plain,
% 1.34/1.53 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[4317, 4294])).
% 1.34/1.53 tff(4319,plain,
% 1.34/1.53 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3828, 4318, 4289, 93, 3427, 4293, 2967])).
% 1.34/1.53 tff(4320,plain,
% 1.34/1.53 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3246, 4319, 2967])).
% 1.34/1.53 tff(4321,plain,
% 1.34/1.53 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[571, 4320, 3132])).
% 1.34/1.53 tff(4322,plain,
% 1.34/1.53 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[4321, 3127])).
% 1.34/1.53 tff(4323,plain,
% 1.34/1.53 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3671, 297, 4322, 3497])).
% 1.34/1.53 tff(4324,plain,
% 1.34/1.53 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[4323, 3490])).
% 1.34/1.53 tff(4325,plain,
% 1.34/1.53 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[595, 4324, 3200])).
% 1.34/1.53 tff(4326,plain,
% 1.34/1.53 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[4325, 3489])).
% 1.34/1.53 tff(4327,plain,
% 1.34/1.53 (~r(s(s(s(s(elem!1)))), z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3264, 297, 4322, 3261])).
% 1.34/1.53 tff(4328,plain,
% 1.34/1.53 (b(s(s(s(s(elem!1)))), z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3268, 51, 604, 4327])).
% 1.34/1.53 tff(4329,plain,
% 1.34/1.53 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 1.34/1.53 inference(symmetry,[status(thm)],[2972])).
% 1.34/1.53 tff(4330,plain,
% 1.34/1.53 ((~b(s(s(s(s(z)))), s(z))) <=> (~b(s(s(s(elem!1))), elem!1))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[4329])).
% 1.34/1.53 tff(4331,plain,
% 1.34/1.53 (((~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(s(z)))), s(s(s(z))))) | (~b(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))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(4332,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)))))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[4331])).
% 1.34/1.53 tff(4333,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[4332, 3541])).
% 1.34/1.53 tff(4334,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(4335,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[4334, 4333])).
% 1.34/1.53 tff(4336,plain,
% 1.34/1.53 (~b(s(s(s(s(z)))), s(z))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[4335, 319, 3427, 4289, 4284])).
% 1.34/1.53 tff(4337,plain,
% 1.34/1.53 (~b(s(s(s(elem!1))), elem!1)),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[4336, 4330])).
% 1.34/1.53 tff(4338,plain,
% 1.34/1.53 (r(s(s(s(elem!1))), elem!1)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[361, 4337, 2976])).
% 1.34/1.53 tff(4339,plain,
% 1.34/1.53 (r(s(s(s(s(z)))), s(z))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[4338, 3102])).
% 1.34/1.53 tff(4340,plain,
% 1.34/1.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(4341,plain,
% 1.34/1.53 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(4342,plain,
% 1.34/1.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[4341])).
% 1.34/1.53 tff(4343,plain,
% 1.34/1.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[4342, 4340])).
% 1.34/1.53 tff(4344,plain,
% 1.34/1.53 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(4345,plain,
% 1.34/1.53 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[4344, 4343])).
% 1.34/1.53 tff(4346,plain,
% 1.34/1.53 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[4345, 297, 2511, 4339])).
% 1.34/1.53 tff(4347,plain,
% 1.34/1.53 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[4346, 3687])).
% 1.34/1.53 tff(4348,plain,
% 1.34/1.53 (b(s(s(z)), s(s(s(elem!1))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1571, 4347])).
% 1.34/1.53 tff(4349,plain,
% 1.34/1.53 (b(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[4348, 3686])).
% 1.34/1.53 tff(4350,plain,
% 1.34/1.53 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3007, 297, 2511, 4339])).
% 1.34/1.53 tff(4351,plain,
% 1.34/1.53 ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3001, 51, 4350])).
% 1.34/1.53 tff(4352,plain,
% 1.34/1.53 (b(s(s(s(s(z)))), s(s(z)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[4351, 2986])).
% 1.34/1.53 tff(4353,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(4354,plain,
% 1.34/1.53 (((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(4355,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[4354])).
% 1.34/1.53 tff(4356,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[4355, 4353])).
% 1.34/1.53 tff(4357,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(4358,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[4357, 4356])).
% 1.34/1.53 tff(4359,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[4358, 319, 3925, 4299, 4352, 4349, 4328, 4326])).
% 1.34/1.53 tff(4360,plain,((~r(z, s(s(elem!1)))) | (~(s(elem!1) = s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(4361,plain,
% 1.34/1.53 (~r(z, s(s(elem!1)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[4360, 4269, 4103, 4282, 2578, 817, 58])).
% 1.34/1.53 tff(4362,plain,
% 1.34/1.53 (b(z, s(s(elem!1)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[56, 4361])).
% 1.34/1.53 tff(4363,plain,
% 1.34/1.53 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1105, 4362, 4281, 817])).
% 1.34/1.53 tff(4364,plain,
% 1.34/1.53 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[348, 4363, 58])).
% 1.34/1.53 tff(4365,plain,
% 1.34/1.53 (r(s(s(s(elem!1))), s(s(s(z))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[4364, 4279])).
% 1.34/1.53 tff(4366,plain,
% 1.34/1.53 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[4365, 4278])).
% 1.34/1.53 tff(4367,plain,
% 1.34/1.53 (r(s(s(z)), s(s(s(z))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3496, 4269, 2578])).
% 1.34/1.53 tff(4368,plain,
% 1.34/1.53 ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3693, 297, 4367])).
% 1.34/1.53 tff(4369,plain,
% 1.34/1.53 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[4368, 4366])).
% 1.34/1.53 tff(4370,plain,
% 1.34/1.53 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[4369, 4276])).
% 1.34/1.53 tff(4371,plain,
% 1.34/1.53 (b(s(s(z)), s(s(s(elem!1))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1571, 4370])).
% 1.34/1.53 tff(4372,plain,
% 1.34/1.53 (b(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[4371, 4274])).
% 1.34/1.53 tff(4373,plain,
% 1.34/1.53 (s(s(z)) = s(elem!1)),
% 1.34/1.53 inference(symmetry,[status(thm)],[4269])).
% 1.34/1.53 tff(4374,plain,
% 1.34/1.53 (b(s(s(s(s(elem!1)))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[4373])).
% 1.34/1.53 tff(4375,plain,
% 1.34/1.53 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.34/1.53 inference(symmetry,[status(thm)],[4374])).
% 1.34/1.53 tff(4376,plain,
% 1.34/1.53 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[4269])).
% 1.34/1.53 tff(4377,plain,
% 1.34/1.53 (elem!1 = s(z)),
% 1.34/1.53 inference(transitivity,[status(thm)],[258, 4376, 126])).
% 1.34/1.53 tff(4378,plain,
% 1.34/1.53 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(elem!1))) = s(z))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[4377])).
% 1.34/1.53 tff(4379,plain,
% 1.34/1.53 ((s(s(s(elem!1))) = s(z)) <=> (s(s(s(elem!1))) = elem!1)),
% 1.34/1.53 inference(symmetry,[status(thm)],[4378])).
% 1.34/1.53 tff(4380,plain,
% 1.34/1.53 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[4379])).
% 1.34/1.53 tff(4381,plain,
% 1.34/1.53 (~(s(s(s(elem!1))) = elem!1)),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[171, 4380])).
% 1.34/1.53 tff(4382,plain,
% 1.34/1.53 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[586, 4381])).
% 1.34/1.53 tff(4383,plain,
% 1.34/1.53 (r(s(s(s(s(elem!1)))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[4373])).
% 1.34/1.53 tff(4384,plain,
% 1.34/1.53 ((~r(s(s(s(s(elem!1)))), s(s(z)))) <=> (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[4383])).
% 1.34/1.53 tff(4385,plain,
% 1.34/1.53 (r(s(s(s(s(elem!1)))), s(s(elem!1))) <=> r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[4270])).
% 1.34/1.53 tff(4386,plain,
% 1.34/1.53 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[4373])).
% 1.34/1.53 tff(4387,plain,
% 1.34/1.53 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.34/1.53 inference(transitivity,[status(thm)],[4386, 276])).
% 1.34/1.53 tff(4388,plain,
% 1.34/1.53 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[4387])).
% 1.34/1.53 tff(4389,plain,
% 1.34/1.53 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[231, 4388])).
% 1.34/1.53 tff(4390,plain,
% 1.34/1.53 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[178, 4389])).
% 1.34/1.53 tff(4391,plain,
% 1.34/1.53 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(z))), s(z))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[4270])).
% 1.34/1.53 tff(4392,plain,
% 1.34/1.53 (b(s(s(s(z))), s(z))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[4281, 4391])).
% 1.34/1.53 tff(4393,plain,
% 1.34/1.53 (s(s(s(z))) = s(s(elem!1))),
% 1.34/1.53 inference(symmetry,[status(thm)],[4270])).
% 1.34/1.53 tff(4394,plain,
% 1.34/1.53 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(elem!1)))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[4393])).
% 1.34/1.53 tff(4395,plain,
% 1.34/1.53 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(z))))),
% 1.34/1.53 inference(symmetry,[status(thm)],[4394])).
% 1.34/1.53 tff(4396,plain,
% 1.34/1.53 (b(s(z), s(s(s(z))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[817, 4395])).
% 1.34/1.53 tff(4397,plain,
% 1.34/1.53 (b(z, s(s(elem!1))) <=> b(z, s(s(s(z))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[4270])).
% 1.34/1.53 tff(4398,plain,
% 1.34/1.53 (b(z, s(s(s(z))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[4362, 4397])).
% 1.34/1.53 tff(4399,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(4400,plain,
% 1.34/1.53 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z))) <=> ((~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(4401,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[4400])).
% 1.34/1.53 tff(4402,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[4401, 4399])).
% 1.34/1.53 tff(4403,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(4404,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[4403, 4402])).
% 1.34/1.53 tff(4405,plain,
% 1.34/1.53 (~b(s(z), z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[4404, 319, 4396, 4398, 4392])).
% 1.34/1.53 tff(4406,plain,
% 1.34/1.53 (r(s(z), z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[65, 51, 62, 4405])).
% 1.34/1.53 tff(4407,plain,
% 1.34/1.53 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3664, 4406, 4398, 4396, 4392, 4269])).
% 1.34/1.53 tff(4408,plain,
% 1.34/1.53 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3246, 4407, 4269])).
% 1.34/1.53 tff(4409,plain,
% 1.34/1.53 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[571, 4408, 4390])).
% 1.34/1.53 tff(4410,plain,
% 1.34/1.53 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[4409, 4385])).
% 1.34/1.53 tff(4411,plain,
% 1.34/1.53 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3671, 297, 4410, 4367])).
% 1.34/1.53 tff(4412,plain,
% 1.34/1.53 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[4411, 4384])).
% 1.34/1.53 tff(4413,plain,
% 1.34/1.53 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[595, 4412, 4382])).
% 1.34/1.53 tff(4414,plain,
% 1.34/1.53 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[4413, 4375])).
% 1.34/1.53 tff(4415,plain,
% 1.34/1.53 ((s(s(s(s(elem!1)))) = s(s(s(s(z))))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[4272])).
% 1.34/1.53 tff(4416,plain,
% 1.34/1.53 ((s(s(s(s(elem!1)))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[4415, 1324])).
% 1.34/1.53 tff(4417,plain,
% 1.34/1.53 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(s(z)))))),
% 1.34/1.53 inference(symmetry,[status(thm)],[4416])).
% 1.34/1.53 tff(4418,plain,
% 1.34/1.53 ((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(s(z))))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[4417])).
% 1.34/1.53 tff(4419,plain,
% 1.34/1.53 (~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[93, 4418])).
% 1.34/1.53 tff(4420,plain,
% 1.34/1.53 (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3682, 297, 4410, 4366])).
% 1.34/1.53 tff(4421,plain,
% 1.34/1.53 ((s(s(s(s(elem!1)))) = s(s(s(s(z))))) | b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3229, 51, 4420])).
% 1.34/1.53 tff(4422,plain,
% 1.34/1.53 (b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[4421, 4419])).
% 1.34/1.53 tff(4423,plain,
% 1.34/1.53 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[4272])).
% 1.34/1.53 tff(4424,plain,
% 1.34/1.53 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(z)) = s(s(s(elem!1))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[4423, 2513])).
% 1.34/1.53 tff(4425,plain,
% 1.34/1.53 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 1.34/1.54 inference(symmetry,[status(thm)],[4424])).
% 1.34/1.54 tff(4426,plain,
% 1.34/1.54 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(s(z)))) = s(s(z))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[4425])).
% 1.34/1.54 tff(4427,plain,
% 1.34/1.54 (~(s(s(s(s(z)))) = s(s(z)))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[231, 4426])).
% 1.34/1.54 tff(4428,plain,
% 1.34/1.54 ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[3704, 297, 4367])).
% 1.34/1.54 tff(4429,plain,
% 1.34/1.54 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[4428, 4366])).
% 1.34/1.54 tff(4430,plain,
% 1.34/1.54 ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[3001, 51, 4429])).
% 1.34/1.54 tff(4431,plain,
% 1.34/1.54 (b(s(s(s(s(z)))), s(s(z)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[4430, 4427])).
% 1.34/1.54 tff(4432,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[3714, 319, 4431, 4422, 4414, 4372])).
% 1.34/1.54 tff(4433,plain,((~b(s(z), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(s(z)), s(s(elem!1)))) | r(s(elem!1), s(s(z))) | b(s(s(s(z))), s(s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (s(s(elem!1)) = s(s(z))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(4434,plain,
% 1.34/1.54 (b(s(s(s(z))), s(s(z)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[4433, 3362, 58, 3303, 3359, 3335, 2522, 2498])).
% 1.34/1.54 tff(4435,plain,
% 1.34/1.54 (b(s(s(elem!1)), s(elem!1))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[4434, 3389])).
% 1.34/1.54 tff(4436,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[534, 4435, 3383, 116, 3380, 3376, 3368])).
% 1.34/1.54 tff(4437,plain,(b(s(elem!1), s(s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (s(s(s(elem!1))) = s(s(elem!1))) | (s(s(z)) = s(s(elem!1))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(4438,plain,
% 1.34/1.54 (b(s(elem!1), s(s(z)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[4437, 70, 2511, 58, 772, 116])).
% 1.34/1.54 tff(4439,plain,
% 1.34/1.54 (~r(s(elem!1), s(s(elem!1)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[4132, 2578, 4438, 70])).
% 1.34/1.54 tff(4440,plain,
% 1.34/1.54 (b(s(elem!1), s(s(elem!1)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[807, 4439, 114])).
% 1.34/1.54 tff(4441,plain,
% 1.34/1.54 (~r(s(s(elem!1)), s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[4108, 2578, 2511])).
% 1.34/1.54 tff(4442,plain,
% 1.34/1.54 (b(s(s(elem!1)), s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[871, 4441])).
% 1.34/1.54 tff(4443,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(4444,plain,
% 1.34/1.54 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(4445,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[4444])).
% 1.34/1.54 tff(4446,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[4445, 4443])).
% 1.34/1.54 tff(4447,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(4448,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[4447, 4446])).
% 1.34/1.54 tff(4449,plain,
% 1.34/1.54 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[4448, 319, 4442, 4440, 116])).
% 1.34/1.54 tff(4450,plain,
% 1.34/1.54 (~r(s(z), s(s(elem!1)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2583, 2578, 2511])).
% 1.34/1.54 tff(4451,plain,
% 1.34/1.54 (b(s(z), s(s(elem!1)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1047, 4450])).
% 1.34/1.54 tff(4452,plain,
% 1.34/1.54 (~b(s(s(s(elem!1))), s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1084, 319, 4442, 4451, 116])).
% 1.34/1.54 tff(4453,plain,
% 1.34/1.54 (r(s(s(s(elem!1))), s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1088, 51, 171, 4452])).
% 1.34/1.54 tff(4454,plain,
% 1.34/1.54 (~b(s(elem!1), s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2575, 4440, 4451, 2511, 2522])).
% 1.34/1.54 tff(4455,plain,
% 1.34/1.54 (r(s(elem!1), s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[783, 4454, 2498])).
% 1.34/1.54 tff(4456,plain,
% 1.34/1.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(4457,plain,
% 1.34/1.54 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(elem!1)))))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(4458,plain,
% 1.34/1.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z)))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[4457])).
% 1.34/1.54 tff(4459,plain,
% 1.34/1.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[4458, 4456])).
% 1.34/1.54 tff(4460,plain,
% 1.34/1.54 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(4461,plain,
% 1.34/1.54 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z)))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[4460, 4459])).
% 1.34/1.54 tff(4462,plain,
% 1.34/1.54 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[4461, 297, 4455, 4453])).
% 1.34/1.54 tff(4463,plain,
% 1.34/1.54 (s(elem!1) = s(s(s(elem!1)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[434, 4462, 4449])).
% 1.34/1.54 tff(4464,plain,
% 1.34/1.54 (b(z, s(elem!1)) <=> b(z, s(s(s(elem!1))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[4463])).
% 1.34/1.54 tff(4465,plain,
% 1.34/1.54 ((~b(z, s(elem!1))) <=> (~b(z, s(s(s(elem!1)))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[4464])).
% 1.34/1.54 tff(4466,plain,
% 1.34/1.54 (~b(z, s(elem!1))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[4178, 319, 4438, 3884, 3877])).
% 1.34/1.54 tff(4467,plain,
% 1.34/1.54 (~b(z, s(s(s(elem!1))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[4466, 4465])).
% 1.34/1.54 tff(4468,plain,
% 1.34/1.54 (r(z, s(s(s(elem!1))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[416, 4467])).
% 1.34/1.54 tff(4469,plain,
% 1.34/1.54 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[4463])).
% 1.34/1.54 tff(4470,plain,
% 1.34/1.54 (elem!1 = s(s(elem!1))),
% 1.34/1.54 inference(transitivity,[status(thm)],[258, 4469, 83])).
% 1.34/1.54 tff(4471,plain,
% 1.34/1.54 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(elem!1)))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[4470])).
% 1.34/1.54 tff(4472,plain,
% 1.34/1.54 ((s(s(z)) = s(s(elem!1))) <=> (s(s(z)) = elem!1)),
% 1.34/1.54 inference(symmetry,[status(thm)],[4471])).
% 1.34/1.54 tff(4473,plain,
% 1.34/1.54 ((~(s(s(z)) = s(s(elem!1)))) <=> (~(s(s(z)) = elem!1))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[4472])).
% 1.34/1.54 tff(4474,plain,
% 1.34/1.54 (~(s(s(z)) = elem!1)),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[772, 4473])).
% 1.34/1.54 tff(4475,plain,
% 1.34/1.54 (~(s(s(s(z))) = s(elem!1))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2759, 4474])).
% 1.34/1.54 tff(4476,plain,
% 1.34/1.54 ((s(s(s(z))) = s(elem!1)) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[266])).
% 1.34/1.54 tff(4477,plain,
% 1.34/1.54 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(elem!1))),
% 1.34/1.54 inference(symmetry,[status(thm)],[4476])).
% 1.34/1.54 tff(4478,plain,
% 1.34/1.54 (s(s(s(z))) = s(elem!1)),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[2505, 4477])).
% 1.34/1.54 tff(4479,assumption,(~(s(s(s(z))) = s(elem!1))), introduced(assumption)).
% 1.34/1.54 tff(4480,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[4479, 4478])).
% 1.34/1.54 tff(4481,plain,((~(s(s(s(z))) = s(s(s(elem!1))))) | (s(s(s(z))) = s(elem!1)) | (~(s(elem!1) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(4482,plain,
% 1.34/1.54 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[4481, 4475, 4463])).
% 1.34/1.54 tff(4483,plain,
% 1.34/1.54 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2827, 4463])).
% 1.34/1.54 tff(4484,plain,
% 1.34/1.54 (s(s(s(elem!1))) = s(elem!1)),
% 1.34/1.54 inference(symmetry,[status(thm)],[4463])).
% 1.34/1.54 tff(4485,plain,
% 1.34/1.54 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(elem!1))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[4484])).
% 1.34/1.54 tff(4486,plain,
% 1.34/1.54 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.34/1.54 inference(symmetry,[status(thm)],[4485])).
% 1.34/1.54 tff(4487,plain,
% 1.34/1.54 (b(elem!1, s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[4470])).
% 1.34/1.54 tff(4488,plain,
% 1.34/1.54 ((s(s(s(elem!1))) = elem!1) <=> (s(elem!1) = elem!1)),
% 1.34/1.54 inference(monotonicity,[status(thm)],[4484])).
% 1.34/1.54 tff(4489,plain,
% 1.34/1.54 ((s(s(s(elem!1))) = elem!1) <=> (elem!1 = s(elem!1))),
% 1.34/1.54 inference(transitivity,[status(thm)],[4488, 184])).
% 1.34/1.54 tff(4490,plain,
% 1.34/1.54 (inj_0(s(s(s(elem!1)))) = inj_0(s(elem!1))),
% 1.34/1.54 inference(symmetry,[status(thm)],[4469])).
% 1.34/1.54 tff(4491,plain,
% 1.34/1.54 (s(s(elem!1)) = elem!1),
% 1.34/1.54 inference(transitivity,[status(thm)],[168, 4490, 141])).
% 1.34/1.54 tff(4492,plain,
% 1.34/1.54 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.34/1.54 inference(monotonicity,[status(thm)],[4491])).
% 1.34/1.54 tff(4493,plain,
% 1.34/1.54 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (elem!1 = s(elem!1))),
% 1.34/1.54 inference(transitivity,[status(thm)],[4492, 4489])).
% 1.34/1.54 tff(4494,plain,
% 1.34/1.54 ((~(s(s(s(elem!1))) = s(s(elem!1)))) <=> (~(elem!1 = s(elem!1)))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[4493])).
% 1.34/1.54 tff(4495,plain,
% 1.34/1.54 (~(elem!1 = s(elem!1))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[58, 4494])).
% 1.34/1.54 tff(4496,plain,
% 1.34/1.54 (r(elem!1, s(elem!1)) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[4470, 4463])).
% 1.34/1.54 tff(4497,plain,
% 1.34/1.54 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(elem!1, s(elem!1))),
% 1.34/1.54 inference(symmetry,[status(thm)],[4496])).
% 1.34/1.54 tff(4498,plain,
% 1.34/1.54 ((~r(s(s(elem!1)), s(s(s(elem!1))))) <=> (~r(elem!1, s(elem!1)))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[4497])).
% 1.34/1.54 tff(4499,plain,
% 1.34/1.54 (b(s(elem!1), z) <=> b(s(s(s(elem!1))), z)),
% 1.34/1.54 inference(monotonicity,[status(thm)],[4463])).
% 1.34/1.54 tff(4500,plain,
% 1.34/1.54 ((~b(s(elem!1), z)) <=> (~b(s(s(s(elem!1))), z))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[4499])).
% 1.34/1.54 tff(4501,plain,
% 1.34/1.54 (~b(s(elem!1), z)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[4186, 319, 4438, 3884, 3877])).
% 1.34/1.54 tff(4502,plain,
% 1.34/1.54 (~b(s(s(s(elem!1))), z)),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[4501, 4500])).
% 1.34/1.54 tff(4503,plain,
% 1.34/1.54 (r(s(s(s(elem!1))), z)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1077, 51, 160, 4502])).
% 1.34/1.54 tff(4504,plain,
% 1.34/1.54 (r(s(elem!1), z)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2602, 4501])).
% 1.34/1.54 tff(4505,plain,
% 1.34/1.54 (~r(z, s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[3982, 4504, 4455])).
% 1.34/1.54 tff(4506,plain,
% 1.34/1.54 (b(z, s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1099, 4505])).
% 1.34/1.54 tff(4507,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(4508,plain,
% 1.34/1.54 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(4509,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z)))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[4508])).
% 1.34/1.54 tff(4510,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[4509, 4507])).
% 1.34/1.54 tff(4511,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(4512,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z)))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[4511, 4510])).
% 1.34/1.54 tff(4513,plain,
% 1.34/1.54 (~b(s(s(elem!1)), z)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[4512, 319, 4442, 4506, 4451])).
% 1.34/1.54 tff(4514,plain,
% 1.34/1.54 (r(s(s(elem!1)), z)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[75, 4513])).
% 1.34/1.54 tff(4515,plain,
% 1.34/1.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(4516,plain,
% 1.34/1.54 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(4517,plain,
% 1.34/1.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[4516])).
% 1.34/1.54 tff(4518,plain,
% 1.34/1.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 1.34/1.54 inference(transitivity,[status(thm)],[4517, 4515])).
% 1.34/1.54 tff(4519,plain,
% 1.34/1.54 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(4520,plain,
% 1.34/1.54 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[4519, 4518])).
% 1.34/1.54 tff(4521,plain,
% 1.34/1.54 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[4520, 297, 4514, 4503])).
% 1.34/1.54 tff(4522,plain,
% 1.34/1.54 (~r(elem!1, s(elem!1))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[4521, 4498])).
% 1.34/1.54 tff(4523,plain,
% 1.34/1.54 (b(elem!1, s(elem!1))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[389, 4522, 4495])).
% 1.34/1.54 tff(4524,plain,
% 1.34/1.54 (b(s(s(elem!1)), s(elem!1))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[4523, 4487])).
% 1.34/1.54 tff(4525,plain,
% 1.34/1.54 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[4524, 4486])).
% 1.34/1.54 tff(4526,plain,
% 1.34/1.54 (b(s(elem!1), s(s(z))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[4463])).
% 1.34/1.54 tff(4527,plain,
% 1.34/1.54 (b(s(s(s(elem!1))), s(s(z)))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[4438, 4526])).
% 1.34/1.54 tff(4528,plain,
% 1.34/1.54 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2682, 297, 2511, 4453])).
% 1.34/1.54 tff(4529,plain,
% 1.34/1.54 (b(s(s(z)), s(s(s(elem!1))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1571, 4528])).
% 1.34/1.54 tff(4530,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(4531,plain,
% 1.34/1.54 (((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(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))))) <=> ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(4532,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[4531])).
% 1.34/1.54 tff(4533,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[4532, 4530])).
% 1.34/1.54 tff(4534,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(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)))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(4535,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[4534, 4533])).
% 1.34/1.54 tff(4536,plain,
% 1.34/1.54 (~b(s(s(elem!1)), s(s(z)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[4535, 319, 4529, 4527, 4525])).
% 1.34/1.54 tff(4537,plain,
% 1.34/1.54 (r(s(s(elem!1)), s(s(z)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2555, 51, 4536, 2522])).
% 1.34/1.54 tff(4538,plain,
% 1.34/1.54 (r(s(s(s(z))), s(s(z)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2920, 2915])).
% 1.34/1.54 tff(4539,assumption,(r(s(s(s(z))), s(z))), introduced(assumption)).
% 1.34/1.54 tff(4540,plain,
% 1.34/1.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(4541,plain,
% 1.34/1.54 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(4542,plain,
% 1.34/1.54 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[4541, 4540])).
% 1.34/1.54 tff(4543,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[4542, 297, 2511, 889, 4539])).
% 1.34/1.54 tff(4544,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(4545,plain,
% 1.34/1.54 (~r(s(s(s(z))), s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[4544, 4538, 2511])).
% 1.34/1.54 tff(4546,assumption,(~r(s(s(s(z))), s(z))), introduced(assumption)).
% 1.34/1.54 tff(4547,assumption,(~b(s(s(s(z))), s(z))), introduced(assumption)).
% 1.34/1.54 tff(4548,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[910, 51, 30, 4547, 4546])).
% 1.34/1.54 tff(4549,plain,(r(s(s(s(z))), s(z)) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(4550,plain,
% 1.34/1.54 (b(s(s(s(z))), s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[4549, 4545])).
% 1.34/1.54 tff(4551,plain,
% 1.34/1.54 (b(s(s(s(z))), s(s(elem!1)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[4226, 2915, 2557, 2839])).
% 1.34/1.54 tff(4552,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(4553,plain,
% 1.34/1.54 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(4554,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[4553])).
% 1.34/1.54 tff(4555,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[4554, 4552])).
% 1.34/1.55 tff(4556,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(4557,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[4556, 4555])).
% 1.34/1.55 tff(4558,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[4557, 319, 1, 817, 4551, 4550])).
% 1.34/1.55 tff(4559,plain,(b(s(s(s(z))), s(s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (s(s(s(z))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(4560,plain,
% 1.34/1.55 (b(s(s(s(z))), s(s(z)))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[4559, 4442, 4451, 2511, 4537, 4483])).
% 1.34/1.55 tff(4561,assumption,(b(s(s(s(z))), s(s(s(elem!1))))), introduced(assumption)).
% 1.34/1.55 tff(4562,assumption,(b(s(s(s(elem!1))), s(s(z)))), introduced(assumption)).
% 1.34/1.55 tff(4563,assumption,(b(s(s(z)), s(s(s(elem!1))))), introduced(assumption)).
% 1.34/1.55 tff(4564,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(4565,plain,
% 1.34/1.55 (((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(4566,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[4565])).
% 1.34/1.55 tff(4567,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[4566, 4564])).
% 1.34/1.55 tff(4568,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(4569,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[4568, 4567])).
% 1.34/1.55 tff(4570,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[4569, 319, 4563, 4562, 3138, 4561])).
% 1.34/1.55 tff(4571,plain,((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(4572,plain,
% 1.34/1.55 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[4571, 4529, 4527, 4560])).
% 1.34/1.55 tff(4573,plain,
% 1.34/1.55 (r(s(s(s(z))), s(s(s(elem!1))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[3794, 4572, 4482])).
% 1.34/1.55 tff(4574,plain,
% 1.34/1.55 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(4575,plain,
% 1.34/1.55 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(4576,plain,
% 1.34/1.55 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[4575])).
% 1.34/1.55 tff(4577,plain,
% 1.34/1.55 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[4576, 4574])).
% 1.34/1.55 tff(4578,plain,
% 1.34/1.55 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(4579,plain,
% 1.34/1.55 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[4578, 4577])).
% 1.34/1.55 tff(4580,plain,
% 1.34/1.55 (~r(s(s(s(z))), z)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[4579, 297, 4573, 4468])).
% 1.34/1.55 tff(4581,assumption,(~r(s(s(s(z))), z)), introduced(assumption)).
% 1.34/1.55 tff(4582,assumption,(~b(s(s(s(z))), z)), introduced(assumption)).
% 1.34/1.55 tff(4583,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[901, 51, 898, 4582, 4581])).
% 1.34/1.55 tff(4584,plain,(r(s(s(s(z))), z) | b(s(s(s(z))), z)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(4585,plain,
% 1.34/1.55 (b(s(s(s(z))), z)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[4584, 4580])).
% 1.34/1.55 tff(4586,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(4587,plain,
% 1.34/1.55 (((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(4588,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[4587])).
% 1.34/1.55 tff(4589,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[4588, 4586])).
% 1.34/1.55 tff(4590,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(4591,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[4590, 4589])).
% 1.34/1.55 tff(4592,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[4591, 319, 4529, 4527, 3884, 4560, 3877, 4585])).
% 1.34/1.55 tff(4593,plain,((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (s(s(s(elem!1))) = s(s(elem!1))) | (s(s(z)) = s(s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(4594,plain,
% 1.34/1.55 (~r(s(s(z)), s(s(elem!1)))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[4593, 70, 58, 772, 116, 2511])).
% 1.34/1.55 tff(4595,plain,
% 1.34/1.55 (b(s(s(z)), s(s(elem!1)))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[122, 4594, 772])).
% 1.34/1.55 tff(4596,plain,
% 1.34/1.55 (~b(s(z), s(s(elem!1)))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[3357, 4595, 116, 2511, 2522])).
% 1.34/1.55 tff(4597,plain,
% 1.34/1.55 (r(s(z), s(s(elem!1)))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1047, 4596])).
% 1.34/1.55 tff(4598,plain,
% 1.34/1.55 (~r(s(elem!1), s(s(elem!1)))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[3333, 4597, 70, 2504])).
% 1.34/1.55 tff(4599,plain,
% 1.34/1.55 (b(s(elem!1), s(s(elem!1)))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[807, 4598, 114])).
% 1.34/1.55 tff(4600,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(4601,plain,
% 1.34/1.55 (((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(4602,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1))))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[4601])).
% 1.34/1.55 tff(4603,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[4602, 4600])).
% 1.34/1.55 tff(4604,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(4605,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[4604, 4603])).
% 1.34/1.55 tff(4606,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[4605, 319, 3926, 2543, 785, 687])).
% 1.34/1.55 tff(4607,plain,((~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(4608,plain,
% 1.34/1.55 (~b(s(s(elem!1)), s(s(z)))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[4607, 4438, 4599, 4595])).
% 1.34/1.55 tff(4609,plain,
% 1.34/1.55 (r(s(s(elem!1)), s(s(z)))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2555, 51, 4608, 2522])).
% 1.34/1.55 tff(4610,plain,
% 1.34/1.55 (~r(s(s(elem!1)), s(z))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2565, 4609, 2511])).
% 1.34/1.55 tff(4611,plain,
% 1.34/1.55 (b(s(s(elem!1)), s(z))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[871, 4610])).
% 1.34/1.55 tff(4612,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2626, 319, 4611, 4438, 4599, 4595])).
% 1.34/1.55 tff(4613,plain,((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(4614,plain,
% 1.34/1.55 (~r(z, s(s(elem!1)))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[4613, 2511, 116, 772, 58])).
% 1.34/1.55 tff(4615,plain,
% 1.34/1.55 (b(z, s(s(elem!1)))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[56, 4614])).
% 1.34/1.55 tff(4616,plain,
% 1.34/1.55 (~b(s(s(z)), z)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[659, 319, 1, 687, 202])).
% 1.34/1.55 tff(4617,plain,
% 1.34/1.55 (r(s(s(z)), z)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[663, 51, 28, 4616])).
% 1.34/1.55 tff(4618,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(4619,plain,
% 1.34/1.55 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(4620,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[4619])).
% 1.34/1.55 tff(4621,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[4620, 4618])).
% 1.34/1.55 tff(4622,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(4623,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[4622, 4621])).
% 1.34/1.55 tff(4624,plain,
% 1.34/1.55 (~b(z, s(s(s(elem!1))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[4623, 319, 1, 202, 116])).
% 1.34/1.55 tff(4625,plain,
% 1.34/1.55 (r(z, s(s(s(elem!1))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[416, 4624])).
% 1.34/1.55 tff(4626,plain,
% 1.34/1.55 (r(s(s(z)), s(s(s(elem!1))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[476, 2675, 231])).
% 1.34/1.55 tff(4627,plain,
% 1.34/1.55 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(elem!1))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(4628,plain,
% 1.34/1.55 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(elem!1))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(4629,plain,
% 1.34/1.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(elem!1)))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[4628])).
% 1.34/1.56 tff(4630,plain,
% 1.34/1.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(elem!1))))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[4629, 4627])).
% 1.34/1.56 tff(4631,plain,
% 1.34/1.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z)))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(4632,plain,
% 1.34/1.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(elem!1)))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[4631, 4630])).
% 1.34/1.56 tff(4633,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[4632, 297, 4626, 4625, 4617])).
% 1.34/1.56 tff(4634,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(4635,plain,
% 1.34/1.56 (~b(s(s(elem!1)), s(z))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[4634, 687, 116, 202])).
% 1.34/1.56 tff(4636,plain,
% 1.34/1.56 (r(s(s(elem!1)), s(z))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[871, 4635])).
% 1.34/1.56 tff(4637,plain,
% 1.34/1.56 (~r(s(s(elem!1)), s(s(z)))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2565, 4636, 2511])).
% 1.34/1.56 tff(4638,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(4639,plain,
% 1.34/1.56 (((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(4640,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[4639])).
% 1.34/1.56 tff(4641,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[4640, 4638])).
% 1.34/1.56 tff(4642,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(4643,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[4642, 4641])).
% 1.34/1.56 tff(4644,plain,
% 1.34/1.56 (~b(s(s(z)), z)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[4643, 319, 2543, 687, 202])).
% 1.34/1.56 tff(4645,plain,
% 1.34/1.56 (r(s(s(z)), z)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[663, 51, 28, 4644])).
% 1.34/1.56 tff(4646,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(4647,plain,
% 1.34/1.56 (((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(4648,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[4647])).
% 1.34/1.56 tff(4649,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[4648, 4646])).
% 1.34/1.56 tff(4650,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(4651,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[4650, 4649])).
% 1.34/1.56 tff(4652,plain,
% 1.34/1.56 (~b(z, s(s(s(elem!1))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[4651, 319, 2543, 202, 116])).
% 1.34/1.56 tff(4653,plain,
% 1.34/1.56 (r(z, s(s(s(elem!1))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[416, 4652])).
% 1.34/1.56 tff(4654,plain,
% 1.34/1.56 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[3353, 319, 2543, 687, 116])).
% 1.34/1.56 tff(4655,plain,
% 1.34/1.56 (r(s(s(z)), s(s(s(elem!1))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1571, 4654])).
% 1.34/1.56 tff(4656,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[4632, 297, 4655, 4653, 4645])).
% 1.34/1.56 tff(4657,plain,((~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(4658,plain,
% 1.34/1.56 (~b(s(s(elem!1)), s(s(z)))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[4657, 687, 116, 202])).
% 1.34/1.56 tff(4659,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2555, 51, 4658, 2542, 4637])).
% 1.34/1.56 tff(4660,plain,((~b(s(s(z)), s(s(elem!1)))) | (s(s(elem!1)) = s(s(z))) | (~r(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(4661,plain,
% 1.34/1.56 (~b(s(s(z)), s(s(elem!1)))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[4660, 2511, 2522, 116, 4615])).
% 1.34/1.56 tff(4662,plain,
% 1.34/1.56 (r(s(s(z)), s(s(elem!1)))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[122, 4661, 772])).
% 1.34/1.56 tff(4663,plain,
% 1.34/1.56 (~r(s(z), s(s(elem!1)))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2583, 4662, 2511])).
% 1.34/1.56 tff(4664,plain,
% 1.34/1.56 (b(s(z), s(s(elem!1)))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1047, 4663])).
% 1.34/1.56 tff(4665,plain,
% 1.34/1.56 (~r(s(s(elem!1)), s(z))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[4108, 4662, 2511])).
% 1.34/1.56 tff(4666,plain,
% 1.34/1.56 (b(s(s(elem!1)), s(z))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[871, 4665])).
% 1.34/1.56 tff(4667,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1105, 4666, 4664, 116, 4615])).
% 1.34/1.56 tff(4668,plain,((~r(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(4669,plain,
% 1.34/1.56 (~r(s(s(z)), s(z))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[4668, 772, 116, 58])).
% 1.34/1.56 tff(4670,plain,
% 1.34/1.56 (b(s(s(z)), s(z))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[4102, 4669])).
% 1.34/1.56 tff(4671,plain,
% 1.34/1.56 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(elem!1))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[175])).
% 1.34/1.56 tff(4672,plain,
% 1.34/1.56 (r(s(z), s(elem!1)) <=> r(s(z), s(s(s(elem!1))))),
% 1.34/1.56 inference(symmetry,[status(thm)],[4671])).
% 1.34/1.56 tff(4673,plain,
% 1.34/1.56 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 1.34/1.56 inference(symmetry,[status(thm)],[173])).
% 1.34/1.56 tff(4674,plain,
% 1.34/1.56 ((elem!1 = s(s(elem!1))) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[4673])).
% 1.34/1.56 tff(4675,plain,
% 1.34/1.56 ((elem!1 = s(s(s(s(elem!1))))) <=> (elem!1 = s(s(elem!1)))),
% 1.34/1.56 inference(symmetry,[status(thm)],[4674])).
% 1.34/1.56 tff(4676,plain,
% 1.34/1.56 ((~(elem!1 = s(s(s(s(elem!1)))))) <=> (~(elem!1 = s(s(elem!1))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[4675])).
% 1.34/1.56 tff(4677,plain,
% 1.34/1.56 (~(elem!1 = s(s(elem!1)))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[1185, 4676])).
% 1.34/1.56 tff(4678,plain,
% 1.34/1.56 (s(s(s(elem!1))) = s(elem!1)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[178, 173])).
% 1.34/1.56 tff(4679,plain,
% 1.34/1.56 (elem!1 = s(s(elem!1))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[262, 4678])).
% 1.34/1.56 tff(4680,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[4679, 4677])).
% 1.34/1.56 tff(4681,plain,((~(s(s(s(s(elem!1)))) = s(s(elem!1)))) | (elem!1 = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(4682,plain,
% 1.34/1.56 (elem!1 = s(s(s(s(elem!1))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[4681, 173])).
% 1.34/1.56 tff(4683,plain,
% 1.34/1.56 (~(s(elem!1) = s(s(z)))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[3120, 4682])).
% 1.34/1.56 tff(4684,plain,
% 1.34/1.56 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[175])).
% 1.34/1.56 tff(4685,plain,
% 1.34/1.56 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.34/1.56 inference(symmetry,[status(thm)],[4684])).
% 1.34/1.56 tff(4686,plain,
% 1.34/1.56 ((~b(s(elem!1), s(s(elem!1)))) <=> (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[4685])).
% 1.34/1.56 tff(4687,assumption,(~b(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 1.34/1.56 tff(4688,plain,
% 1.34/1.56 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[4687, 4686])).
% 1.34/1.56 tff(4689,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[116, 4688])).
% 1.34/1.56 tff(4690,plain,((~(s(s(s(s(elem!1)))) = s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | b(s(elem!1), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(4691,plain,
% 1.34/1.56 (b(s(elem!1), s(s(elem!1)))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[4690, 173, 116])).
% 1.34/1.56 tff(4692,plain,
% 1.34/1.56 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(s(elem!1)) = s(elem!1))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[173])).
% 1.34/1.56 tff(4693,plain,
% 1.34/1.56 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(elem!1) = s(s(elem!1)))),
% 1.34/1.56 inference(transitivity,[status(thm)],[4692, 2494])).
% 1.34/1.56 tff(4694,plain,
% 1.34/1.56 ((s(elem!1) = s(s(elem!1))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 1.34/1.56 inference(symmetry,[status(thm)],[4693])).
% 1.34/1.56 tff(4695,plain,
% 1.34/1.56 ((~(s(elem!1) = s(s(elem!1)))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[4694])).
% 1.34/1.56 tff(4696,plain,
% 1.34/1.56 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[2142, 4695])).
% 1.34/1.56 tff(4697,plain,
% 1.34/1.56 (r(s(s(s(s(elem!1)))), s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[173])).
% 1.34/1.56 tff(4698,plain,
% 1.34/1.56 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.34/1.56 inference(symmetry,[status(thm)],[4697])).
% 1.34/1.56 tff(4699,plain,
% 1.34/1.56 ((~r(s(s(elem!1)), s(elem!1))) <=> (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[4698])).
% 1.34/1.56 tff(4700,plain,
% 1.34/1.56 (b(s(s(s(z))), s(z))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[1, 4283])).
% 1.34/1.56 tff(4701,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(4702,plain,
% 1.34/1.56 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(4703,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z)))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[4702])).
% 1.34/1.56 tff(4704,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[4703, 4701])).
% 1.34/1.56 tff(4705,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(4706,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[4705, 4704])).
% 1.34/1.56 tff(4707,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[4706, 319, 3390, 2493, 4700, 2990])).
% 1.34/1.56 tff(4708,plain,((~(s(elem!1) = s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(4709,plain,
% 1.34/1.56 (~(s(elem!1) = s(s(z)))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[4708, 1, 2493, 687, 3390])).
% 1.34/1.56 tff(4710,plain,
% 1.34/1.56 (~r(s(z), s(s(z)))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2656, 4709, 1, 785, 136, 687])).
% 1.34/1.56 tff(4711,plain,
% 1.34/1.56 (b(s(z), s(s(z)))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[685, 4710])).
% 1.34/1.56 tff(4712,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[706, 319, 1, 3390, 687, 4711])).
% 1.34/1.56 tff(4713,plain,((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (s(z) = s(elem!1)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(4714,plain,
% 1.34/1.56 (~b(s(s(elem!1)), s(z))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[4713, 4691, 687, 3390, 136, 2493])).
% 1.34/1.56 tff(4715,plain,
% 1.34/1.56 (r(s(s(elem!1)), s(z))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[871, 4714])).
% 1.34/1.56 tff(4716,plain,
% 1.34/1.56 (r(s(s(s(elem!1))), s(z)) <=> r(s(elem!1), s(z))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[175])).
% 1.34/1.56 tff(4717,plain,
% 1.34/1.56 (~r(z, s(z))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2177, 4715, 70])).
% 1.34/1.56 tff(4718,plain,
% 1.34/1.56 (b(z, s(z))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1099, 4717])).
% 1.34/1.56 tff(4719,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(z))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(4720,plain,
% 1.34/1.56 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(z))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(4721,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(z)))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[4720])).
% 1.34/1.56 tff(4722,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(z))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[4721, 4719])).
% 1.34/1.56 tff(4723,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(4724,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(z)))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[4723, 4722])).
% 1.34/1.56 tff(4725,plain,
% 1.34/1.56 (~b(s(s(z)), z)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[4724, 319, 3390, 2706, 2493])).
% 1.34/1.56 tff(4726,plain,
% 1.34/1.56 (r(s(s(z)), z)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[663, 51, 28, 4725])).
% 1.34/1.56 tff(4727,assumption,(b(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 1.34/1.56 tff(4728,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(4729,plain,
% 1.34/1.56 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(4730,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[4729])).
% 1.34/1.56 tff(4731,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[4730, 4728])).
% 1.34/1.56 tff(4732,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(4733,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[4732, 4731])).
% 1.34/1.56 tff(4734,plain,
% 1.34/1.56 (~b(z, s(s(s(elem!1))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[4733, 319, 2706, 2493, 4727])).
% 1.34/1.56 tff(4735,plain,
% 1.34/1.56 (r(z, s(s(s(elem!1))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[416, 4734])).
% 1.34/1.56 tff(4736,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(4737,plain,
% 1.34/1.56 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(4738,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[4737])).
% 1.34/1.56 tff(4739,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[4738, 4736])).
% 1.34/1.56 tff(4740,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(4741,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[4740, 4739])).
% 1.34/1.56 tff(4742,plain,
% 1.34/1.56 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[4741, 319, 3390, 2493, 4727])).
% 1.34/1.56 tff(4743,plain,
% 1.34/1.56 (r(s(s(z)), s(s(s(elem!1))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1571, 4742])).
% 1.34/1.56 tff(4744,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[4632, 297, 4743, 4735, 4726])).
% 1.34/1.56 tff(4745,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(4746,plain,
% 1.34/1.56 (~b(s(s(s(elem!1))), s(z))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[4745, 4718, 2493, 3390])).
% 1.34/1.56 tff(4747,assumption,(~r(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 1.34/1.56 tff(4748,assumption,(~b(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 1.34/1.56 tff(4749,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1088, 51, 171, 4748, 4747])).
% 1.34/1.56 tff(4750,plain,(r(s(s(s(elem!1))), s(z)) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(4751,plain,
% 1.34/1.56 (r(s(s(s(elem!1))), s(z))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[4750, 4746])).
% 1.34/1.56 tff(4752,plain,
% 1.34/1.56 (r(s(elem!1), s(z))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[4751, 4716])).
% 1.34/1.56 tff(4753,plain,
% 1.34/1.56 (~r(s(s(elem!1)), s(elem!1))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[3077, 4752, 4715])).
% 1.34/1.56 tff(4754,plain,
% 1.34/1.56 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[4753, 4699])).
% 1.34/1.56 tff(4755,plain,
% 1.34/1.56 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[595, 4754, 4696])).
% 1.34/1.56 tff(4756,plain,
% 1.34/1.56 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[173])).
% 1.34/1.56 tff(4757,plain,
% 1.34/1.56 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.34/1.56 inference(symmetry,[status(thm)],[4756])).
% 1.34/1.56 tff(4758,plain,
% 1.34/1.56 ((~b(s(s(elem!1)), s(elem!1))) <=> (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[4757])).
% 1.34/1.56 tff(4759,assumption,(~b(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 1.34/1.56 tff(4760,plain,
% 1.34/1.56 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[4759, 4758])).
% 1.34/1.56 tff(4761,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[547, 4760])).
% 1.34/1.56 tff(4762,plain,((~(s(s(s(s(elem!1)))) = s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | b(s(s(elem!1)), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(4763,plain,
% 1.34/1.57 (b(s(s(elem!1)), s(elem!1))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[4762, 4755, 173])).
% 1.34/1.57 tff(4764,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(4765,plain,
% 1.34/1.57 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z))))) <=> ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(4766,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1))))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[4765])).
% 1.34/1.57 tff(4767,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[4766, 4764])).
% 1.34/1.57 tff(4768,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(4769,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[4768, 4767])).
% 1.34/1.57 tff(4770,plain,
% 1.34/1.57 (~b(s(elem!1), s(s(z)))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[4769, 319, 4763, 4691, 687])).
% 1.34/1.57 tff(4771,plain,
% 1.34/1.57 (r(s(elem!1), s(s(z)))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2529, 4770, 4683])).
% 1.34/1.57 tff(4772,plain,
% 1.34/1.57 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[175])).
% 1.34/1.57 tff(4773,plain,
% 1.34/1.57 (r(s(elem!1), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 1.34/1.57 inference(symmetry,[status(thm)],[4772])).
% 1.34/1.57 tff(4774,plain,
% 1.34/1.57 (r(s(s(s(elem!1))), s(s(z)))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[4771, 4773])).
% 1.34/1.57 tff(4775,assumption,(r(s(s(s(elem!1))), s(s(z)))), introduced(assumption)).
% 1.34/1.57 tff(4776,assumption,(r(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 1.34/1.57 tff(4777,plain,
% 1.34/1.57 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(4778,plain,
% 1.34/1.57 (((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(4779,plain,
% 1.34/1.57 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[4778])).
% 1.34/1.57 tff(4780,plain,
% 1.34/1.57 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[4779, 4777])).
% 1.34/1.57 tff(4781,plain,
% 1.34/1.57 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(4782,plain,
% 1.34/1.57 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[4781, 4780])).
% 1.34/1.57 tff(4783,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[4782, 297, 903, 4776, 4775])).
% 1.34/1.57 tff(4784,plain,((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(4785,plain,
% 1.34/1.57 (~r(s(z), s(s(z)))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[4784, 4774, 4751])).
% 1.34/1.57 tff(4786,plain,
% 1.34/1.57 (b(s(z), s(s(z)))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[685, 4785])).
% 1.34/1.57 tff(4787,assumption,(b(s(z), s(s(z)))), introduced(assumption)).
% 1.34/1.57 tff(4788,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(4789,plain,
% 1.34/1.57 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z)))) <=> ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(4790,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z)))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[4789])).
% 1.34/1.57 tff(4791,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[4790, 4788])).
% 1.34/1.57 tff(4792,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(4793,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z)))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[4792, 4791])).
% 1.34/1.57 tff(4794,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[4793, 319, 3390, 711, 2706, 4787])).
% 1.34/1.57 tff(4795,plain,((~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(4796,plain,
% 1.34/1.57 (~b(z, s(s(z)))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[4795, 4786, 3390, 4718])).
% 1.34/1.57 tff(4797,plain,
% 1.34/1.57 (r(z, s(s(z)))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[729, 4796])).
% 1.34/1.57 tff(4798,plain,
% 1.34/1.57 (~r(s(elem!1), z)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[740, 4797, 4771])).
% 1.34/1.57 tff(4799,plain,
% 1.34/1.57 (b(s(elem!1), z)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2602, 4798])).
% 1.34/1.57 tff(4800,plain,
% 1.34/1.57 (~r(z, s(elem!1))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[755, 297, 4797, 4771])).
% 1.34/1.57 tff(4801,assumption,(~r(z, s(elem!1))), introduced(assumption)).
% 1.34/1.57 tff(4802,assumption,(~b(z, s(elem!1))), introduced(assumption)).
% 1.34/1.57 tff(4803,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[759, 51, 4802, 4801, 2878])).
% 1.34/1.57 tff(4804,plain,(b(z, s(elem!1)) | r(z, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(4805,plain,
% 1.34/1.57 (b(z, s(elem!1))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[4804, 4800])).
% 1.34/1.57 tff(4806,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(4807,plain,
% 1.34/1.57 (((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1)))) <=> ((~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(4808,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[4807])).
% 1.34/1.57 tff(4809,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))),
% 1.34/1.57 inference(transitivity,[status(thm)],[4808, 4806])).
% 1.34/1.57 tff(4810,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(4811,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[4810, 4809])).
% 1.34/1.57 tff(4812,plain,
% 1.34/1.57 (~b(s(z), s(elem!1))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[4811, 319, 4805, 4799, 2493])).
% 1.34/1.57 tff(4813,assumption,(~b(s(z), s(elem!1))), introduced(assumption)).
% 1.34/1.57 tff(4814,assumption,(~r(s(z), s(elem!1))), introduced(assumption)).
% 1.34/1.57 tff(4815,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2638, 51, 4814, 136, 4813])).
% 1.34/1.57 tff(4816,plain,(r(s(z), s(elem!1)) | (s(z) = s(elem!1)) | b(s(z), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(4817,plain,
% 1.34/1.57 (r(s(z), s(elem!1))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[4816, 4812, 136])).
% 1.34/1.57 tff(4818,plain,
% 1.34/1.57 (r(s(z), s(s(s(elem!1))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[4817, 4672])).
% 1.34/1.57 tff(4819,plain,
% 1.34/1.57 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(elem!1), s(elem!1))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[175])).
% 1.34/1.57 tff(4820,plain,
% 1.34/1.57 (b(s(elem!1), s(elem!1)) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.34/1.57 inference(symmetry,[status(thm)],[4819])).
% 1.34/1.57 tff(4821,plain,
% 1.34/1.57 ((~b(s(elem!1), s(elem!1))) <=> (~b(s(elem!1), s(s(s(elem!1)))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[4820])).
% 1.34/1.57 tff(4822,plain,
% 1.34/1.57 (^[X: $i] : refl((~b(X, X)) <=> (~b(X, X)))),
% 1.34/1.57 inference(bind,[status(th)],[])).
% 1.34/1.57 tff(4823,plain,
% 1.34/1.57 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 1.34/1.57 inference(quant_intro,[status(thm)],[4822])).
% 1.34/1.57 tff(4824,plain,
% 1.34/1.57 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(4825,axiom,(![X: $i] : (~b(X, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bi')).
% 1.34/1.57 tff(4826,plain,
% 1.34/1.57 (![X: $i] : (~b(X, X))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[4825, 4824])).
% 1.34/1.57 tff(4827,plain,(
% 1.34/1.57 ![X: $i] : (~b(X, X))),
% 1.34/1.57 inference(skolemize,[status(sab)],[4826])).
% 1.34/1.57 tff(4828,plain,
% 1.34/1.57 (![X: $i] : (~b(X, X))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[4827, 4823])).
% 1.34/1.57 tff(4829,plain,
% 1.34/1.57 ((~![X: $i] : (~b(X, X))) | (~b(s(elem!1), s(elem!1)))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(4830,plain,
% 1.34/1.57 (~b(s(elem!1), s(elem!1))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[4829, 4828])).
% 1.34/1.57 tff(4831,plain,
% 1.34/1.57 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[4830, 4821])).
% 1.34/1.57 tff(4832,plain,
% 1.34/1.57 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(elem!1), s(elem!1))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[175])).
% 1.34/1.57 tff(4833,plain,
% 1.34/1.57 (r(s(elem!1), s(elem!1)) <=> r(s(elem!1), s(s(s(elem!1))))),
% 1.34/1.57 inference(symmetry,[status(thm)],[4832])).
% 1.34/1.57 tff(4834,plain,
% 1.34/1.57 ((~r(s(elem!1), s(elem!1))) <=> (~r(s(elem!1), s(s(s(elem!1)))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[4833])).
% 1.34/1.57 tff(4835,plain,
% 1.34/1.57 (^[X: $i] : refl((~r(X, X)) <=> (~r(X, X)))),
% 1.34/1.57 inference(bind,[status(th)],[])).
% 1.34/1.57 tff(4836,plain,
% 1.34/1.57 (![X: $i] : (~r(X, X)) <=> ![X: $i] : (~r(X, X))),
% 1.34/1.57 inference(quant_intro,[status(thm)],[4835])).
% 1.34/1.57 tff(4837,plain,
% 1.34/1.57 (![X: $i] : (~r(X, X)) <=> ![X: $i] : (~r(X, X))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(4838,axiom,(![X: $i] : (~r(X, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ri')).
% 1.34/1.57 tff(4839,plain,
% 1.34/1.57 (![X: $i] : (~r(X, X))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[4838, 4837])).
% 1.34/1.57 tff(4840,plain,(
% 1.34/1.57 ![X: $i] : (~r(X, X))),
% 1.34/1.57 inference(skolemize,[status(sab)],[4839])).
% 1.34/1.57 tff(4841,plain,
% 1.34/1.57 (![X: $i] : (~r(X, X))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[4840, 4836])).
% 1.34/1.57 tff(4842,plain,
% 1.34/1.57 ((~![X: $i] : (~r(X, X))) | (~r(s(elem!1), s(elem!1)))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(4843,plain,
% 1.34/1.57 (~r(s(elem!1), s(elem!1))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[4842, 4841])).
% 1.34/1.57 tff(4844,plain,
% 1.34/1.57 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[4843, 4834])).
% 1.34/1.57 tff(4845,plain,
% 1.34/1.57 (s(elem!1) = s(s(s(elem!1)))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[434, 4844, 4831])).
% 1.34/1.57 tff(4846,plain,
% 1.34/1.57 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2827, 4845])).
% 1.34/1.57 tff(4847,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(4848,plain,
% 1.34/1.57 (((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(4849,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1)))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[4848])).
% 1.34/1.57 tff(4850,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[4849, 4847])).
% 1.34/1.57 tff(4851,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(4852,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1)))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[4851, 4850])).
% 1.34/1.57 tff(4853,plain,
% 1.34/1.57 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[4852, 319, 786, 274, 2841])).
% 1.34/1.57 tff(4854,plain,
% 1.34/1.57 (r(s(s(s(z))), s(s(elem!1)))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[4066, 51, 2839, 4853])).
% 1.34/1.57 tff(4855,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(4856,plain,
% 1.34/1.57 (((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(4857,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1)))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[4856])).
% 1.34/1.57 tff(4858,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[4857, 4855])).
% 1.34/1.57 tff(4859,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(4860,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1)))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[4859, 4858])).
% 1.34/1.57 tff(4861,plain,
% 1.34/1.57 (~b(s(s(s(z))), z)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[4860, 319, 2389, 786, 2841])).
% 1.34/1.57 tff(4862,plain,
% 1.34/1.57 (r(s(s(s(z))), z)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[4584, 4861])).
% 1.34/1.57 tff(4863,plain,
% 1.34/1.57 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(4864,plain,
% 1.34/1.57 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(4865,plain,
% 1.34/1.57 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[4864, 4863])).
% 1.34/1.57 tff(4866,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[4865, 297, 115, 4862, 4854])).
% 1.34/1.57 tff(4867,plain,((~b(s(s(s(z))), s(elem!1))) | (~r(s(s(elem!1)), z)) | (s(s(s(z))) = s(s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(4868,plain,
% 1.34/1.57 (~b(s(s(s(z))), s(elem!1))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[4867, 4846, 115, 4799, 4763, 4805])).
% 1.34/1.57 tff(4869,plain,
% 1.34/1.57 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[266])).
% 1.34/1.57 tff(4870,plain,
% 1.34/1.57 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(elem!1))),
% 1.34/1.57 inference(symmetry,[status(thm)],[4869])).
% 1.34/1.57 tff(4871,plain,
% 1.34/1.57 (b(s(s(s(z))), s(elem!1))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[4561, 4870])).
% 1.34/1.57 tff(4872,assumption,(~b(s(s(s(z))), s(elem!1))), introduced(assumption)).
% 1.34/1.57 tff(4873,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[4872, 4871])).
% 1.34/1.57 tff(4874,plain,((~b(s(s(s(z))), s(s(s(elem!1))))) | b(s(s(s(z))), s(elem!1)) | (~(s(elem!1) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(4875,plain,
% 1.34/1.58 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[4874, 4868, 4845])).
% 1.34/1.58 tff(4876,plain,
% 1.34/1.58 (r(s(s(s(z))), s(s(s(elem!1))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[3794, 4875, 3739])).
% 1.34/1.58 tff(4877,assumption,(r(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 1.34/1.58 tff(4878,assumption,(r(s(s(s(z))), s(s(s(elem!1))))), introduced(assumption)).
% 1.34/1.58 tff(4879,plain,
% 1.34/1.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(4880,plain,
% 1.34/1.58 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(4881,plain,
% 1.34/1.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[4880])).
% 1.34/1.58 tff(4882,plain,
% 1.34/1.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[4881, 4879])).
% 1.34/1.58 tff(4883,plain,
% 1.34/1.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(4884,plain,
% 1.34/1.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[4883, 4882])).
% 1.34/1.58 tff(4885,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[4884, 297, 4878, 4877, 4539])).
% 1.34/1.58 tff(4886,plain,((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(4887,plain,
% 1.34/1.58 (~r(s(s(s(z))), s(z))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[4886, 4876, 4818])).
% 1.34/1.58 tff(4888,plain,
% 1.34/1.58 (b(s(s(s(z))), s(z))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[4549, 4887])).
% 1.34/1.58 tff(4889,plain,
% 1.34/1.58 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 1.34/1.58 inference(symmetry,[status(thm)],[174])).
% 1.34/1.58 tff(4890,plain,
% 1.34/1.58 (s(elem!1) = s(s(s(elem!1)))),
% 1.34/1.58 inference(transitivity,[status(thm)],[206, 4889, 88])).
% 1.34/1.58 tff(4891,plain,
% 1.34/1.58 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[4890])).
% 1.34/1.58 tff(4892,plain,
% 1.34/1.58 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(elem!1))),
% 1.34/1.58 inference(symmetry,[status(thm)],[4891])).
% 1.34/1.58 tff(4893,plain,
% 1.34/1.58 (r(s(s(s(z))), s(elem!1))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[4876, 4892])).
% 1.34/1.58 tff(4894,plain,
% 1.34/1.58 (r(s(s(z)), s(elem!1)) <=> r(s(s(z)), s(s(s(elem!1))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[4890])).
% 1.34/1.58 tff(4895,plain,
% 1.34/1.58 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(s(z)), s(elem!1))),
% 1.34/1.58 inference(symmetry,[status(thm)],[4894])).
% 1.34/1.58 tff(4896,plain,
% 1.34/1.58 (b(s(s(z)), s(elem!1)) <=> b(s(s(z)), s(s(s(elem!1))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[4890])).
% 1.34/1.58 tff(4897,plain,
% 1.34/1.58 ((~b(s(s(z)), s(elem!1))) <=> (~b(s(s(z)), s(s(s(elem!1)))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[4896])).
% 1.34/1.58 tff(4898,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(4899,plain,
% 1.34/1.58 (((~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(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(4900,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1)))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[4899])).
% 1.34/1.58 tff(4901,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[4900, 4898])).
% 1.34/1.58 tff(4902,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(4903,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1)))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[4902, 4901])).
% 1.34/1.58 tff(4904,plain,
% 1.34/1.58 (~b(s(s(z)), s(elem!1))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[4903, 319, 4763, 4691, 687])).
% 1.34/1.58 tff(4905,plain,
% 1.34/1.58 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[4904, 4897])).
% 1.34/1.58 tff(4906,plain,
% 1.34/1.58 (r(s(s(z)), s(s(s(elem!1))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1571, 4905])).
% 1.34/1.58 tff(4907,plain,
% 1.34/1.58 (r(s(s(z)), s(elem!1))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[4906, 4895])).
% 1.34/1.58 tff(4908,plain,
% 1.34/1.58 ((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(z))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2913, 297, 4907])).
% 1.34/1.58 tff(4909,plain,
% 1.34/1.58 (~r(s(s(s(z))), s(s(z)))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[4908, 4893])).
% 1.34/1.58 tff(4910,plain,
% 1.34/1.58 (b(s(s(s(z))), s(s(z)))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2920, 4909])).
% 1.34/1.58 tff(4911,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(4912,plain,
% 1.34/1.58 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(4913,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z))))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[4912])).
% 1.34/1.58 tff(4914,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[4913, 4911])).
% 1.34/1.58 tff(4915,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(4916,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[4915, 4914])).
% 1.34/1.58 tff(4917,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[4916, 319, 3390, 4786, 4910, 4888])).
% 1.34/1.58 tff(4918,plain,((~(s(s(s(s(elem!1)))) = s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (s(z) = s(elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | (~r(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(4919,plain,
% 1.34/1.58 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[4918, 4670, 2510, 115, 2504, 2493, 687, 114, 70, 116])).
% 1.34/1.58 tff(4920,plain,
% 1.34/1.58 (~b(s(elem!1), s(s(elem!1)))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[4713, 1, 687, 3390, 136, 2493])).
% 1.34/1.58 tff(4921,plain,
% 1.34/1.58 (r(s(elem!1), s(s(elem!1)))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[807, 4920, 2142])).
% 1.34/1.58 tff(4922,plain,
% 1.34/1.58 (~r(s(z), s(s(elem!1)))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[3333, 4921, 70, 136])).
% 1.34/1.58 tff(4923,plain,
% 1.34/1.58 (b(s(z), s(s(elem!1)))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1047, 4922])).
% 1.34/1.58 tff(4924,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(4925,plain,
% 1.34/1.58 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(4926,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[4925])).
% 1.34/1.58 tff(4927,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[4926, 4924])).
% 1.34/1.58 tff(4928,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(4929,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[4928, 4927])).
% 1.34/1.58 tff(4930,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[4929, 319, 1, 3390, 687, 4923])).
% 1.34/1.58 tff(4931,plain,((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (s(z) = s(elem!1)) | (s(elem!1) = s(s(elem!1))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(4932,plain,
% 1.34/1.58 (~b(s(s(elem!1)), s(z))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[4931, 4670, 687, 70, 2504, 114, 2493])).
% 1.34/1.58 tff(4933,plain,
% 1.34/1.58 (r(s(s(elem!1)), s(z))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[871, 4932])).
% 1.34/1.58 tff(4934,plain,
% 1.34/1.58 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(z) = s(s(s(s(elem!1)))))),
% 1.34/1.58 inference(commutativity,[status(thm)],[])).
% 1.34/1.58 tff(4935,plain,
% 1.34/1.58 ((s(z) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(z))),
% 1.34/1.58 inference(symmetry,[status(thm)],[4934])).
% 1.34/1.58 tff(4936,plain,
% 1.34/1.58 ((~(s(z) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(z)))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[4935])).
% 1.34/1.58 tff(4937,plain,
% 1.34/1.58 (~(s(s(s(s(elem!1)))) = s(z))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[2212, 4936])).
% 1.34/1.58 tff(4938,assumption,(r(s(s(s(s(elem!1)))), z)), introduced(assumption)).
% 1.34/1.58 tff(4939,plain,
% 1.34/1.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(4940,plain,
% 1.34/1.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(4941,plain,
% 1.34/1.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[4940, 4939])).
% 1.34/1.58 tff(4942,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[4941, 297, 70, 984, 4938])).
% 1.34/1.58 tff(4943,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(4944,plain,
% 1.34/1.58 (~r(s(s(s(s(elem!1)))), z)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[4943, 984, 70])).
% 1.34/1.58 tff(4945,plain,
% 1.34/1.58 (b(s(s(s(s(elem!1)))), z)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[3268, 51, 604, 4944])).
% 1.34/1.58 tff(4946,plain,
% 1.34/1.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(4947,plain,
% 1.34/1.58 (((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1))))))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(4948,plain,
% 1.34/1.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1))))))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[4947])).
% 1.34/1.58 tff(4949,plain,
% 1.34/1.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[4948, 4946])).
% 1.34/1.58 tff(4950,plain,
% 1.34/1.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(4951,plain,
% 1.34/1.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1))))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[4950, 4949])).
% 1.34/1.58 tff(4952,plain,
% 1.34/1.58 (~r(z, s(s(s(s(elem!1)))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[4951, 297, 70, 984])).
% 1.34/1.58 tff(4953,plain,
% 1.34/1.58 ((z = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = z)),
% 1.34/1.58 inference(commutativity,[status(thm)],[])).
% 1.34/1.58 tff(4954,plain,
% 1.34/1.58 ((s(s(s(s(elem!1)))) = z) <=> (z = s(s(s(s(elem!1)))))),
% 1.34/1.58 inference(symmetry,[status(thm)],[4953])).
% 1.34/1.58 tff(4955,plain,
% 1.34/1.58 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(z = s(s(s(s(elem!1))))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[4954])).
% 1.34/1.58 tff(4956,plain,
% 1.34/1.58 (~(z = s(s(s(s(elem!1)))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[604, 4955])).
% 1.34/1.58 tff(4957,plain,
% 1.34/1.58 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(4958,plain,
% 1.34/1.58 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1))))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(4959,plain,
% 1.34/1.58 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1)))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[4958, 4957])).
% 1.34/1.58 tff(4960,plain,
% 1.34/1.58 ((z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1)))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[4959, 51])).
% 1.34/1.58 tff(4961,plain,
% 1.34/1.58 (b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1)))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[4960, 4956])).
% 1.34/1.58 tff(4962,plain,
% 1.34/1.58 (b(z, s(s(s(s(elem!1)))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[4961, 4952])).
% 1.34/1.58 tff(4963,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(4964,plain,
% 1.34/1.58 (((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(4965,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1))))))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[4964])).
% 1.34/1.58 tff(4966,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[4965, 4963])).
% 1.34/1.58 tff(4967,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(4968,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1))))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[4967, 4966])).
% 1.34/1.58 tff(4969,plain,
% 1.34/1.58 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[4968, 319, 4962, 2493, 4945])).
% 1.34/1.58 tff(4970,plain,
% 1.34/1.58 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z)))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(4971,plain,
% 1.34/1.58 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z)))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(4972,plain,
% 1.34/1.58 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[4971, 4970])).
% 1.34/1.58 tff(4973,plain,
% 1.34/1.59 ((s(s(s(s(elem!1)))) = s(z)) | r(s(s(s(s(elem!1)))), s(z))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[4972, 51, 4969])).
% 1.34/1.59 tff(4974,plain,
% 1.34/1.59 (r(s(s(s(s(elem!1)))), s(z))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[4973, 4937])).
% 1.34/1.59 tff(4975,plain,
% 1.34/1.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(4976,plain,
% 1.34/1.59 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(4977,plain,
% 1.34/1.59 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[4976, 4975])).
% 1.34/1.59 tff(4978,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[4977, 297, 2169, 984, 4974])).
% 1.34/1.59 tff(4979,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(4980,plain,
% 1.34/1.59 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[4979, 4933, 2493, 70])).
% 1.34/1.59 tff(4981,plain,
% 1.34/1.59 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[571, 4980, 4919])).
% 1.34/1.59 tff(4982,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(4983,plain,
% 1.34/1.59 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(4984,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z))))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[4983])).
% 1.34/1.59 tff(4985,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[4984, 4982])).
% 1.34/1.59 tff(4986,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(4987,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[4986, 4985])).
% 1.34/1.59 tff(4988,plain,
% 1.34/1.59 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[4987, 319, 274, 687, 1021])).
% 1.34/1.59 tff(4989,plain,
% 1.34/1.59 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(z))) | b(s(s(s(s(elem!1)))), s(s(z))) | r(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(z))) | b(s(s(s(s(elem!1)))), s(s(z))) | r(s(s(s(s(elem!1)))), s(s(z))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(4990,plain,
% 1.34/1.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(z))) | b(s(s(s(s(elem!1)))), s(s(z))) | r(s(s(s(s(elem!1)))), s(s(z))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(4991,plain,
% 1.34/1.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(z))) | b(s(s(s(s(elem!1)))), s(s(z))) | r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[4990, 4989])).
% 1.34/1.59 tff(4992,plain,
% 1.34/1.59 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[4991, 51, 2140, 4988])).
% 1.34/1.59 tff(4993,assumption,(s(s(s(elem!1))) = s(s(z))), introduced(assumption)).
% 1.34/1.59 tff(4994,plain,
% 1.34/1.59 (s(s(z)) = s(s(s(elem!1)))),
% 1.34/1.59 inference(symmetry,[status(thm)],[4993])).
% 1.34/1.59 tff(4995,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[231, 4994])).
% 1.34/1.59 tff(4996,plain,(~(s(s(s(elem!1))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(4997,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(4998,plain,
% 1.34/1.59 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(4999,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[4998])).
% 1.34/1.59 tff(5000,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[4999, 4997])).
% 1.34/1.59 tff(5001,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(5002,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[5001, 5000])).
% 1.34/1.59 tff(5003,plain,
% 1.34/1.59 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[5002, 319, 274, 687, 116])).
% 1.34/1.59 tff(5004,plain,
% 1.34/1.59 (r(s(s(s(elem!1))), s(s(z)))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2728, 51, 5003, 4996])).
% 1.34/1.59 tff(5005,plain,
% 1.34/1.59 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[558, 51, 99, 1848])).
% 1.34/1.59 tff(5006,plain,
% 1.34/1.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(5007,plain,
% 1.34/1.59 (((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(5008,plain,
% 1.34/1.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[5007])).
% 1.34/1.59 tff(5009,plain,
% 1.34/1.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[5008, 5006])).
% 1.34/1.59 tff(5010,plain,
% 1.34/1.59 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(5011,plain,
% 1.34/1.59 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[5010, 5009])).
% 1.34/1.59 tff(5012,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[5011, 297, 5005, 5004, 4992])).
% 1.34/1.59 tff(5013,plain,((~b(s(s(elem!1)), s(elem!1))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(5014,plain,
% 1.34/1.59 (~b(s(s(elem!1)), s(elem!1))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[5013, 4981, 116, 93, 687])).
% 1.34/1.59 tff(5015,plain,
% 1.34/1.59 ((s(s(elem!1)) = s(elem!1)) | r(s(s(elem!1)), s(elem!1))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2780, 51, 5014])).
% 1.34/1.59 tff(5016,plain,
% 1.34/1.59 (r(s(s(elem!1)), s(elem!1))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[5015, 2497])).
% 1.34/1.59 tff(5017,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2776, 297, 115, 2390, 731])).
% 1.34/1.59 tff(5018,plain,((~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(5019,plain,
% 1.34/1.59 (~r(s(elem!1), z)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[5018, 5016, 115])).
% 1.34/1.59 tff(5020,plain,
% 1.34/1.59 (b(s(elem!1), z)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2602, 5019])).
% 1.34/1.59 tff(5021,plain,
% 1.34/1.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(5022,plain,
% 1.34/1.59 (((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(5023,plain,
% 1.34/1.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1))))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[5022])).
% 1.34/1.59 tff(5024,plain,
% 1.34/1.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[5023, 5021])).
% 1.34/1.59 tff(5025,plain,
% 1.34/1.59 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(5026,plain,
% 1.34/1.59 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[5025, 5024])).
% 1.34/1.59 tff(5027,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[5026, 297, 2390, 70, 4112])).
% 1.34/1.59 tff(5028,plain,((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(5029,plain,
% 1.34/1.59 (~r(z, s(elem!1))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[5028, 5016, 70])).
% 1.34/1.59 tff(5030,plain,
% 1.34/1.59 (b(z, s(elem!1))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[4804, 5029])).
% 1.34/1.59 tff(5031,plain,
% 1.34/1.59 (~r(s(elem!1), s(z))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[3077, 5016, 4933])).
% 1.34/1.59 tff(5032,plain,
% 1.34/1.59 (b(s(elem!1), s(z))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[783, 5031, 2498])).
% 1.34/1.59 tff(5033,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[767, 319, 5032, 5030, 5020, 2493])).
% 1.34/1.59 tff(5034,plain,((s(s(z)) = s(s(elem!1))) | (~b(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(5035,plain,
% 1.34/1.59 (s(s(z)) = s(s(elem!1))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[5034, 116, 115, 70, 68, 2492, 58])).
% 1.34/1.59 tff(5036,plain,
% 1.34/1.59 (s(z) = s(elem!1)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[138, 5035])).
% 1.34/1.59 tff(5037,plain,
% 1.34/1.59 (z = elem!1),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[148, 5036])).
% 1.34/1.59 tff(5038,plain,
% 1.34/1.59 (s(z) = s(elem!1)),
% 1.34/1.59 inference(monotonicity,[status(thm)],[5037])).
% 1.34/1.59 tff(5039,plain,
% 1.34/1.59 (s(s(z)) = s(s(elem!1))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[5038])).
% 1.34/1.59 tff(5040,plain,
% 1.34/1.59 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(elem!1)), s(s(elem!1)))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[5039])).
% 1.34/1.59 tff(5041,plain,
% 1.34/1.59 (b(s(s(elem!1)), s(s(elem!1))) <=> b(s(s(z)), s(s(elem!1)))),
% 1.34/1.59 inference(symmetry,[status(thm)],[5040])).
% 1.34/1.59 tff(5042,plain,
% 1.34/1.59 ((~b(s(s(elem!1)), s(s(elem!1)))) <=> (~b(s(s(z)), s(s(elem!1))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[5041])).
% 1.34/1.59 tff(5043,plain,
% 1.34/1.59 ((~![X: $i] : (~b(X, X))) | (~b(s(s(elem!1)), s(s(elem!1))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(5044,plain,
% 1.34/1.59 (~b(s(s(elem!1)), s(s(elem!1)))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[5043, 4828])).
% 1.34/1.59 tff(5045,plain,
% 1.34/1.59 (~b(s(s(z)), s(s(elem!1)))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[5044, 5042])).
% 1.34/1.59 tff(5046,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2492, 5045])).
% 1.34/1.59 tff(5047,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | r(s(z), z) | r(s(s(z)), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(5048,plain,
% 1.34/1.59 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[5047, 76, 70, 58, 59, 69])).
% 1.34/1.59 tff(5049,plain,
% 1.34/1.59 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[348, 5048, 58])).
% 1.34/1.59 tff(5050,assumption,(r(z, s(s(s(elem!1))))), introduced(assumption)).
% 1.34/1.59 tff(5051,plain,
% 1.34/1.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(5052,plain,
% 1.34/1.59 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, 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))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(5053,plain,
% 1.34/1.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1)))))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[5052])).
% 1.34/1.59 tff(5054,plain,
% 1.34/1.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[5053, 5051])).
% 1.34/1.59 tff(5055,plain,
% 1.34/1.59 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(5056,plain,
% 1.34/1.59 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1)))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[5055, 5054])).
% 1.34/1.59 tff(5057,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[5056, 297, 70, 5050, 335])).
% 1.34/1.59 tff(5058,plain,((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(5059,plain,
% 1.34/1.59 (~r(z, s(s(s(elem!1))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[5058, 5049, 70])).
% 1.34/1.59 tff(5060,plain,
% 1.34/1.59 (b(z, s(s(s(elem!1))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[416, 5059])).
% 1.34/1.59 tff(5061,plain,
% 1.34/1.59 (~r(s(s(s(elem!1))), z)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[3880, 297, 70, 5049])).
% 1.34/1.59 tff(5062,plain,
% 1.34/1.59 (b(s(s(s(elem!1))), z)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1077, 51, 160, 5061])).
% 1.34/1.59 tff(5063,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(5064,plain,
% 1.34/1.59 (((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(5065,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[5064])).
% 1.34/1.59 tff(5066,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[5065, 5063])).
% 1.34/1.59 tff(5067,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(5068,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[5067, 5066])).
% 1.34/1.59 tff(5069,plain,
% 1.34/1.59 (~b(s(s(s(elem!1))), s(z))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[5068, 319, 5062, 5060, 68])).
% 1.34/1.59 tff(5070,plain,
% 1.34/1.59 (r(s(s(s(elem!1))), s(z))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[4750, 5069])).
% 1.34/1.59 tff(5071,plain,
% 1.34/1.59 (s(s(z)) = s(s(elem!1))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2521, 2518])).
% 1.34/1.59 tff(5072,plain,
% 1.34/1.59 (s(z) = s(elem!1)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[138, 5071])).
% 1.34/1.59 tff(5073,plain,
% 1.34/1.59 (z = elem!1),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[148, 5072])).
% 1.34/1.59 tff(5074,plain,
% 1.34/1.59 (elem!1 = z),
% 1.34/1.59 inference(symmetry,[status(thm)],[5073])).
% 1.34/1.59 tff(5075,plain,
% 1.34/1.59 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), z)),
% 1.34/1.59 inference(monotonicity,[status(thm)],[5074])).
% 1.34/1.59 tff(5076,plain,
% 1.34/1.59 (r(s(s(s(z))), z) <=> r(s(s(s(z))), elem!1)),
% 1.34/1.59 inference(symmetry,[status(thm)],[5075])).
% 1.34/1.59 tff(5077,plain,
% 1.34/1.59 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[2518])).
% 1.34/1.59 tff(5078,plain,
% 1.34/1.59 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(z))), z)),
% 1.34/1.59 inference(monotonicity,[status(thm)],[5077, 5074])).
% 1.34/1.59 tff(5079,plain,
% 1.34/1.59 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(elem!1))) = z)),
% 1.34/1.59 inference(monotonicity,[status(thm)],[5074])).
% 1.34/1.59 tff(5080,plain,
% 1.34/1.60 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 1.34/1.60 inference(symmetry,[status(thm)],[5079])).
% 1.34/1.60 tff(5081,plain,
% 1.34/1.60 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.34/1.60 inference(monotonicity,[status(thm)],[5080])).
% 1.34/1.60 tff(5082,plain,
% 1.34/1.60 (~(s(s(s(elem!1))) = elem!1)),
% 1.34/1.60 inference(modus_ponens,[status(thm)],[160, 5081])).
% 1.34/1.60 tff(5083,plain,
% 1.34/1.60 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.34/1.60 inference(monotonicity,[status(thm)],[2518])).
% 1.34/1.60 tff(5084,plain,
% 1.34/1.60 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 1.34/1.60 inference(symmetry,[status(thm)],[5083])).
% 1.34/1.60 tff(5085,plain,
% 1.34/1.60 (s(z) = s(elem!1)),
% 1.34/1.60 inference(transitivity,[status(thm)],[127, 5084, 118])).
% 1.34/1.60 tff(5086,plain,
% 1.34/1.60 (b(z, s(z)) <=> b(elem!1, s(elem!1))),
% 1.34/1.60 inference(monotonicity,[status(thm)],[5073, 5085])).
% 1.34/1.60 tff(5087,plain,
% 1.34/1.60 (~r(z, s(z))),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[3560, 2169, 115])).
% 1.34/1.60 tff(5088,plain,
% 1.34/1.60 (b(z, s(z))),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[1099, 5087])).
% 1.34/1.60 tff(5089,plain,
% 1.34/1.60 (b(elem!1, s(elem!1))),
% 1.34/1.60 inference(modus_ponens,[status(thm)],[5088, 5086])).
% 1.34/1.60 tff(5090,plain,
% 1.34/1.60 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 1.34/1.60 inference(rewrite,[status(thm)],[])).
% 1.34/1.60 tff(5091,plain,
% 1.34/1.60 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 1.34/1.60 inference(quant_inst,[status(thm)],[])).
% 1.34/1.60 tff(5092,plain,
% 1.34/1.60 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z)))),
% 1.34/1.60 inference(modus_ponens,[status(thm)],[5091, 5090])).
% 1.34/1.60 tff(5093,plain,
% 1.34/1.60 ($false),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[5092, 297, 2169, 666, 115])).
% 1.34/1.60 tff(5094,plain,((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.60 tff(5095,plain,
% 1.34/1.60 (~r(s(z), z)),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[5094, 2169, 115])).
% 1.34/1.60 tff(5096,plain,
% 1.34/1.60 (~r(s(elem!1), elem!1)),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[868, 5095, 133])).
% 1.34/1.60 tff(5097,plain,
% 1.34/1.60 (b(s(elem!1), elem!1)),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[375, 5096, 194])).
% 1.34/1.60 tff(5098,plain,
% 1.34/1.60 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[2362, 319, 275, 5097, 448])).
% 1.34/1.60 tff(5099,plain,
% 1.34/1.60 (r(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[521, 51, 5098, 183])).
% 1.34/1.60 tff(5100,plain,
% 1.34/1.60 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(z))),
% 1.34/1.60 inference(monotonicity,[status(thm)],[216])).
% 1.34/1.60 tff(5101,plain,
% 1.34/1.60 (r(s(s(elem!1)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 1.34/1.60 inference(symmetry,[status(thm)],[5100])).
% 1.34/1.60 tff(5102,plain,
% 1.34/1.60 (r(s(s(elem!1)), s(elem!1))),
% 1.34/1.60 inference(modus_ponens,[status(thm)],[2169, 5101])).
% 1.34/1.60 tff(5103,plain,
% 1.34/1.60 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.34/1.60 inference(rewrite,[status(thm)],[])).
% 1.34/1.60 tff(5104,plain,
% 1.34/1.60 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.34/1.60 inference(quant_inst,[status(thm)],[])).
% 1.34/1.60 tff(5105,plain,
% 1.34/1.60 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.34/1.60 inference(modus_ponens,[status(thm)],[5104, 5103])).
% 1.34/1.60 tff(5106,plain,
% 1.34/1.60 ($false),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[5105, 297, 5102, 335, 5099])).
% 1.34/1.60 tff(5107,plain,((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~(s(s(z)) = s(s(elem!1)))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.60 tff(5108,plain,
% 1.44/1.60 (~b(s(s(s(elem!1))), elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[5107, 335, 5071, 115, 2169, 5089])).
% 1.44/1.60 tff(5109,plain,
% 1.44/1.60 (r(s(s(s(elem!1))), elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[361, 5108, 5082])).
% 1.44/1.60 tff(5110,plain,
% 1.44/1.60 (r(s(s(s(z))), z)),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[5109, 5078])).
% 1.44/1.60 tff(5111,plain,
% 1.44/1.60 (r(s(s(s(z))), elem!1)),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[5110, 5076])).
% 1.44/1.60 tff(5112,plain,
% 1.44/1.60 (r(s(s(s(z))), s(s(z)))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[943, 335, 5071])).
% 1.44/1.60 tff(5113,plain,
% 1.44/1.60 (r(s(s(z)), z) <=> r(s(s(z)), elem!1)),
% 1.44/1.60 inference(monotonicity,[status(thm)],[5073])).
% 1.44/1.60 tff(5114,plain,
% 1.44/1.60 (r(s(s(elem!1)), z) <=> r(s(s(z)), z)),
% 1.44/1.60 inference(monotonicity,[status(thm)],[2518])).
% 1.44/1.60 tff(5115,plain,
% 1.44/1.60 (r(s(s(z)), z)),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[115, 5114])).
% 1.44/1.60 tff(5116,plain,
% 1.44/1.60 (r(s(s(z)), elem!1)),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[5115, 5113])).
% 1.44/1.60 tff(5117,plain,
% 1.44/1.60 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(5118,plain,
% 1.44/1.60 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(5119,plain,
% 1.44/1.60 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[5118, 5117])).
% 1.44/1.60 tff(5120,plain,
% 1.44/1.60 (~r(s(s(s(z))), elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[5119, 297, 5116, 5112])).
% 1.44/1.60 tff(5121,plain,
% 1.44/1.60 ($false),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[5120, 5111])).
% 1.44/1.60 tff(5122,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~(s(s(elem!1)) = s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.60 tff(5123,plain,
% 1.44/1.60 (~(s(s(elem!1)) = s(s(z)))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[5122, 2128, 115, 335])).
% 1.44/1.60 tff(5124,plain,
% 1.44/1.60 ((s(s(z)) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(z)))),
% 1.44/1.60 inference(symmetry,[status(thm)],[2517])).
% 1.44/1.60 tff(5125,plain,
% 1.44/1.60 (s(s(elem!1)) = s(s(z))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[133, 5124])).
% 1.44/1.60 tff(5126,plain,
% 1.44/1.60 ($false),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2542, 5125])).
% 1.44/1.60 tff(5127,plain,((~(s(s(z)) = s(s(elem!1)))) | (s(s(elem!1)) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.60 tff(5128,plain,
% 1.44/1.60 ($false),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[5127, 5123, 123])).
% 1.44/1.60 tff(5129,plain,(b(s(s(z)), s(s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | r(s(s(z)), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.60 tff(5130,plain,
% 1.44/1.60 (b(s(s(z)), s(s(elem!1)))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[5129, 76, 5049, 69])).
% 1.44/1.60 tff(5131,plain,
% 1.44/1.60 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(5132,plain,
% 1.44/1.60 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(5133,plain,
% 1.44/1.60 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z)))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[5132, 5131])).
% 1.44/1.60 tff(5134,plain,
% 1.44/1.60 ($false),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[5133, 297, 444, 335, 4776])).
% 1.44/1.60 tff(5135,plain,((~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)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.60 tff(5136,plain,
% 1.44/1.60 (~r(s(z), s(s(elem!1)))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[5135, 5070, 5049])).
% 1.44/1.60 tff(5137,plain,
% 1.44/1.60 (b(s(z), s(s(elem!1)))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1047, 5136])).
% 1.44/1.60 tff(5138,assumption,(b(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.44/1.60 tff(5139,plain,
% 1.44/1.60 (~b(s(s(s(elem!1))), s(z))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[5068, 319, 5138, 3741, 2493])).
% 1.44/1.60 tff(5140,plain,
% 1.44/1.60 (r(s(s(s(elem!1))), s(z))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[4750, 5139])).
% 1.44/1.60 tff(5141,plain,
% 1.44/1.60 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(5142,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[5141])).
% 1.44/1.60 tff(5143,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.44/1.60 inference(transitivity,[status(thm)],[5142, 4924])).
% 1.44/1.60 tff(5144,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(5145,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[5144, 5143])).
% 1.44/1.60 tff(5146,plain,
% 1.44/1.60 (~b(s(s(z)), s(z))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[5145, 319, 872, 687, 817])).
% 1.44/1.60 tff(5147,plain,
% 1.44/1.60 (r(s(s(z)), s(z))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[4102, 5146])).
% 1.44/1.60 tff(5148,plain,
% 1.44/1.60 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2682, 297, 5147, 5140])).
% 1.44/1.60 tff(5149,plain,
% 1.44/1.60 (b(s(s(z)), s(s(s(elem!1))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1571, 5148])).
% 1.44/1.60 tff(5150,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(5151,plain,
% 1.44/1.60 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(5152,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[5151])).
% 1.44/1.60 tff(5153,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.44/1.60 inference(transitivity,[status(thm)],[5152, 5150])).
% 1.44/1.60 tff(5154,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(5155,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[5154, 5153])).
% 1.44/1.60 tff(5156,plain,
% 1.44/1.60 (~b(s(s(z)), z)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[5155, 319, 5149, 5138, 3741])).
% 1.44/1.60 tff(5157,plain,
% 1.44/1.60 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(z))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[133])).
% 1.44/1.60 tff(5158,plain,
% 1.44/1.60 (r(s(s(elem!1)), s(z))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[2511, 5157])).
% 1.44/1.60 tff(5159,plain,
% 1.44/1.60 ($false),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[180, 5158])).
% 1.44/1.60 tff(5160,plain,(r(s(s(elem!1)), s(z)) | (~r(s(s(z)), s(z))) | (~(s(s(z)) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.60 tff(5161,plain,
% 1.44/1.60 (~(s(s(z)) = s(s(elem!1)))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[5160, 5147, 180])).
% 1.44/1.60 tff(5162,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(5163,plain,
% 1.44/1.60 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(5164,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[5163])).
% 1.44/1.60 tff(5165,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.44/1.60 inference(transitivity,[status(thm)],[5164, 5162])).
% 1.44/1.60 tff(5166,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(z)))))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(5167,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[5166, 5165])).
% 1.44/1.60 tff(5168,plain,
% 1.44/1.60 (~b(z, s(s(z)))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[5167, 319, 5149, 5138, 3741])).
% 1.44/1.60 tff(5169,plain,
% 1.44/1.60 (r(z, s(s(z)))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[729, 5168])).
% 1.44/1.60 tff(5170,plain,
% 1.44/1.60 (b(s(elem!1), z) <=> b(s(s(elem!1)), z)),
% 1.44/1.60 inference(monotonicity,[status(thm)],[109])).
% 1.44/1.60 tff(5171,plain,
% 1.44/1.60 (b(s(s(elem!1)), z) <=> b(s(elem!1), z)),
% 1.44/1.60 inference(symmetry,[status(thm)],[5170])).
% 1.44/1.60 tff(5172,plain,
% 1.44/1.60 ((~b(s(s(elem!1)), z)) <=> (~b(s(elem!1), z))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[5171])).
% 1.44/1.60 tff(5173,plain,
% 1.44/1.60 (~b(s(elem!1), z)),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[71, 5172])).
% 1.44/1.60 tff(5174,plain,
% 1.44/1.60 ($false),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[786, 5173])).
% 1.44/1.60 tff(5175,plain,((~(s(elem!1) = s(s(elem!1)))) | (~b(s(elem!1), z)) | b(s(s(elem!1)), z)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.60 tff(5176,plain,
% 1.44/1.60 (~(s(elem!1) = s(s(elem!1)))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[5175, 786, 71])).
% 1.44/1.60 tff(5177,assumption,(s(s(s(elem!1))) = s(s(elem!1))), introduced(assumption)).
% 1.44/1.60 tff(5178,plain,
% 1.44/1.60 (s(s(elem!1)) = s(s(s(elem!1)))),
% 1.44/1.60 inference(symmetry,[status(thm)],[5177])).
% 1.44/1.60 tff(5179,plain,
% 1.44/1.60 (inj_0(s(s(elem!1))) = inj_0(s(s(s(elem!1))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[5178])).
% 1.44/1.60 tff(5180,plain,
% 1.44/1.60 (s(elem!1) = s(s(elem!1))),
% 1.44/1.60 inference(transitivity,[status(thm)],[206, 5179, 83])).
% 1.44/1.60 tff(5181,plain,
% 1.44/1.60 ($false),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2142, 5180])).
% 1.44/1.60 tff(5182,plain,((~(s(s(s(elem!1))) = s(s(elem!1)))) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.60 tff(5183,plain,
% 1.44/1.60 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[5182, 5176])).
% 1.44/1.60 tff(5184,plain,
% 1.44/1.60 (~r(s(s(z)), s(s(elem!1)))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[3463, 732, 70])).
% 1.44/1.60 tff(5185,plain,
% 1.44/1.60 (b(s(s(z)), s(s(elem!1)))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[122, 772, 5184])).
% 1.44/1.60 tff(5186,plain,
% 1.44/1.60 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(5187,plain,
% 1.44/1.60 (((~r(s(s(z)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(5188,plain,
% 1.44/1.60 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z))))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[5187])).
% 1.44/1.60 tff(5189,plain,
% 1.44/1.60 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.44/1.60 inference(transitivity,[status(thm)],[5188, 5186])).
% 1.44/1.60 tff(5190,plain,
% 1.44/1.60 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(5191,plain,
% 1.44/1.60 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[5190, 5189])).
% 1.44/1.60 tff(5192,plain,
% 1.44/1.60 (~r(s(s(elem!1)), s(s(z)))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[5191, 297, 76, 2605])).
% 1.44/1.60 tff(5193,plain,
% 1.44/1.60 (b(s(s(elem!1)), s(s(z)))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2555, 51, 2522, 5192])).
% 1.44/1.60 tff(5194,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(5195,plain,
% 1.44/1.60 (((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(5196,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z))))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[5195])).
% 1.44/1.60 tff(5197,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.44/1.60 inference(transitivity,[status(thm)],[5196, 5194])).
% 1.44/1.60 tff(5198,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(z)))))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(5199,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[5198, 5197])).
% 1.44/1.61 tff(5200,plain,
% 1.44/1.61 (~b(s(z), s(s(z)))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[5199, 319, 5193, 5185, 817])).
% 1.44/1.61 tff(5201,plain,
% 1.44/1.61 (r(s(z), s(s(z)))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[685, 5200])).
% 1.44/1.61 tff(5202,plain,
% 1.44/1.61 (~r(s(z), z)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[839, 297, 5201, 732])).
% 1.44/1.61 tff(5203,plain,
% 1.44/1.61 (b(s(z), z)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[65, 51, 62, 5202])).
% 1.44/1.61 tff(5204,plain,
% 1.44/1.61 (~r(z, s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[922, 5201, 732])).
% 1.44/1.61 tff(5205,plain,
% 1.44/1.61 (b(z, s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[926, 51, 5204, 916])).
% 1.44/1.61 tff(5206,plain,
% 1.44/1.61 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)) | (~b(z, s(z))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(5207,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)) | (~b(z, s(z)))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[5206])).
% 1.44/1.61 tff(5208,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)) | (~b(z, s(z))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[5207, 2593])).
% 1.44/1.61 tff(5209,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(5210,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)) | (~b(z, s(z)))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[5209, 5208])).
% 1.44/1.61 tff(5211,plain,
% 1.44/1.61 (~b(s(elem!1), s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[5210, 319, 786, 5205, 5203])).
% 1.44/1.61 tff(5212,plain,
% 1.44/1.61 (r(s(elem!1), s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[783, 5211, 2498])).
% 1.44/1.61 tff(5213,plain,
% 1.44/1.61 (~(s(s(elem!1)) = s(elem!1))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[5176, 2496])).
% 1.44/1.61 tff(5214,plain,
% 1.44/1.61 (~(s(elem!1) = s(s(z)))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[3187, 786, 2604])).
% 1.44/1.61 tff(5215,plain,
% 1.44/1.61 (~r(s(elem!1), s(s(z)))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2536, 297, 5212, 2511])).
% 1.44/1.61 tff(5216,plain,
% 1.44/1.61 (b(s(elem!1), s(s(z)))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2529, 5215, 5214])).
% 1.44/1.61 tff(5217,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(5218,plain,
% 1.44/1.61 (((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(5219,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[5218])).
% 1.44/1.61 tff(5220,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[5219, 5217])).
% 1.44/1.61 tff(5221,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(5222,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[5221, 5220])).
% 1.44/1.61 tff(5223,plain,
% 1.44/1.61 (~b(s(s(elem!1)), s(elem!1))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[5222, 319, 5216, 5193, 5185])).
% 1.44/1.61 tff(5224,plain,
% 1.44/1.61 ((s(s(elem!1)) = s(elem!1)) | r(s(s(elem!1)), s(elem!1))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2780, 51, 5223])).
% 1.44/1.61 tff(5225,plain,
% 1.44/1.61 (r(s(s(elem!1)), s(elem!1))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[5224, 5213])).
% 1.44/1.61 tff(5226,plain,
% 1.44/1.61 (~r(s(s(elem!1)), s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[3077, 5225, 5212])).
% 1.44/1.61 tff(5227,plain,
% 1.44/1.61 (b(s(s(elem!1)), s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[871, 5226])).
% 1.44/1.61 tff(5228,plain,
% 1.44/1.61 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2684, 5227, 2511, 5185, 817])).
% 1.44/1.61 tff(5229,plain,
% 1.44/1.61 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[348, 5228, 5183])).
% 1.44/1.61 tff(5230,plain,
% 1.44/1.61 (~r(s(s(s(elem!1))), z)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[3880, 297, 70, 5229])).
% 1.44/1.61 tff(5231,plain,
% 1.44/1.61 (b(s(s(s(elem!1))), z)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1077, 51, 160, 5230])).
% 1.44/1.61 tff(5232,plain,
% 1.44/1.61 (~b(s(elem!1), s(s(elem!1)))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[4605, 319, 5216, 5193, 5185])).
% 1.44/1.61 tff(5233,plain,
% 1.44/1.61 (r(s(elem!1), s(s(elem!1)))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[807, 5232, 5176])).
% 1.44/1.61 tff(5234,plain,
% 1.44/1.61 (~r(z, s(elem!1))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[4120, 5233, 70])).
% 1.44/1.61 tff(5235,plain,
% 1.44/1.61 (b(z, s(elem!1))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[759, 51, 5234, 2878])).
% 1.44/1.61 tff(5236,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(5237,plain,
% 1.44/1.61 (((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(5238,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[5237])).
% 1.44/1.61 tff(5239,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)))),
% 1.44/1.61 inference(transitivity,[status(thm)],[5238, 5236])).
% 1.44/1.61 tff(5240,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(5241,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[5240, 5239])).
% 1.44/1.61 tff(5242,plain,
% 1.44/1.61 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[5241, 319, 5235, 786, 5231])).
% 1.44/1.61 tff(5243,plain,
% 1.44/1.61 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[544, 297, 5233, 5229])).
% 1.44/1.61 tff(5244,plain,
% 1.44/1.61 ((s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[521, 51, 5243])).
% 1.44/1.61 tff(5245,plain,
% 1.44/1.61 (s(s(s(elem!1))) = s(elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[5244, 5242])).
% 1.44/1.61 tff(5246,plain,
% 1.44/1.61 (s(elem!1) = s(s(s(elem!1)))),
% 1.44/1.61 inference(symmetry,[status(thm)],[5245])).
% 1.44/1.61 tff(5247,plain,
% 1.44/1.61 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[5246])).
% 1.44/1.61 tff(5248,plain,
% 1.44/1.61 ((~b(s(s(s(z))), s(elem!1))) <=> (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[5247])).
% 1.44/1.61 tff(5249,plain,
% 1.44/1.61 (inj_0(s(s(s(elem!1)))) = inj_0(s(elem!1))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[5245])).
% 1.44/1.61 tff(5250,plain,
% 1.44/1.61 (s(s(elem!1)) = elem!1),
% 1.44/1.61 inference(transitivity,[status(thm)],[168, 5249, 141])).
% 1.44/1.61 tff(5251,plain,
% 1.44/1.61 (b(s(z), s(s(elem!1))) <=> b(s(z), elem!1)),
% 1.44/1.61 inference(monotonicity,[status(thm)],[5250])).
% 1.44/1.61 tff(5252,plain,
% 1.44/1.61 (b(s(z), elem!1)),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[817, 5251])).
% 1.44/1.61 tff(5253,plain,
% 1.44/1.61 (~r(s(s(s(z))), s(s(z)))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[935, 5252, 732, 5201])).
% 1.44/1.61 tff(5254,plain,
% 1.44/1.61 (b(s(s(s(z))), s(s(z)))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2918, 51, 2248, 5253])).
% 1.44/1.61 tff(5255,plain,
% 1.44/1.61 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(z)), elem!1)),
% 1.44/1.61 inference(monotonicity,[status(thm)],[5250])).
% 1.44/1.61 tff(5256,plain,
% 1.44/1.61 (b(s(s(z)), elem!1)),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[5185, 5255])).
% 1.44/1.61 tff(5257,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(5258,plain,
% 1.44/1.61 (((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(5259,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(elem!1)))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[5258])).
% 1.44/1.61 tff(5260,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[5259, 5257])).
% 1.44/1.61 tff(5261,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(5262,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(elem!1)))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[5261, 5260])).
% 1.44/1.61 tff(5263,plain,
% 1.44/1.61 (~b(s(s(s(z))), s(elem!1))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[5262, 319, 5216, 5256, 5254])).
% 1.44/1.61 tff(5264,plain,
% 1.44/1.61 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[5263, 5248])).
% 1.44/1.61 tff(5265,plain,
% 1.44/1.61 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[5246])).
% 1.44/1.61 tff(5266,plain,
% 1.44/1.61 ((~r(s(s(s(z))), s(elem!1))) <=> (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[5265])).
% 1.44/1.61 tff(5267,plain,
% 1.44/1.61 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.44/1.61 inference(symmetry,[status(thm)],[5249])).
% 1.44/1.61 tff(5268,plain,
% 1.44/1.61 (elem!1 = s(s(elem!1))),
% 1.44/1.61 inference(transitivity,[status(thm)],[258, 5267, 83])).
% 1.44/1.61 tff(5269,plain,
% 1.44/1.61 ((s(s(s(z))) = elem!1) <=> (s(s(s(z))) = s(s(elem!1)))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[5268])).
% 1.44/1.61 tff(5270,plain,
% 1.44/1.61 ((s(s(s(z))) = s(s(elem!1))) <=> (s(s(s(z))) = elem!1)),
% 1.44/1.61 inference(symmetry,[status(thm)],[5269])).
% 1.44/1.61 tff(5271,plain,
% 1.44/1.61 ((~(s(s(s(z))) = s(s(elem!1)))) <=> (~(s(s(s(z))) = elem!1))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[5270])).
% 1.44/1.61 tff(5272,plain,
% 1.44/1.61 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[343, 5229, 5233])).
% 1.44/1.61 tff(5273,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(5274,plain,
% 1.44/1.61 (((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(5275,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[5274])).
% 1.44/1.61 tff(5276,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)))),
% 1.44/1.61 inference(transitivity,[status(thm)],[5275, 5273])).
% 1.44/1.61 tff(5277,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(5278,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[5277, 5276])).
% 1.44/1.61 tff(5279,plain,
% 1.44/1.61 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[5278, 319, 5235, 786, 5231])).
% 1.44/1.61 tff(5280,plain,
% 1.44/1.61 (s(elem!1) = s(s(s(elem!1)))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[434, 5279, 5272])).
% 1.44/1.61 tff(5281,plain,
% 1.44/1.61 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2827, 5280])).
% 1.44/1.61 tff(5282,plain,
% 1.44/1.61 (~(s(s(s(z))) = elem!1)),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[5281, 5271])).
% 1.44/1.61 tff(5283,plain,
% 1.44/1.61 (elem!1 = s(s(elem!1))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[262, 5245])).
% 1.44/1.61 tff(5284,plain,
% 1.44/1.61 (b(elem!1, s(s(z)))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2794, 5283, 5193])).
% 1.44/1.61 tff(5285,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(5286,plain,
% 1.44/1.61 (((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(5287,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[5286])).
% 1.44/1.61 tff(5288,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)))),
% 1.44/1.61 inference(transitivity,[status(thm)],[5287, 5285])).
% 1.44/1.61 tff(5289,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), elem!1)))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(5290,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[5289, 5288])).
% 1.44/1.61 tff(5291,plain,
% 1.44/1.61 (~b(s(s(s(z))), elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[5290, 319, 5284, 5256, 5254])).
% 1.44/1.61 tff(5292,plain,
% 1.44/1.61 ((s(s(s(z))) = elem!1) | r(s(s(s(z))), elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2865, 51, 5291])).
% 1.44/1.61 tff(5293,plain,
% 1.44/1.61 (r(s(s(s(z))), elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[5292, 5282])).
% 1.44/1.61 tff(5294,plain,
% 1.44/1.61 (r(s(elem!1), s(s(elem!1))) <=> r(s(elem!1), elem!1)),
% 1.44/1.61 inference(monotonicity,[status(thm)],[5250])).
% 1.44/1.61 tff(5295,plain,
% 1.44/1.61 (r(s(elem!1), elem!1)),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[5233, 5294])).
% 1.44/1.61 tff(5296,plain,
% 1.44/1.61 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(5297,plain,
% 1.44/1.61 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(5298,plain,
% 1.44/1.61 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1)))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[5297, 5296])).
% 1.44/1.62 tff(5299,plain,
% 1.44/1.62 (~r(s(s(s(z))), s(elem!1))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[5298, 297, 5295, 5293])).
% 1.44/1.62 tff(5300,plain,
% 1.44/1.62 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[5299, 5266])).
% 1.44/1.62 tff(5301,plain,
% 1.44/1.62 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[3794, 5300, 5264])).
% 1.44/1.62 tff(5302,plain,
% 1.44/1.62 (s(s(s(z))) = s(elem!1)),
% 1.44/1.62 inference(transitivity,[status(thm)],[5301, 5245])).
% 1.44/1.62 tff(5303,plain,
% 1.44/1.62 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[5302])).
% 1.44/1.62 tff(5304,plain,
% 1.44/1.62 (s(s(z)) = elem!1),
% 1.44/1.62 inference(transitivity,[status(thm)],[18, 5303, 141])).
% 1.44/1.62 tff(5305,plain,
% 1.44/1.62 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(elem!1)))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[5268])).
% 1.44/1.62 tff(5306,plain,
% 1.44/1.62 ((s(s(z)) = s(s(elem!1))) <=> (s(s(z)) = elem!1)),
% 1.44/1.62 inference(symmetry,[status(thm)],[5305])).
% 1.44/1.62 tff(5307,plain,
% 1.44/1.62 ((~(s(s(z)) = s(s(elem!1)))) <=> (~(s(s(z)) = elem!1))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[5306])).
% 1.44/1.62 tff(5308,plain,
% 1.44/1.62 (~(s(s(z)) = elem!1)),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[772, 5307])).
% 1.44/1.62 tff(5309,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[5308, 5304])).
% 1.44/1.62 tff(5310,plain,((~b(s(elem!1), z)) | (~r(z, s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(z))) | b(s(s(z)), z) | b(s(s(elem!1)), z)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(5311,plain,
% 1.44/1.62 (~b(s(elem!1), z)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[5310, 5169, 70, 5147, 5161, 71, 817, 5156])).
% 1.44/1.62 tff(5312,plain,
% 1.44/1.62 (r(s(elem!1), z)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2602, 5311])).
% 1.44/1.62 tff(5313,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[3317, 297, 197, 70, 731])).
% 1.44/1.62 tff(5314,plain,((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(5315,plain,
% 1.44/1.62 (~r(s(elem!1), s(s(elem!1)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[5314, 5312, 70])).
% 1.44/1.62 tff(5316,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[823, 319, 1, 687, 817, 4787])).
% 1.44/1.62 tff(5317,plain,((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(5318,plain,
% 1.44/1.62 (~b(s(z), s(s(z)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[5317, 872, 817, 687])).
% 1.44/1.62 tff(5319,plain,
% 1.44/1.62 (r(s(z), s(s(z)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[685, 5318])).
% 1.44/1.62 tff(5320,plain,
% 1.44/1.62 (~r(z, s(z))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[922, 5169, 5319])).
% 1.44/1.62 tff(5321,plain,
% 1.44/1.62 (b(z, s(z))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1099, 5320])).
% 1.44/1.62 tff(5322,plain,
% 1.44/1.62 (~(s(s(elem!1)) = s(s(z)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2521, 5161])).
% 1.44/1.62 tff(5323,plain,
% 1.44/1.62 (~r(s(s(elem!1)), s(s(z)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[4014, 5169, 76])).
% 1.44/1.62 tff(5324,assumption,(~r(s(s(elem!1)), s(s(z)))), introduced(assumption)).
% 1.44/1.62 tff(5325,assumption,(~b(s(s(elem!1)), s(s(z)))), introduced(assumption)).
% 1.44/1.62 tff(5326,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2555, 51, 5325, 2542, 5324])).
% 1.44/1.62 tff(5327,plain,(b(s(s(elem!1)), s(s(z))) | (s(s(elem!1)) = s(s(z))) | r(s(s(elem!1)), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(5328,plain,
% 1.44/1.62 (b(s(s(elem!1)), s(s(z)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[5327, 5323, 5322])).
% 1.44/1.62 tff(5329,plain,
% 1.44/1.62 (~r(s(elem!1), s(s(z)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[740, 5312, 5169])).
% 1.44/1.62 tff(5330,plain,
% 1.44/1.62 (~r(s(s(elem!1)), s(elem!1))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[5018, 5312, 76])).
% 1.44/1.62 tff(5331,plain,
% 1.44/1.62 (~b(s(z), s(s(z)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[5199, 319, 2543, 687, 817])).
% 1.44/1.62 tff(5332,plain,
% 1.44/1.62 (r(s(z), s(s(z)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[685, 5331])).
% 1.44/1.62 tff(5333,plain,
% 1.44/1.62 (~(s(elem!1) = s(s(z)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[3088, 2915, 2248, 3083])).
% 1.44/1.62 tff(5334,plain,
% 1.44/1.62 (b(s(elem!1), s(s(z)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2529, 5333, 2524])).
% 1.44/1.62 tff(5335,plain,
% 1.44/1.62 (~b(s(elem!1), s(s(elem!1)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[4605, 319, 5334, 2543, 687])).
% 1.44/1.62 tff(5336,plain,
% 1.44/1.62 (s(elem!1) = s(s(elem!1))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[807, 5335, 1042])).
% 1.44/1.62 tff(5337,plain,
% 1.44/1.62 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[113, 5336])).
% 1.44/1.62 tff(5338,plain,
% 1.44/1.62 (inj_0(s(elem!1)) = inj_0(s(s(elem!1)))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[5180])).
% 1.44/1.62 tff(5339,plain,
% 1.44/1.62 (elem!1 = s(s(elem!1))),
% 1.44/1.62 inference(transitivity,[status(thm)],[258, 5338, 5179, 83])).
% 1.44/1.62 tff(5340,plain,
% 1.44/1.62 ((s(s(elem!1)) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 1.44/1.62 inference(commutativity,[status(thm)],[])).
% 1.44/1.62 tff(5341,plain,
% 1.44/1.62 ((s(s(s(elem!1))) = elem!1) <=> (s(s(elem!1)) = elem!1)),
% 1.44/1.62 inference(monotonicity,[status(thm)],[5177])).
% 1.44/1.62 tff(5342,plain,
% 1.44/1.62 ((s(s(s(elem!1))) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 1.44/1.62 inference(transitivity,[status(thm)],[5341, 5340])).
% 1.44/1.62 tff(5343,plain,
% 1.44/1.62 ((~(s(s(s(elem!1))) = elem!1)) <=> (~(elem!1 = s(s(elem!1))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[5342])).
% 1.44/1.62 tff(5344,plain,
% 1.44/1.62 (~(elem!1 = s(s(elem!1)))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[512, 5343])).
% 1.44/1.62 tff(5345,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[5344, 5339])).
% 1.44/1.62 tff(5346,plain,((~(s(s(s(elem!1))) = s(s(elem!1)))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(5347,plain,
% 1.44/1.62 (s(s(s(elem!1))) = elem!1),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[5346, 5337])).
% 1.44/1.62 tff(5348,plain,
% 1.44/1.62 (elem!1 = s(s(s(elem!1)))),
% 1.44/1.62 inference(symmetry,[status(thm)],[5347])).
% 1.44/1.62 tff(5349,plain,
% 1.44/1.62 (elem!1 = s(s(elem!1))),
% 1.44/1.62 inference(transitivity,[status(thm)],[5348, 5337])).
% 1.44/1.62 tff(5350,plain,
% 1.44/1.62 (b(s(z), elem!1) <=> b(s(z), s(s(elem!1)))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[5349])).
% 1.44/1.62 tff(5351,plain,
% 1.44/1.62 (b(s(z), s(s(elem!1))) <=> b(s(z), elem!1)),
% 1.44/1.62 inference(symmetry,[status(thm)],[5350])).
% 1.44/1.62 tff(5352,plain,
% 1.44/1.62 (b(s(z), elem!1)),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[817, 5351])).
% 1.44/1.62 tff(5353,plain,
% 1.44/1.62 (~r(s(s(s(z))), s(s(z)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[935, 5352, 732, 5332])).
% 1.44/1.62 tff(5354,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2918, 51, 2248, 2915, 5353])).
% 1.44/1.62 tff(5355,plain,(b(s(s(s(z))), s(s(z))) | (~r(z, s(s(z)))) | (~b(s(z), s(s(elem!1)))) | r(s(elem!1), s(s(elem!1))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | r(s(elem!1), s(s(z))) | r(s(s(elem!1)), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(5356,plain,
% 1.44/1.62 (b(s(s(s(z))), s(s(z)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[5355, 5315, 817, 687, 5169, 5328, 5329, 5330])).
% 1.44/1.62 tff(5357,plain,
% 1.44/1.62 (b(s(elem!1), s(s(elem!1)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[807, 2142, 1042])).
% 1.44/1.62 tff(5358,plain,
% 1.44/1.62 (((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z))))) <=> ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(5359,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1))))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[5358])).
% 1.44/1.62 tff(5360,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.44/1.62 inference(transitivity,[status(thm)],[5359, 4600])).
% 1.44/1.62 tff(5361,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(5362,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[5361, 5360])).
% 1.44/1.62 tff(5363,plain,
% 1.44/1.62 (~b(s(elem!1), s(s(z)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[5362, 319, 2543, 5357, 687])).
% 1.44/1.62 tff(5364,plain,
% 1.44/1.62 (s(elem!1) = s(s(z))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2529, 5363, 2524])).
% 1.44/1.62 tff(5365,plain,
% 1.44/1.62 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[5364])).
% 1.44/1.62 tff(5366,plain,
% 1.44/1.62 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 1.44/1.62 inference(symmetry,[status(thm)],[5365])).
% 1.44/1.62 tff(5367,plain,
% 1.44/1.62 (s(z) = elem!1),
% 1.44/1.62 inference(transitivity,[status(thm)],[127, 5366, 141])).
% 1.44/1.62 tff(5368,plain,
% 1.44/1.62 (b(s(z), s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[5367])).
% 1.44/1.62 tff(5369,plain,
% 1.44/1.62 (b(elem!1, s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(elem!1)))))),
% 1.44/1.62 inference(symmetry,[status(thm)],[5368])).
% 1.44/1.62 tff(5370,plain,
% 1.44/1.62 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[3120, 5364])).
% 1.44/1.62 tff(5371,plain,
% 1.44/1.62 (elem!1 = s(z)),
% 1.44/1.62 inference(transitivity,[status(thm)],[258, 5365, 126])).
% 1.44/1.62 tff(5372,plain,
% 1.44/1.62 (r(elem!1, s(elem!1)) <=> r(s(z), s(s(z)))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[5371, 5364])).
% 1.44/1.62 tff(5373,plain,
% 1.44/1.62 (r(s(z), s(s(z))) <=> r(elem!1, s(elem!1))),
% 1.44/1.62 inference(symmetry,[status(thm)],[5372])).
% 1.44/1.62 tff(5374,plain,
% 1.44/1.62 (r(elem!1, s(elem!1))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[5332, 5373])).
% 1.44/1.62 tff(5375,plain,
% 1.44/1.62 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(elem!1))) = s(z))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[5371])).
% 1.44/1.62 tff(5376,plain,
% 1.44/1.62 ((s(s(s(elem!1))) = s(z)) <=> (s(s(s(elem!1))) = elem!1)),
% 1.44/1.62 inference(symmetry,[status(thm)],[5375])).
% 1.44/1.62 tff(5377,plain,
% 1.44/1.62 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[5376])).
% 1.44/1.62 tff(5378,plain,
% 1.44/1.62 (~(s(s(s(elem!1))) = elem!1)),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[171, 5377])).
% 1.44/1.62 tff(5379,plain,
% 1.44/1.62 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[586, 5378])).
% 1.44/1.62 tff(5380,plain,
% 1.44/1.62 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[5182, 2142])).
% 1.44/1.62 tff(5381,plain,
% 1.44/1.62 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(s(z)))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[5364])).
% 1.44/1.62 tff(5382,plain,
% 1.44/1.62 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(elem!1)), s(elem!1))),
% 1.44/1.62 inference(symmetry,[status(thm)],[5381])).
% 1.44/1.62 tff(5383,plain,
% 1.44/1.62 (b(s(s(elem!1)), s(elem!1))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[2543, 5382])).
% 1.44/1.62 tff(5384,plain,
% 1.44/1.62 (s(s(z)) = s(elem!1)),
% 1.44/1.62 inference(symmetry,[status(thm)],[5364])).
% 1.44/1.62 tff(5385,plain,
% 1.44/1.62 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[5384])).
% 1.44/1.62 tff(5386,plain,
% 1.44/1.62 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.44/1.62 inference(transitivity,[status(thm)],[5385, 276])).
% 1.44/1.62 tff(5387,plain,
% 1.44/1.62 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[5386])).
% 1.44/1.62 tff(5388,plain,
% 1.44/1.62 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[231, 5387])).
% 1.44/1.62 tff(5389,plain,
% 1.44/1.62 (r(s(elem!1), elem!1) <=> r(s(s(z)), elem!1)),
% 1.44/1.62 inference(monotonicity,[status(thm)],[5364])).
% 1.44/1.62 tff(5390,plain,
% 1.44/1.62 (r(s(s(z)), elem!1) <=> r(s(elem!1), elem!1)),
% 1.44/1.62 inference(symmetry,[status(thm)],[5389])).
% 1.44/1.62 tff(5391,plain,
% 1.44/1.62 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(z))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[5371])).
% 1.44/1.62 tff(5392,plain,
% 1.44/1.62 (r(s(s(z)), s(z)) <=> r(s(s(z)), elem!1)),
% 1.44/1.62 inference(symmetry,[status(thm)],[5391])).
% 1.44/1.62 tff(5393,plain,
% 1.44/1.62 (r(s(s(z)), s(z)) <=> r(s(elem!1), elem!1)),
% 1.44/1.62 inference(transitivity,[status(thm)],[5392, 5390])).
% 1.44/1.62 tff(5394,plain,
% 1.44/1.62 (r(s(elem!1), elem!1)),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[2511, 5393])).
% 1.44/1.62 tff(5395,plain,
% 1.44/1.62 (b(elem!1, s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[5371])).
% 1.44/1.62 tff(5396,plain,
% 1.44/1.62 (b(s(z), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 1.44/1.62 inference(symmetry,[status(thm)],[5395])).
% 1.44/1.62 tff(5397,plain,
% 1.44/1.62 (b(elem!1, s(s(elem!1)))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[817, 5396])).
% 1.44/1.62 tff(5398,plain,
% 1.44/1.62 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[534, 5397, 5394, 5388, 5378, 5383])).
% 1.44/1.62 tff(5399,plain,
% 1.44/1.62 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[348, 5398, 5380])).
% 1.44/1.62 tff(5400,plain,
% 1.44/1.62 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[5364])).
% 1.44/1.62 tff(5401,plain,
% 1.44/1.62 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.62 inference(symmetry,[status(thm)],[5400])).
% 1.44/1.62 tff(5402,plain,
% 1.44/1.62 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 1.44/1.62 inference(monotonicity,[status(thm)],[5367])).
% 1.44/1.62 tff(5403,plain,
% 1.44/1.62 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(z))),
% 1.44/1.62 inference(symmetry,[status(thm)],[5402])).
% 1.44/1.62 tff(5404,plain,
% 1.44/1.62 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 1.44/1.62 inference(monotonicity,[status(thm)],[5367])).
% 1.44/1.62 tff(5405,plain,
% 1.44/1.62 ((~b(s(s(s(elem!1))), s(z))) <=> (~b(s(s(s(elem!1))), elem!1))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[5404])).
% 1.44/1.62 tff(5406,plain,
% 1.44/1.62 (s(s(elem!1)) = s(s(s(z)))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[5364])).
% 1.44/1.62 tff(5407,plain,
% 1.44/1.62 (s(s(s(z))) = s(s(elem!1))),
% 1.44/1.62 inference(symmetry,[status(thm)],[5406])).
% 1.44/1.62 tff(5408,plain,
% 1.44/1.62 (r(z, s(s(s(z)))) <=> r(z, s(s(elem!1)))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[5407])).
% 1.44/1.62 tff(5409,plain,
% 1.44/1.62 (r(z, s(s(elem!1))) <=> r(z, s(s(s(z))))),
% 1.44/1.62 inference(symmetry,[status(thm)],[5408])).
% 1.44/1.62 tff(5410,plain,
% 1.44/1.62 (r(z, s(s(s(z))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[70, 5409])).
% 1.44/1.62 tff(5411,plain,
% 1.44/1.62 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[5406])).
% 1.44/1.62 tff(5412,plain,
% 1.44/1.62 (r(s(s(s(elem!1))), s(s(s(z))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[5399, 5411])).
% 1.44/1.62 tff(5413,plain,
% 1.44/1.62 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), z)))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(5414,plain,
% 1.44/1.62 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), z)))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(5415,plain,
% 1.44/1.62 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), z))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[5414, 5413])).
% 1.44/1.62 tff(5416,plain,
% 1.44/1.62 ((~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), z))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[5415, 297, 5412])).
% 1.44/1.62 tff(5417,plain,
% 1.44/1.62 (~r(s(s(s(elem!1))), z)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[5416, 5410])).
% 1.44/1.62 tff(5418,plain,
% 1.44/1.62 (b(s(s(s(elem!1))), z)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1077, 51, 160, 5417])).
% 1.44/1.62 tff(5419,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))), s(z))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(5420,plain,
% 1.44/1.62 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(5421,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))), s(z)))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[5420])).
% 1.44/1.62 tff(5422,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))), s(z))))),
% 1.44/1.62 inference(transitivity,[status(thm)],[5421, 5419])).
% 1.44/1.62 tff(5423,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(5424,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))), s(z)))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[5423, 5422])).
% 1.44/1.62 tff(5425,plain,
% 1.44/1.62 (~b(s(s(s(elem!1))), s(z))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[5424, 319, 5418, 2706, 2493])).
% 1.44/1.62 tff(5426,plain,
% 1.44/1.62 (~b(s(s(s(elem!1))), elem!1)),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[5425, 5405])).
% 1.44/1.62 tff(5427,plain,
% 1.44/1.62 (r(s(s(s(elem!1))), elem!1)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[361, 5426, 5378])).
% 1.44/1.62 tff(5428,plain,
% 1.44/1.62 (r(s(s(s(elem!1))), s(z))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[5427, 5403])).
% 1.44/1.62 tff(5429,plain,
% 1.44/1.62 ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2682, 297, 2511])).
% 1.44/1.62 tff(5430,plain,
% 1.44/1.62 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[5429, 5428])).
% 1.44/1.62 tff(5431,plain,
% 1.44/1.62 (b(s(s(z)), s(s(s(elem!1))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1571, 5430])).
% 1.44/1.62 tff(5432,plain,
% 1.44/1.62 (b(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[5431, 5401])).
% 1.44/1.62 tff(5433,plain,
% 1.44/1.62 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[178, 5388])).
% 1.44/1.62 tff(5434,plain,
% 1.44/1.62 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[92, 5380])).
% 1.44/1.62 tff(5435,plain,
% 1.44/1.62 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(s(z)))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[5364])).
% 1.44/1.62 tff(5436,plain,
% 1.44/1.62 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.62 inference(symmetry,[status(thm)],[5435])).
% 1.44/1.62 tff(5437,plain,
% 1.44/1.62 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(5438,plain,
% 1.44/1.62 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(5439,plain,
% 1.44/1.62 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[5438, 5437])).
% 1.44/1.62 tff(5440,plain,
% 1.44/1.62 ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[5439, 297, 2511])).
% 1.44/1.62 tff(5441,plain,
% 1.44/1.62 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[5440, 5428])).
% 1.44/1.62 tff(5442,plain,
% 1.44/1.62 ((s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2728, 51, 5441])).
% 1.44/1.62 tff(5443,plain,
% 1.44/1.62 (b(s(s(s(elem!1))), s(s(z)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[5442, 2516])).
% 1.44/1.62 tff(5444,plain,
% 1.44/1.62 (b(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[5443, 5436])).
% 1.44/1.62 tff(5445,plain,
% 1.44/1.62 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[580, 5444, 5434, 5383, 5433, 5432, 5399])).
% 1.44/1.62 tff(5446,plain,
% 1.44/1.62 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[595, 5445, 5379])).
% 1.44/1.62 tff(5447,plain,
% 1.44/1.62 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[629, 5446, 5374])).
% 1.44/1.62 tff(5448,plain,
% 1.44/1.62 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[634, 5447, 5370])).
% 1.44/1.62 tff(5449,plain,
% 1.44/1.62 (b(s(z), s(s(s(s(elem!1)))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[5448, 5369])).
% 1.44/1.62 tff(5450,plain,
% 1.44/1.62 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(elem!1)))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[5407])).
% 1.44/1.62 tff(5451,plain,
% 1.44/1.62 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(z))))),
% 1.44/1.62 inference(symmetry,[status(thm)],[5450])).
% 1.44/1.62 tff(5452,plain,
% 1.44/1.62 (b(s(z), s(s(s(z))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[817, 5451])).
% 1.44/1.62 tff(5453,plain,
% 1.44/1.62 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[5406])).
% 1.44/1.62 tff(5454,plain,
% 1.44/1.62 (r(s(s(s(s(elem!1)))), s(s(elem!1))) <=> r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[5406])).
% 1.44/1.62 tff(5455,plain,
% 1.44/1.62 (r(s(s(s(s(elem!1)))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.44/1.62 inference(symmetry,[status(thm)],[5454])).
% 1.44/1.62 tff(5456,plain,
% 1.44/1.62 ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) <=> (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[5455])).
% 1.44/1.62 tff(5457,assumption,(r(s(s(s(s(elem!1)))), s(s(s(z))))), introduced(assumption)).
% 1.44/1.62 tff(5458,plain,
% 1.44/1.62 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(5459,plain,
% 1.44/1.62 (((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(5460,plain,
% 1.44/1.62 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[5459])).
% 1.44/1.62 tff(5461,plain,
% 1.44/1.62 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.44/1.62 inference(transitivity,[status(thm)],[5460, 5458])).
% 1.44/1.62 tff(5462,plain,
% 1.44/1.62 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(5463,plain,
% 1.44/1.62 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[5462, 5461])).
% 1.44/1.62 tff(5464,plain,
% 1.44/1.62 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[5463, 297, 5457, 3608])).
% 1.44/1.62 tff(5465,plain,
% 1.44/1.62 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[558, 51, 99, 5464])).
% 1.44/1.62 tff(5466,plain,
% 1.44/1.62 (~r(s(s(s(s(elem!1)))), z)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[3264, 297, 5457, 3503])).
% 1.44/1.62 tff(5467,plain,
% 1.44/1.62 (b(s(s(s(s(elem!1)))), z)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[3268, 51, 604, 5466])).
% 1.44/1.62 tff(5468,plain,
% 1.44/1.62 ((~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), z))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[5415, 297, 3608])).
% 1.44/1.62 tff(5469,plain,
% 1.44/1.62 (~r(s(s(s(elem!1))), z)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[5468, 3503])).
% 1.44/1.62 tff(5470,plain,
% 1.44/1.62 (b(s(s(s(elem!1))), z)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1077, 51, 160, 5469])).
% 1.44/1.62 tff(5471,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(5472,plain,
% 1.44/1.62 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(5473,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[5472])).
% 1.44/1.62 tff(5474,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.44/1.63 inference(transitivity,[status(thm)],[5473, 5471])).
% 1.44/1.63 tff(5475,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(5476,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[5475, 5474])).
% 1.44/1.63 tff(5477,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[5476, 319, 5470, 2706, 5467, 5465])).
% 1.44/1.63 tff(5478,plain,((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(z))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(5479,plain,
% 1.44/1.63 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[5478, 5434, 2706, 5412, 5410])).
% 1.44/1.63 tff(5480,plain,
% 1.44/1.63 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[5479, 5456])).
% 1.44/1.63 tff(5481,plain,
% 1.44/1.63 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[571, 5480, 5433])).
% 1.44/1.63 tff(5482,plain,
% 1.44/1.63 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[5481, 5453])).
% 1.44/1.63 tff(5483,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(5484,plain,
% 1.44/1.63 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1))))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(5485,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[5484])).
% 1.44/1.63 tff(5486,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.44/1.63 inference(transitivity,[status(thm)],[5485, 5483])).
% 1.44/1.63 tff(5487,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(5488,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[5487, 5486])).
% 1.44/1.63 tff(5489,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[5488, 319, 3138, 5482, 5452, 5449])).
% 1.44/1.63 tff(5490,plain,((s(elem!1) = s(s(elem!1))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~b(s(z), z)) | (~r(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | r(s(elem!1), s(s(z))) | (~b(s(s(z)), s(s(elem!1)))) | r(s(elem!1), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(5491,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[5490, 5356, 5329, 5328, 2142, 5321, 5147, 70, 2493, 817, 687, 5315])).
% 1.44/1.63 tff(5492,plain,(r(s(s(elem!1)), s(z)) | (s(elem!1) = s(s(elem!1))) | (~r(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | b(s(s(elem!1)), z) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(5493,plain,
% 1.44/1.63 (r(s(s(elem!1)), s(z))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[5492, 5137, 70, 68, 114, 5130, 71, 5062, 5060])).
% 1.44/1.63 tff(5494,plain,
% 1.44/1.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(5495,plain,
% 1.44/1.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(5496,plain,
% 1.44/1.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[5495, 5494])).
% 1.44/1.63 tff(5497,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[5496, 297, 5493, 5049, 5070])).
% 1.44/1.63 tff(5498,plain,(b(s(s(elem!1)), z) | (~r(z, s(s(elem!1)))) | r(s(s(z)), s(s(elem!1))) | (s(s(s(elem!1))) = s(s(elem!1))) | r(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(5499,plain,
% 1.44/1.63 (b(s(s(elem!1)), z)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[5498, 69, 57, 58, 59])).
% 1.44/1.63 tff(5500,plain,
% 1.44/1.63 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[4979, 2128, 2493, 57])).
% 1.44/1.63 tff(5501,plain,
% 1.44/1.63 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[571, 2370, 5500])).
% 1.44/1.63 tff(5502,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)],[2144])).
% 1.44/1.63 tff(5503,plain,
% 1.44/1.63 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.44/1.63 inference(transitivity,[status(thm)],[5502, 597])).
% 1.44/1.63 tff(5504,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(transitivity,[status(thm)],[5503, 598])).
% 1.44/1.63 tff(5505,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)],[5504])).
% 1.44/1.63 tff(5506,plain,
% 1.44/1.63 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[604, 5505])).
% 1.44/1.63 tff(5507,plain,
% 1.44/1.63 (elem!1 = z),
% 1.44/1.63 inference(symmetry,[status(thm)],[2144])).
% 1.44/1.63 tff(5508,plain,
% 1.44/1.63 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(elem!1))) = z)),
% 1.44/1.63 inference(monotonicity,[status(thm)],[5507])).
% 1.44/1.63 tff(5509,plain,
% 1.44/1.63 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 1.44/1.63 inference(symmetry,[status(thm)],[5508])).
% 1.44/1.63 tff(5510,plain,
% 1.44/1.63 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[5509])).
% 1.44/1.63 tff(5511,plain,
% 1.44/1.63 (~(s(s(s(elem!1))) = elem!1)),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[160, 5510])).
% 1.44/1.63 tff(5512,plain,
% 1.44/1.63 (~r(z, s(z))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2177, 2128, 57])).
% 1.44/1.63 tff(5513,plain,
% 1.44/1.63 (b(z, s(z))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1099, 5512])).
% 1.44/1.63 tff(5514,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(monotonicity,[status(thm)],[129])).
% 1.44/1.63 tff(5515,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(symmetry,[status(thm)],[5514])).
% 1.44/1.63 tff(5516,plain,
% 1.44/1.63 (~b(z, s(s(z)))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[879, 123, 35])).
% 1.44/1.63 tff(5517,plain,
% 1.44/1.63 (r(z, s(s(z)))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[729, 5516])).
% 1.44/1.63 tff(5518,plain,
% 1.44/1.63 (s(s(elem!1)) = s(s(z))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[5127, 123])).
% 1.44/1.63 tff(5519,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(5520,plain,
% 1.44/1.63 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(5521,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z)))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[5520])).
% 1.44/1.63 tff(5522,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))))),
% 1.44/1.63 inference(transitivity,[status(thm)],[5521, 5519])).
% 1.44/1.63 tff(5523,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(5524,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z)))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[5523, 5522])).
% 1.44/1.63 tff(5525,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[5524, 319, 2706, 817, 496, 2493])).
% 1.44/1.63 tff(5526,plain,((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(5527,plain,
% 1.44/1.63 (~b(s(z), s(s(elem!1)))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[5526, 5513, 496, 2493])).
% 1.44/1.63 tff(5528,plain,
% 1.44/1.63 (r(s(z), s(s(elem!1)))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1047, 5527])).
% 1.44/1.63 tff(5529,plain,
% 1.44/1.63 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(z)))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2518])).
% 1.44/1.63 tff(5530,plain,
% 1.44/1.63 (r(s(z), s(s(z))) <=> r(s(z), s(s(elem!1)))),
% 1.44/1.63 inference(symmetry,[status(thm)],[5529])).
% 1.44/1.63 tff(5531,plain,
% 1.44/1.63 ((~r(s(z), s(s(z)))) <=> (~r(s(z), s(s(elem!1))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[5530])).
% 1.44/1.63 tff(5532,assumption,(~r(s(z), s(s(z)))), introduced(assumption)).
% 1.44/1.63 tff(5533,plain,
% 1.44/1.63 (~r(s(z), s(s(elem!1)))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[5532, 5531])).
% 1.44/1.63 tff(5534,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[444, 5533])).
% 1.44/1.63 tff(5535,plain,((~(s(s(elem!1)) = s(s(z)))) | (~r(s(z), s(s(elem!1)))) | r(s(z), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(5536,plain,
% 1.44/1.63 (r(s(z), s(s(z)))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[5535, 5528, 5518])).
% 1.44/1.63 tff(5537,plain,
% 1.44/1.63 (b(s(z), z) <=> b(s(z), elem!1)),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2144])).
% 1.44/1.63 tff(5538,plain,
% 1.44/1.63 (b(s(z), elem!1)),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[2493, 5537])).
% 1.44/1.63 tff(5539,plain,
% 1.44/1.63 (~r(s(s(s(z))), s(s(z)))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[935, 5538, 5536, 5517])).
% 1.44/1.63 tff(5540,plain,
% 1.44/1.63 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[943, 5539, 123])).
% 1.44/1.63 tff(5541,plain,
% 1.44/1.63 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[348, 5540, 58])).
% 1.44/1.63 tff(5542,plain,
% 1.44/1.63 (b(s(s(s(z))), s(s(elem!1)))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[5541, 5515])).
% 1.44/1.63 tff(5543,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(z))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(5544,plain,
% 1.44/1.63 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(z))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(5545,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(z)))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[5544])).
% 1.44/1.63 tff(5546,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(z))))),
% 1.44/1.63 inference(transitivity,[status(thm)],[5545, 5543])).
% 1.44/1.63 tff(5547,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(5548,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(z)))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[5547, 5546])).
% 1.44/1.63 tff(5549,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[5548, 319, 2706, 496, 4230, 3585])).
% 1.44/1.63 tff(5550,plain,((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(5551,plain,
% 1.44/1.63 (~b(s(s(s(z))), z)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[5550, 5542, 496, 5513])).
% 1.44/1.63 tff(5552,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)],[187])).
% 1.44/1.63 tff(5553,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)],[5552])).
% 1.44/1.63 tff(5554,plain,
% 1.44/1.63 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.44/1.63 inference(monotonicity,[status(thm)],[937])).
% 1.44/1.63 tff(5555,plain,
% 1.44/1.63 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.44/1.63 inference(symmetry,[status(thm)],[5554])).
% 1.44/1.63 tff(5556,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)],[5555, 5553])).
% 1.44/1.63 tff(5557,plain,
% 1.44/1.63 (b(s(s(s(z))), z)),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[448, 5556])).
% 1.44/1.63 tff(5558,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[4582, 5557])).
% 1.44/1.63 tff(5559,plain,((~b(s(s(s(elem!1))), elem!1)) | b(s(s(s(z))), z) | (~(s(s(z)) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(5560,plain,
% 1.44/1.63 (~b(s(s(s(elem!1))), elem!1)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[5559, 5551, 123])).
% 1.44/1.63 tff(5561,plain,
% 1.44/1.63 (r(s(s(s(elem!1))), elem!1)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[361, 5560, 5511])).
% 1.44/1.63 tff(5562,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(monotonicity,[status(thm)],[130, 129])).
% 1.44/1.63 tff(5563,plain,
% 1.44/1.63 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[130, 129])).
% 1.44/1.63 tff(5564,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(symmetry,[status(thm)],[5563])).
% 1.44/1.63 tff(5565,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)],[5564])).
% 1.44/1.63 tff(5566,plain,
% 1.44/1.63 (b(s(s(elem!1)), elem!1)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[500, 2144, 496])).
% 1.44/1.63 tff(5567,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(5568,plain,
% 1.44/1.63 (((~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(s(s(elem!1)))), 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(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(5569,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1)))), 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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[5568])).
% 1.44/1.63 tff(5570,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1)))), 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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.44/1.63 inference(transitivity,[status(thm)],[5569, 5567])).
% 1.44/1.63 tff(5571,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1)))), 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))))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(5572,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[5571, 5570])).
% 1.44/1.63 tff(5573,plain,
% 1.44/1.63 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[5572, 319, 5566, 5541, 5501])).
% 1.44/1.63 tff(5574,plain,
% 1.44/1.63 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[5573, 5565])).
% 1.44/1.63 tff(5575,plain,
% 1.44/1.63 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2252, 5574])).
% 1.44/1.63 tff(5576,plain,
% 1.44/1.63 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[5575, 5562])).
% 1.44/1.63 tff(5577,plain,
% 1.44/1.63 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2259, 5576, 5561])).
% 1.44/1.63 tff(5578,plain,
% 1.44/1.63 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[616, 5577, 5506])).
% 1.44/1.63 tff(5579,plain,
% 1.44/1.63 (~(s(elem!1) = elem!1)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2159, 114])).
% 1.44/1.63 tff(5580,plain,
% 1.44/1.63 (~(elem!1 = s(elem!1))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2167, 5579])).
% 1.44/1.63 tff(5581,plain,
% 1.44/1.63 (~r(elem!1, s(elem!1))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[978, 123, 5512])).
% 1.44/1.63 tff(5582,plain,
% 1.44/1.63 (b(elem!1, s(elem!1))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[389, 5581, 5580])).
% 1.44/1.63 tff(5583,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(5584,plain,
% 1.44/1.63 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(5585,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[5584])).
% 1.44/1.64 tff(5586,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.44/1.64 inference(transitivity,[status(thm)],[5585, 5583])).
% 1.44/1.64 tff(5587,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(5588,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[5587, 5586])).
% 1.44/1.64 tff(5589,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[5588, 319, 5582, 5566, 5578, 5501])).
% 1.44/1.64 tff(5590,plain,(b(s(s(z)), s(s(elem!1))) | (~b(s(s(elem!1)), z)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(s(z), z)) | b(z, s(s(elem!1))) | r(s(s(z)), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(5591,plain,
% 1.44/1.64 (b(s(s(z)), s(s(elem!1)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[5590, 5499, 58, 68, 35, 69])).
% 1.44/1.64 tff(5592,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(elem!1))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(5593,plain,
% 1.44/1.64 (((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(elem!1))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(5594,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(elem!1)))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[5593])).
% 1.44/1.64 tff(5595,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(elem!1))))))),
% 1.44/1.64 inference(transitivity,[status(thm)],[5594, 5592])).
% 1.44/1.64 tff(5596,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(5597,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(elem!1)))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[5596, 5595])).
% 1.44/1.64 tff(5598,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[5597, 319, 1, 496, 3741, 2493])).
% 1.44/1.64 tff(5599,plain,((~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(5600,plain,
% 1.44/1.64 (~b(z, s(s(s(elem!1))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[5599, 1, 496, 2493])).
% 1.44/1.64 tff(5601,plain,
% 1.44/1.64 (r(z, s(s(s(elem!1))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[416, 5600])).
% 1.44/1.64 tff(5602,plain,
% 1.44/1.64 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[5058, 5601, 57])).
% 1.44/1.64 tff(5603,plain,
% 1.44/1.64 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[348, 5602, 58])).
% 1.44/1.64 tff(5604,plain,
% 1.44/1.64 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2674, 319, 1, 687, 5603])).
% 1.44/1.64 tff(5605,plain,
% 1.44/1.64 (r(s(s(z)), s(s(s(elem!1))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1571, 5604])).
% 1.44/1.64 tff(5606,plain,
% 1.44/1.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(5607,plain,
% 1.44/1.64 (((~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z))))) <=> ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(5608,plain,
% 1.44/1.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1)))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[5607])).
% 1.44/1.64 tff(5609,plain,
% 1.44/1.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))))),
% 1.44/1.64 inference(transitivity,[status(thm)],[5608, 5606])).
% 1.44/1.64 tff(5610,plain,
% 1.44/1.64 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(5611,plain,
% 1.44/1.64 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1)))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[5610, 5609])).
% 1.44/1.64 tff(5612,plain,
% 1.44/1.64 (~r(z, s(s(z)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[5611, 297, 5605, 5601])).
% 1.44/1.64 tff(5613,plain,
% 1.44/1.64 (b(z, s(s(z)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[729, 5612])).
% 1.44/1.64 tff(5614,plain,
% 1.44/1.64 (~(s(s(z)) = s(s(elem!1)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[879, 5613, 35])).
% 1.44/1.64 tff(5615,plain,
% 1.44/1.64 (~(s(elem!1) = s(z))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[774, 5614])).
% 1.44/1.64 tff(5616,plain,
% 1.44/1.64 (~(s(z) = s(elem!1))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2503, 5615])).
% 1.44/1.64 tff(5617,plain,
% 1.44/1.64 (~r(s(s(z)), s(z))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[4668, 5614, 5603, 58])).
% 1.44/1.64 tff(5618,plain,
% 1.44/1.64 (b(s(s(z)), s(z))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[4102, 5617])).
% 1.44/1.64 tff(5619,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[4931, 5618, 5616, 687, 57, 1, 114, 2493])).
% 1.44/1.64 tff(5620,plain,((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), z)) | (s(s(s(elem!1))) = s(s(elem!1))) | b(z, s(s(elem!1))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(5621,plain,
% 1.44/1.64 (~b(s(s(elem!1)), s(z))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[5620, 5591, 68, 58, 35, 5499])).
% 1.44/1.64 tff(5622,plain,
% 1.44/1.64 (r(s(s(elem!1)), s(z))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[871, 5621])).
% 1.44/1.64 tff(5623,plain,
% 1.44/1.64 (~r(z, s(z))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2177, 5622, 57])).
% 1.44/1.64 tff(5624,plain,
% 1.44/1.64 (b(z, s(z))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1099, 5623])).
% 1.44/1.64 tff(5625,plain,
% 1.44/1.64 (~b(s(z), s(s(elem!1)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[5526, 5624, 5499, 68])).
% 1.44/1.64 tff(5626,plain,
% 1.44/1.64 (r(s(z), s(s(elem!1)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1047, 5625])).
% 1.44/1.64 tff(5627,plain,
% 1.44/1.64 (~r(s(s(s(elem!1))), s(z))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[5135, 335, 444])).
% 1.44/1.64 tff(5628,plain,
% 1.44/1.64 (b(s(s(s(elem!1))), s(z))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[4750, 5627])).
% 1.44/1.64 tff(5629,plain,
% 1.44/1.64 (~r(z, s(s(s(elem!1))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[5058, 335, 70])).
% 1.44/1.64 tff(5630,plain,
% 1.44/1.64 (b(z, s(s(s(elem!1))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[416, 5629])).
% 1.44/1.64 tff(5631,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(5632,plain,
% 1.44/1.64 (((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(5633,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[5632])).
% 1.44/1.64 tff(5634,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.44/1.64 inference(transitivity,[status(thm)],[5633, 5631])).
% 1.44/1.64 tff(5635,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(5636,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[5635, 5634])).
% 1.44/1.64 tff(5637,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[5636, 319, 3882, 2706, 5630, 2493, 5628])).
% 1.44/1.64 tff(5638,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(5639,plain,
% 1.44/1.64 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[5638, 5624, 68, 57, 5626])).
% 1.44/1.64 tff(5640,plain,
% 1.44/1.64 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[348, 5639, 58])).
% 1.44/1.64 tff(5641,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(5642,plain,
% 1.44/1.64 (((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(5643,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[5642])).
% 1.44/1.64 tff(5644,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.44/1.64 inference(transitivity,[status(thm)],[5643, 5641])).
% 1.44/1.64 tff(5645,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(5646,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[5645, 5644])).
% 1.44/1.64 tff(5647,plain,
% 1.44/1.64 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[5646, 319, 687, 496, 116])).
% 1.44/1.64 tff(5648,plain,
% 1.44/1.64 ((s(s(s(elem!1))) = s(s(z))) | r(s(s(s(elem!1))), s(s(z)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2728, 51, 5647])).
% 1.44/1.64 tff(5649,plain,
% 1.44/1.64 (r(s(s(s(elem!1))), s(s(z)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[5648, 2516])).
% 1.44/1.64 tff(5650,plain,
% 1.44/1.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(5651,plain,
% 1.44/1.64 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(5652,plain,
% 1.44/1.64 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[5651, 5650])).
% 1.44/1.64 tff(5653,plain,
% 1.44/1.64 (~r(s(s(s(elem!1))), z)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[5652, 297, 732, 5649])).
% 1.44/1.64 tff(5654,plain,
% 1.44/1.64 (b(s(s(s(elem!1))), z)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1077, 51, 160, 5653])).
% 1.44/1.64 tff(5655,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(5656,plain,
% 1.44/1.64 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(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))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(5657,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[5656])).
% 1.44/1.64 tff(5658,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.44/1.64 inference(transitivity,[status(thm)],[5657, 5655])).
% 1.44/1.64 tff(5659,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(5660,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[5659, 5658])).
% 1.44/1.64 tff(5661,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[5660, 319, 5654, 2706, 496, 116])).
% 1.44/1.64 tff(5662,plain,((~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(5663,plain,
% 1.44/1.64 (~r(z, s(s(z)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[5662, 5640, 5499, 5591, 5624])).
% 1.44/1.64 tff(5664,plain,
% 1.44/1.64 (b(z, s(s(z)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[729, 5663])).
% 1.44/1.64 tff(5665,plain,
% 1.44/1.64 (~(s(s(z)) = s(s(elem!1)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[879, 5664, 35])).
% 1.44/1.64 tff(5666,plain,
% 1.44/1.64 (~r(s(s(z)), s(z))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[4668, 5665, 5640, 58])).
% 1.44/1.64 tff(5667,plain,
% 1.44/1.64 (b(s(s(z)), s(z))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[4102, 5666])).
% 1.44/1.64 tff(5668,plain,
% 1.44/1.64 (~b(s(s(s(elem!1))), s(z))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[4745, 5667, 68, 5624])).
% 1.44/1.64 tff(5669,plain,
% 1.44/1.64 (r(s(s(s(elem!1))), s(z))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[4750, 5668])).
% 1.44/1.64 tff(5670,plain,
% 1.44/1.64 (~b(s(z), s(s(z)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[4795, 5667, 5664, 5624])).
% 1.44/1.64 tff(5671,plain,
% 1.44/1.64 (r(s(z), s(s(z)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[685, 5670])).
% 1.44/1.64 tff(5672,plain,
% 1.44/1.64 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[4784, 5671, 5669])).
% 1.44/1.64 tff(5673,assumption,(~r(s(s(s(elem!1))), s(s(z)))), introduced(assumption)).
% 1.44/1.64 tff(5674,assumption,(~b(s(s(s(elem!1))), s(s(z)))), introduced(assumption)).
% 1.44/1.64 tff(5675,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2728, 51, 5674, 5673, 4996])).
% 1.44/1.64 tff(5676,plain,(b(s(s(s(elem!1))), s(s(z))) | r(s(s(s(elem!1))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(5677,plain,
% 1.44/1.64 (b(s(s(s(elem!1))), s(s(z)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[5676, 5672])).
% 1.44/1.64 tff(5678,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[5646, 319, 5677, 5591, 5499, 5640])).
% 1.44/1.64 tff(5679,plain,(r(s(s(z)), s(s(elem!1))) | (s(s(s(elem!1))) = s(s(elem!1))) | b(z, s(s(elem!1))) | r(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(5680,plain,
% 1.44/1.64 (r(s(s(z)), s(s(elem!1)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[5679, 59, 35, 58])).
% 1.44/1.64 tff(5681,plain,
% 1.44/1.64 (~r(s(z), z)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[865, 70, 444])).
% 1.44/1.64 tff(5682,plain,
% 1.44/1.64 (b(s(z), z)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[65, 51, 62, 5681])).
% 1.44/1.64 tff(5683,plain,
% 1.44/1.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(5684,plain,
% 1.44/1.64 (((~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(5685,plain,
% 1.44/1.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[5684])).
% 1.44/1.64 tff(5686,plain,
% 1.44/1.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.44/1.64 inference(transitivity,[status(thm)],[5685, 5683])).
% 1.44/1.64 tff(5687,plain,
% 1.44/1.64 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(5688,plain,
% 1.44/1.65 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[5687, 5686])).
% 1.44/1.65 tff(5689,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[5688, 297, 444, 2578, 903])).
% 1.44/1.65 tff(5690,plain,((~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(5691,plain,
% 1.44/1.65 (~r(s(z), s(s(z)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[5690, 444, 2578])).
% 1.44/1.65 tff(5692,plain,
% 1.44/1.65 (b(s(z), s(s(z)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[685, 5691])).
% 1.44/1.65 tff(5693,plain,
% 1.44/1.65 (~r(s(s(z)), s(z))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2583, 444, 2578])).
% 1.44/1.65 tff(5694,plain,
% 1.44/1.65 (b(s(s(z)), s(z))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[4102, 5693])).
% 1.44/1.65 tff(5695,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(5696,plain,
% 1.44/1.65 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(5697,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z))))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[5696])).
% 1.44/1.65 tff(5698,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[5697, 5695])).
% 1.44/1.65 tff(5699,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(5700,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[5699, 5698])).
% 1.44/1.65 tff(5701,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[5700, 319, 5694, 3925, 5692, 5682])).
% 1.44/1.65 tff(5702,plain,((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(5703,plain,
% 1.44/1.65 (~r(s(z), s(s(elem!1)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[5702, 5680, 57])).
% 1.44/1.65 tff(5704,plain,
% 1.44/1.65 (b(s(z), s(s(elem!1)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1047, 5703])).
% 1.44/1.65 tff(5705,plain,
% 1.44/1.65 (~r(z, s(s(z)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[3463, 5680, 57])).
% 1.44/1.65 tff(5706,plain,
% 1.44/1.65 (b(z, s(s(z)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[729, 5705])).
% 1.44/1.65 tff(5707,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(5708,plain,
% 1.44/1.65 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(5709,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1))))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[5708])).
% 1.44/1.65 tff(5710,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[5709, 5707])).
% 1.44/1.65 tff(5711,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(5712,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[5711, 5710])).
% 1.44/1.65 tff(5713,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[5712, 319, 711, 817, 496, 2493])).
% 1.44/1.65 tff(5714,plain,((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(5715,plain,
% 1.44/1.65 (~b(s(s(elem!1)), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[5714, 5706, 5704, 68])).
% 1.44/1.65 tff(5716,plain,
% 1.44/1.65 (r(s(s(elem!1)), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[75, 5715])).
% 1.44/1.65 tff(5717,plain,
% 1.44/1.65 (~r(s(s(z)), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[3526, 5716, 5680])).
% 1.44/1.65 tff(5718,plain,
% 1.44/1.65 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[3900, 5680, 57])).
% 1.44/1.65 tff(5719,plain,
% 1.44/1.65 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[348, 5718, 58])).
% 1.44/1.65 tff(5720,plain,
% 1.44/1.65 (~(s(s(z)) = s(s(elem!1)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[879, 5706, 35])).
% 1.44/1.65 tff(5721,plain,
% 1.44/1.65 (~r(s(s(z)), s(z))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[4668, 5720, 5719, 58])).
% 1.44/1.65 tff(5722,plain,
% 1.44/1.65 (b(s(s(z)), s(z))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[4102, 5721])).
% 1.44/1.65 tff(5723,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(5724,plain,
% 1.44/1.65 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(5725,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[5724])).
% 1.44/1.65 tff(5726,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.44/1.65 inference(transitivity,[status(thm)],[5725, 5723])).
% 1.44/1.65 tff(5727,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(5728,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[5727, 5726])).
% 1.44/1.65 tff(5729,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[5728, 319, 3390, 711, 3204, 2493])).
% 1.44/1.65 tff(5730,plain,((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(5731,plain,
% 1.44/1.65 (~b(s(s(z)), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[5730, 5722, 68, 5706])).
% 1.44/1.65 tff(5732,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[663, 51, 28, 5731, 5717])).
% 1.44/1.65 tff(5733,plain,(r(s(z), z) | (s(s(s(elem!1))) = s(s(elem!1))) | b(z, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(5734,plain,
% 1.44/1.65 (r(s(z), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[5733, 58, 35])).
% 1.44/1.65 tff(5735,plain,
% 1.44/1.65 (~r(s(z), s(s(elem!1)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[865, 5734, 57])).
% 1.44/1.65 tff(5736,plain,
% 1.44/1.65 (b(s(z), s(s(elem!1)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1047, 5735])).
% 1.44/1.65 tff(5737,plain,
% 1.44/1.65 (~r(s(s(z)), s(s(elem!1)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[3900, 335, 70])).
% 1.44/1.65 tff(5738,plain,
% 1.44/1.65 (r(s(s(elem!1)), s(z))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2127, 5737, 33])).
% 1.44/1.65 tff(5739,plain,
% 1.44/1.65 (s(s(z)) = s(s(elem!1))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[122, 5737, 33])).
% 1.44/1.65 tff(5740,plain,
% 1.44/1.65 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[5739])).
% 1.44/1.65 tff(5741,plain,
% 1.44/1.65 (s(z) = s(elem!1)),
% 1.44/1.65 inference(transitivity,[status(thm)],[127, 5740, 118])).
% 1.44/1.65 tff(5742,plain,
% 1.44/1.65 (b(s(z), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[5741])).
% 1.44/1.65 tff(5743,plain,
% 1.44/1.65 (b(s(elem!1), s(s(elem!1)))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[817, 5742])).
% 1.44/1.65 tff(5744,plain,
% 1.44/1.65 (b(s(elem!1), s(s(z))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[5739])).
% 1.44/1.65 tff(5745,plain,
% 1.44/1.65 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(z)))),
% 1.44/1.65 inference(symmetry,[status(thm)],[5744])).
% 1.44/1.65 tff(5746,plain,
% 1.44/1.65 (b(s(z), s(s(elem!1))) <=> b(s(elem!1), s(s(z)))),
% 1.44/1.65 inference(transitivity,[status(thm)],[5742, 5745])).
% 1.44/1.65 tff(5747,plain,
% 1.44/1.65 (b(s(elem!1), s(s(z)))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[817, 5746])).
% 1.44/1.65 tff(5748,plain,
% 1.44/1.65 (r(elem!1, s(s(elem!1)))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[70, 982])).
% 1.44/1.65 tff(5749,plain,
% 1.44/1.65 ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1183, 297, 335])).
% 1.44/1.65 tff(5750,plain,
% 1.44/1.65 (~r(s(s(s(elem!1))), elem!1)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[5749, 5748])).
% 1.44/1.65 tff(5751,plain,
% 1.44/1.65 (b(s(s(s(elem!1))), elem!1)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[361, 5750, 249])).
% 1.44/1.65 tff(5752,plain,
% 1.44/1.65 (~r(z, s(z))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2177, 2169, 70])).
% 1.44/1.65 tff(5753,plain,
% 1.44/1.65 (~r(elem!1, s(elem!1))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[978, 5752, 133])).
% 1.44/1.65 tff(5754,plain,
% 1.44/1.65 (b(elem!1, s(elem!1))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[389, 5753, 272])).
% 1.44/1.65 tff(5755,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(5756,plain,
% 1.44/1.65 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(5757,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[5756])).
% 1.44/1.65 tff(5758,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[5757, 5755])).
% 1.44/1.65 tff(5759,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(5760,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[5759, 5758])).
% 1.44/1.65 tff(5761,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[5760, 319, 275, 448, 996, 1187])).
% 1.44/1.65 tff(5762,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = elem!1) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(5763,plain,
% 1.44/1.65 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[5762, 5754, 5751, 99, 605, 335, 5748])).
% 1.44/1.65 tff(5764,plain,
% 1.44/1.65 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[571, 5763, 971])).
% 1.44/1.65 tff(5765,plain,
% 1.44/1.65 (~r(s(s(elem!1)), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[5107, 5754, 2169, 5751, 133, 335])).
% 1.44/1.65 tff(5766,plain,
% 1.44/1.65 (b(s(s(elem!1)), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[75, 5765])).
% 1.44/1.65 tff(5767,plain,
% 1.44/1.65 (b(s(s(elem!1)), elem!1)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[500, 5766, 187])).
% 1.44/1.65 tff(5768,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(5769,plain,
% 1.44/1.65 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(5770,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[5769])).
% 1.44/1.65 tff(5771,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[5770, 5768])).
% 1.44/1.65 tff(5772,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(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(5773,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[5772, 5771])).
% 1.44/1.65 tff(5774,plain,
% 1.44/1.65 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[5773, 319, 785, 5767, 5764])).
% 1.44/1.65 tff(5775,plain,
% 1.44/1.65 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[595, 5774, 587])).
% 1.44/1.65 tff(5776,plain,
% 1.44/1.65 (b(z, s(elem!1)) <=> b(elem!1, s(elem!1))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[187])).
% 1.44/1.65 tff(5777,plain,
% 1.44/1.65 (b(elem!1, s(elem!1)) <=> b(z, s(elem!1))),
% 1.44/1.65 inference(symmetry,[status(thm)],[5776])).
% 1.44/1.65 tff(5778,plain,
% 1.44/1.65 (b(z, s(elem!1))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[5754, 5777])).
% 1.44/1.65 tff(5779,plain,
% 1.44/1.65 (b(s(s(z)), z) <=> b(s(s(elem!1)), z)),
% 1.44/1.65 inference(monotonicity,[status(thm)],[133])).
% 1.44/1.65 tff(5780,plain,
% 1.44/1.65 (b(s(s(elem!1)), z) <=> b(s(s(z)), z)),
% 1.44/1.65 inference(symmetry,[status(thm)],[5779])).
% 1.44/1.65 tff(5781,plain,
% 1.44/1.65 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), z)),
% 1.44/1.65 inference(symmetry,[status(thm)],[280])).
% 1.44/1.65 tff(5782,plain,
% 1.44/1.65 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), z)),
% 1.44/1.65 inference(transitivity,[status(thm)],[5781, 5780])).
% 1.44/1.65 tff(5783,plain,
% 1.44/1.65 (b(s(s(z)), z)),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[5767, 5782])).
% 1.44/1.65 tff(5784,plain,
% 1.44/1.65 (~b(s(elem!1), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[4130, 5783, 3926, 5778])).
% 1.44/1.65 tff(5785,plain,
% 1.44/1.65 (~b(s(elem!1), elem!1)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1176, 5784, 187])).
% 1.44/1.65 tff(5786,plain,
% 1.44/1.65 (r(s(elem!1), elem!1)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[375, 5785, 194])).
% 1.44/1.65 tff(5787,plain,
% 1.44/1.65 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1168, 5786, 5775])).
% 1.44/1.65 tff(5788,plain,
% 1.44/1.65 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[616, 5787, 605])).
% 1.44/1.65 tff(5789,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[5588, 319, 5754, 5767, 5788, 5764])).
% 1.44/1.65 tff(5790,plain,((~r(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~(s(s(z)) = s(s(elem!1)))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(5791,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[5790, 5747, 5743, 70, 335, 99, 5739, 5738])).
% 1.44/1.65 tff(5792,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | b(s(s(z)), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(5793,plain,
% 1.44/1.65 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[5792, 33, 93, 5736, 57])).
% 1.44/1.65 tff(5794,plain,
% 1.44/1.65 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[348, 5793, 58])).
% 1.44/1.65 tff(5795,assumption,(s(z) = s(s(s(elem!1)))), introduced(assumption)).
% 1.44/1.65 tff(5796,plain,
% 1.44/1.65 (s(s(s(elem!1))) = s(z)),
% 1.44/1.65 inference(symmetry,[status(thm)],[5795])).
% 1.44/1.65 tff(5797,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[171, 5796])).
% 1.44/1.65 tff(5798,plain,(~(s(z) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(5799,plain,
% 1.44/1.65 (~b(s(s(s(elem!1))), s(z))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1084, 319, 872, 5736, 5794])).
% 1.44/1.65 tff(5800,plain,
% 1.44/1.65 (r(s(s(s(elem!1))), s(z))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[4750, 5799])).
% 1.44/1.65 tff(5801,plain,
% 1.44/1.65 (r(s(s(z)), s(s(elem!1)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2127, 180, 33])).
% 1.44/1.65 tff(5802,plain,
% 1.44/1.65 (~r(z, s(s(z)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[3463, 5801, 57])).
% 1.44/1.65 tff(5803,plain,
% 1.44/1.65 (b(z, s(s(z)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[729, 5802])).
% 1.44/1.65 tff(5804,plain,
% 1.44/1.65 (~(s(s(z)) = s(s(elem!1)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[879, 5803, 35])).
% 1.44/1.65 tff(5805,plain,
% 1.44/1.65 (~(s(elem!1) = s(z))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[774, 5804])).
% 1.44/1.65 tff(5806,plain,
% 1.44/1.65 (~(s(s(elem!1)) = s(s(z)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2521, 5804])).
% 1.44/1.66 tff(5807,plain,
% 1.44/1.66 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2509, 5804])).
% 1.44/1.66 tff(5808,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), 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(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), 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(s(elem!1))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(5809,plain,
% 1.44/1.66 (((~b(s(s(elem!1)), s(z))) | (~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(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(z), 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(s(elem!1))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(5810,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~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(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), 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(s(elem!1)))))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[5809])).
% 1.44/1.66 tff(5811,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~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(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), 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(s(elem!1))))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[5810, 5808])).
% 1.44/1.66 tff(5812,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~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(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(5813,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), 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(s(elem!1)))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[5812, 5811])).
% 1.44/1.66 tff(5814,plain,
% 1.44/1.66 (~b(s(z), s(s(s(elem!1))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[5813, 319, 872, 5736, 5794])).
% 1.44/1.66 tff(5815,plain,
% 1.44/1.66 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1)))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(5816,plain,
% 1.44/1.66 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1)))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(5817,plain,
% 1.44/1.66 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[5816, 5815])).
% 1.44/1.66 tff(5818,plain,
% 1.44/1.66 (r(s(z), s(s(s(elem!1))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[5817, 51, 5814, 5798])).
% 1.44/1.66 tff(5819,plain,
% 1.44/1.66 (~r(s(s(z)), s(z))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[4668, 5804, 5794, 58])).
% 1.44/1.66 tff(5820,plain,
% 1.44/1.66 (b(s(s(z)), s(z))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[4102, 5819])).
% 1.44/1.66 tff(5821,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(5822,plain,
% 1.44/1.66 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(5823,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(z, 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z)))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[5822])).
% 1.44/1.66 tff(5824,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(z, 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[5823, 5821])).
% 1.44/1.66 tff(5825,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(5826,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z)))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[5825, 5824])).
% 1.44/1.66 tff(5827,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[5826, 319, 3390, 711, 2706, 817])).
% 1.44/1.66 tff(5828,plain,((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(5829,plain,
% 1.44/1.66 (~b(z, s(z))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[5828, 5820, 5803, 5736])).
% 1.44/1.66 tff(5830,plain,
% 1.44/1.66 (r(z, s(z))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1099, 5829])).
% 1.44/1.66 tff(5831,plain,
% 1.44/1.66 (~r(s(s(s(elem!1))), z)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1103, 297, 917, 4776])).
% 1.44/1.66 tff(5832,plain,
% 1.44/1.66 (b(s(s(s(elem!1))), z)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1077, 51, 160, 5831])).
% 1.44/1.66 tff(5833,plain,
% 1.44/1.66 (~r(s(elem!1), s(s(elem!1)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[5314, 731, 70])).
% 1.44/1.66 tff(5834,plain,
% 1.44/1.66 (b(s(elem!1), s(s(elem!1)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[807, 5833, 2142])).
% 1.44/1.66 tff(5835,plain,
% 1.44/1.66 (~r(s(elem!1), s(z))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3982, 731, 917])).
% 1.44/1.66 tff(5836,plain,
% 1.44/1.66 (b(s(elem!1), s(z))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[783, 5835, 776])).
% 1.44/1.66 tff(5837,plain,
% 1.44/1.66 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(5838,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1), s(s(elem!1)))) | (~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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1))))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[5837])).
% 1.44/1.66 tff(5839,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1), s(s(elem!1)))) | (~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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[5838, 2568])).
% 1.44/1.66 tff(5840,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(5841,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[5840, 5839])).
% 1.44/1.66 tff(5842,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[5841, 319, 1, 5836, 5834, 817])).
% 1.44/1.66 tff(5843,plain,((~r(s(elem!1), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (s(elem!1) = s(z)) | (s(elem!1) = s(s(elem!1))) | (~r(z, s(z))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(5844,plain,
% 1.44/1.66 (~r(s(elem!1), z)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[5843, 917, 817, 776, 114, 1, 70])).
% 1.44/1.66 tff(5845,plain,
% 1.44/1.66 (b(s(elem!1), z)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2602, 5844])).
% 1.44/1.66 tff(5846,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(5847,plain,
% 1.44/1.66 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(5848,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[5847])).
% 1.44/1.66 tff(5849,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)))),
% 1.44/1.66 inference(transitivity,[status(thm)],[5848, 5846])).
% 1.44/1.66 tff(5850,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(5851,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[5850, 5849])).
% 1.44/1.66 tff(5852,plain,
% 1.44/1.66 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[5851, 319, 3884, 5845, 5832])).
% 1.44/1.66 tff(5853,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(5854,plain,
% 1.44/1.66 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(5855,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[5854])).
% 1.44/1.66 tff(5856,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)))),
% 1.44/1.66 inference(transitivity,[status(thm)],[5855, 5853])).
% 1.44/1.66 tff(5857,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(5858,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[5857, 5856])).
% 1.44/1.66 tff(5859,plain,
% 1.44/1.66 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[5858, 319, 3884, 5832, 3877])).
% 1.44/1.66 tff(5860,plain,
% 1.44/1.66 (r(s(s(s(elem!1))), s(s(z)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[5676, 5859])).
% 1.44/1.66 tff(5861,plain,
% 1.44/1.66 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z))))) <=> ((~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(5862,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(elem!1), z))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[5861])).
% 1.44/1.66 tff(5863,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)))),
% 1.44/1.66 inference(transitivity,[status(thm)],[5862, 4181])).
% 1.44/1.66 tff(5864,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z)))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(5865,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(elem!1), z))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[5864, 5863])).
% 1.44/1.66 tff(5866,plain,
% 1.44/1.66 (~b(s(elem!1), s(s(z)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[5865, 319, 3884, 5845, 3877])).
% 1.44/1.66 tff(5867,plain,
% 1.44/1.66 (~b(s(s(elem!1)), s(s(z)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[4000, 319, 1, 3390, 817])).
% 1.44/1.66 tff(5868,plain,
% 1.44/1.66 (~r(s(elem!1), s(s(z)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3361, 197, 2578])).
% 1.44/1.66 tff(5869,plain,
% 1.44/1.66 (s(elem!1) = s(s(z))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2529, 5868, 2512])).
% 1.44/1.66 tff(5870,plain,
% 1.44/1.66 (s(s(elem!1)) = s(s(s(z)))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[5869])).
% 1.44/1.66 tff(5871,plain,
% 1.44/1.66 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(s(z))), s(s(z)))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[5870])).
% 1.44/1.66 tff(5872,plain,
% 1.44/1.66 (b(s(s(s(z))), s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 1.44/1.66 inference(symmetry,[status(thm)],[5871])).
% 1.44/1.66 tff(5873,plain,
% 1.44/1.66 (b(s(s(s(z))), s(s(z)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[4433, 197, 2578, 58, 817, 5868, 2542, 776])).
% 1.44/1.66 tff(5874,plain,
% 1.44/1.66 (b(s(s(elem!1)), s(s(z)))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[5873, 5872])).
% 1.44/1.66 tff(5875,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[5325, 5874])).
% 1.44/1.66 tff(5876,plain,((~r(s(elem!1), s(s(elem!1)))) | b(s(s(elem!1)), s(s(z))) | b(s(elem!1), s(s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (s(s(elem!1)) = s(s(z))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(5877,plain,
% 1.44/1.66 (~r(s(elem!1), s(s(elem!1)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[5876, 5867, 5866, 2578, 58, 817, 2542, 776])).
% 1.44/1.66 tff(5878,plain,
% 1.44/1.66 (b(s(elem!1), s(s(elem!1)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[807, 5877, 114])).
% 1.44/1.66 tff(5879,plain,
% 1.44/1.66 (~b(s(elem!1), s(z))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[5841, 319, 1, 5878, 817])).
% 1.44/1.66 tff(5880,plain,
% 1.44/1.66 (b(s(elem!1), s(z)) <=> b(s(s(z)), s(z))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[2967])).
% 1.44/1.66 tff(5881,plain,
% 1.44/1.66 (b(s(s(z)), s(z)) <=> b(s(elem!1), s(z))),
% 1.44/1.66 inference(symmetry,[status(thm)],[5880])).
% 1.44/1.66 tff(5882,plain,
% 1.44/1.66 (b(s(elem!1), s(z))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[3390, 5881])).
% 1.44/1.66 tff(5883,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[778, 5882])).
% 1.44/1.66 tff(5884,plain,((~(s(elem!1) = s(s(z)))) | b(s(elem!1), s(z)) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(5885,plain,
% 1.44/1.66 (~(s(elem!1) = s(s(z)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[5884, 5879, 3390])).
% 1.44/1.66 tff(5886,plain,
% 1.44/1.66 (r(s(elem!1), s(s(z)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2529, 5885, 5866])).
% 1.44/1.66 tff(5887,plain,
% 1.44/1.66 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2820, 297, 5886, 5860])).
% 1.44/1.66 tff(5888,plain,
% 1.44/1.66 (s(elem!1) = s(s(s(elem!1)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[434, 5887, 5852])).
% 1.44/1.66 tff(5889,plain,
% 1.44/1.66 (b(z, s(elem!1)) <=> b(z, s(s(s(elem!1))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[5888])).
% 1.44/1.66 tff(5890,plain,
% 1.44/1.66 (b(z, s(s(s(elem!1)))) <=> b(z, s(elem!1))),
% 1.44/1.66 inference(symmetry,[status(thm)],[5889])).
% 1.44/1.66 tff(5891,plain,
% 1.44/1.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(5892,plain,
% 1.44/1.66 (((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(5893,plain,
% 1.44/1.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1)))))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[5892])).
% 1.44/1.66 tff(5894,plain,
% 1.44/1.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[5893, 5891])).
% 1.44/1.66 tff(5895,plain,
% 1.44/1.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(5896,plain,
% 1.44/1.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1)))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[5895, 5894])).
% 1.44/1.66 tff(5897,plain,
% 1.44/1.66 (~r(z, s(s(s(elem!1))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[5896, 297, 917, 4776])).
% 1.44/1.66 tff(5898,plain,
% 1.44/1.66 (b(z, s(s(s(elem!1))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[416, 5897])).
% 1.44/1.66 tff(5899,plain,
% 1.44/1.66 (b(z, s(elem!1))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[5898, 5890])).
% 1.44/1.66 tff(5900,plain,
% 1.44/1.66 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2827, 5888])).
% 1.44/1.66 tff(5901,plain,
% 1.44/1.66 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[5888])).
% 1.44/1.66 tff(5902,plain,
% 1.44/1.66 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(elem!1))),
% 1.44/1.66 inference(symmetry,[status(thm)],[5901])).
% 1.44/1.66 tff(5903,plain,
% 1.44/1.66 (r(s(s(elem!1)), s(s(z)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[5327, 5867, 2542])).
% 1.44/1.66 tff(5904,plain,
% 1.44/1.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(5905,plain,
% 1.44/1.67 (((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(elem!1)), 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(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(5906,plain,
% 1.44/1.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[5905])).
% 1.44/1.67 tff(5907,plain,
% 1.44/1.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[5906, 5904])).
% 1.44/1.67 tff(5908,plain,
% 1.44/1.67 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(5909,plain,
% 1.44/1.67 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[5908, 5907])).
% 1.44/1.67 tff(5910,plain,
% 1.44/1.67 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[5909, 297, 5903, 5860])).
% 1.44/1.67 tff(5911,plain,
% 1.44/1.67 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2222, 51, 5910, 81])).
% 1.44/1.67 tff(5912,plain,
% 1.44/1.67 (b(s(s(elem!1)), s(elem!1))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[5911, 5902])).
% 1.44/1.67 tff(5913,plain,
% 1.44/1.67 (~b(s(s(s(z))), s(elem!1))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[4867, 5912, 115, 5845, 5900, 5899])).
% 1.44/1.67 tff(5914,plain,
% 1.44/1.67 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[4874, 5913, 5888])).
% 1.44/1.67 tff(5915,plain,
% 1.44/1.67 (r(s(s(s(z))), s(s(s(elem!1))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3794, 5914, 3739])).
% 1.44/1.67 tff(5916,plain,
% 1.44/1.67 (~r(s(s(s(z))), s(z))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[4886, 5915, 4877])).
% 1.44/1.67 tff(5917,plain,
% 1.44/1.67 (b(s(s(s(z))), s(z))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[4549, 5916])).
% 1.44/1.67 tff(5918,plain,
% 1.44/1.67 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3898, 319, 3884, 5832, 3877])).
% 1.44/1.67 tff(5919,plain,
% 1.44/1.67 (r(s(s(z)), s(s(s(elem!1))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1571, 5918])).
% 1.44/1.67 tff(5920,plain,
% 1.44/1.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(5921,plain,
% 1.44/1.67 (((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(5922,plain,
% 1.44/1.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1)))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[5921])).
% 1.44/1.67 tff(5923,plain,
% 1.44/1.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[5922, 5920])).
% 1.44/1.67 tff(5924,plain,
% 1.44/1.67 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(5925,plain,
% 1.44/1.67 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[5924, 5923])).
% 1.44/1.67 tff(5926,plain,
% 1.44/1.67 (~r(s(s(s(z))), s(s(z)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[5925, 297, 5919, 5915])).
% 1.44/1.67 tff(5927,plain,
% 1.44/1.67 (b(s(s(s(z))), s(s(z)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2920, 5926])).
% 1.44/1.67 tff(5928,plain,
% 1.44/1.67 (~r(s(z), s(s(z)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[4784, 5860, 4776])).
% 1.44/1.67 tff(5929,plain,
% 1.44/1.67 (b(s(z), s(s(z)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[685, 5928])).
% 1.44/1.67 tff(5930,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(5931,plain,
% 1.44/1.67 (((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(5932,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z)))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[5931])).
% 1.44/1.67 tff(5933,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[5932, 5930])).
% 1.44/1.67 tff(5934,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(5935,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z)))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[5934, 5933])).
% 1.44/1.67 tff(5936,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[5935, 319, 1, 3390, 817, 5929, 5927, 5917])).
% 1.44/1.67 tff(5937,plain,((~r(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (s(s(elem!1)) = s(s(z))) | (s(elem!1) = s(z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(5938,plain,
% 1.44/1.67 (~r(s(s(elem!1)), z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[5937, 5830, 5820, 5736, 5818, 5807, 872, 5801, 58, 5806, 5805, 57, 5800])).
% 1.44/1.67 tff(5939,plain,
% 1.44/1.67 (b(s(s(elem!1)), z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[75, 5938])).
% 1.44/1.67 tff(5940,plain,
% 1.44/1.67 (~r(s(s(s(elem!1))), z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1103, 297, 5830, 5800])).
% 1.44/1.67 tff(5941,plain,
% 1.44/1.67 (b(s(s(s(elem!1))), z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1077, 51, 160, 5940])).
% 1.44/1.67 tff(5942,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(5943,plain,
% 1.44/1.67 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(5944,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[5943])).
% 1.44/1.67 tff(5945,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[5944, 5942])).
% 1.44/1.67 tff(5946,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(5947,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[5946, 5945])).
% 1.44/1.67 tff(5948,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[5947, 319, 5803, 5941, 5939, 5794])).
% 1.44/1.67 tff(5949,plain,(r(s(s(elem!1)), s(z)) | (s(s(s(elem!1))) = s(s(elem!1))) | b(z, s(s(elem!1))) | b(s(s(z)), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(5950,plain,
% 1.44/1.67 (r(s(s(elem!1)), s(z))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[5949, 33, 35, 58])).
% 1.44/1.67 tff(5951,plain,
% 1.44/1.67 (~r(s(s(elem!1)), z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[5094, 5950, 5734])).
% 1.44/1.67 tff(5952,plain,
% 1.44/1.67 (b(s(s(elem!1)), z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[75, 5951])).
% 1.44/1.67 tff(5953,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(5954,plain,
% 1.44/1.67 (((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(5955,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[5954])).
% 1.44/1.67 tff(5956,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[5955, 5953])).
% 1.44/1.67 tff(5957,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(5958,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[5957, 5956])).
% 1.44/1.67 tff(5959,plain,
% 1.44/1.67 (~b(s(z), s(s(s(elem!1))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[5958, 319, 5736, 5952, 5794])).
% 1.44/1.67 tff(5960,plain,
% 1.44/1.67 (r(s(z), s(s(s(elem!1))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[5817, 51, 5959, 5798])).
% 1.44/1.67 tff(5961,plain,
% 1.44/1.67 (~r(z, s(z))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2177, 5950, 57])).
% 1.44/1.67 tff(5962,plain,
% 1.44/1.67 (b(z, s(z))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1099, 5961])).
% 1.44/1.67 tff(5963,plain,
% 1.44/1.67 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[133])).
% 1.44/1.67 tff(5964,plain,
% 1.44/1.67 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[937, 133])).
% 1.44/1.67 tff(5965,plain,
% 1.44/1.67 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(z)))),
% 1.44/1.67 inference(symmetry,[status(thm)],[5964])).
% 1.44/1.67 tff(5966,plain,
% 1.44/1.67 (b(s(s(s(z))), s(s(z)))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[116, 5965])).
% 1.44/1.67 tff(5967,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2915, 5966])).
% 1.44/1.67 tff(5968,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | b(s(s(s(z))), s(s(z))) | (~(s(s(z)) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(5969,plain,
% 1.44/1.67 (b(s(s(s(z))), s(s(z)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[5968, 133, 116])).
% 1.44/1.67 tff(5970,plain,
% 1.44/1.67 (b(s(s(s(z))), s(s(elem!1)))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[5969, 5963])).
% 1.44/1.67 tff(5971,plain,
% 1.44/1.67 (~b(s(s(s(z))), z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[5550, 5970, 496, 2706])).
% 1.44/1.67 tff(5972,plain,
% 1.44/1.67 (r(s(z), s(s(s(z)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[135, 937])).
% 1.44/1.67 tff(5973,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(symmetry,[status(thm)],[5972])).
% 1.44/1.67 tff(5974,plain,
% 1.44/1.67 (r(s(z), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[135])).
% 1.44/1.67 tff(5975,plain,
% 1.44/1.67 (r(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[4877, 5974])).
% 1.44/1.67 tff(5976,plain,
% 1.44/1.67 (r(s(z), s(s(s(z))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[5975, 5973])).
% 1.44/1.67 tff(5977,assumption,(r(s(z), s(s(s(z))))), introduced(assumption)).
% 1.44/1.67 tff(5978,assumption,(r(s(s(s(z))), z)), introduced(assumption)).
% 1.44/1.67 tff(5979,plain,
% 1.44/1.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(5980,plain,
% 1.44/1.67 (((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(5981,plain,
% 1.44/1.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[5980])).
% 1.44/1.67 tff(5982,plain,
% 1.44/1.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[5981, 5979])).
% 1.44/1.67 tff(5983,plain,
% 1.44/1.67 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(5984,plain,
% 1.44/1.67 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[5983, 5982])).
% 1.44/1.67 tff(5985,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[5984, 297, 666, 5978, 5977])).
% 1.44/1.67 tff(5986,plain,((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(5987,plain,
% 1.44/1.67 (~r(s(s(s(z))), z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[5986, 5976, 666])).
% 1.44/1.67 tff(5988,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[4584, 5987, 5971])).
% 1.44/1.67 tff(5989,plain,((~(s(s(z)) = s(s(elem!1)))) | (~r(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(5990,plain,
% 1.44/1.67 (~(s(s(z)) = s(s(elem!1)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[5989, 5952, 5734, 5962, 5960, 5794])).
% 1.44/1.67 tff(5991,plain,
% 1.44/1.67 (r(s(s(z)), s(s(elem!1)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[122, 5990, 33])).
% 1.44/1.67 tff(5992,plain,
% 1.44/1.67 (~r(z, s(s(z)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3463, 5991, 57])).
% 1.44/1.67 tff(5993,plain,
% 1.44/1.67 (~r(s(s(z)), s(z))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[4668, 5990, 5794, 58])).
% 1.44/1.67 tff(5994,plain,
% 1.44/1.67 (b(s(s(z)), s(z))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[4102, 5993])).
% 1.44/1.67 tff(5995,plain,
% 1.44/1.67 (~b(z, s(s(z)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[5828, 5994, 5962, 5736])).
% 1.44/1.67 tff(5996,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[729, 5995, 5992])).
% 1.44/1.67 tff(5997,plain,(b(s(s(z)), s(s(elem!1))) | (s(s(s(elem!1))) = s(s(elem!1))) | b(z, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(5998,plain,
% 1.44/1.67 (b(s(s(z)), s(s(elem!1)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[5997, 58, 35])).
% 1.44/1.67 tff(5999,plain,
% 1.44/1.67 (~r(s(z), s(s(elem!1)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[865, 666, 70])).
% 1.44/1.67 tff(6000,plain,
% 1.44/1.67 (b(s(z), s(s(elem!1)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1047, 5999])).
% 1.44/1.67 tff(6001,plain,
% 1.44/1.67 (~b(s(z), s(s(z)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[5317, 1, 6000, 687])).
% 1.44/1.67 tff(6002,plain,
% 1.44/1.67 (r(s(z), s(s(z)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[685, 6001])).
% 1.44/1.67 tff(6003,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[839, 297, 666, 903, 732])).
% 1.44/1.67 tff(6004,plain,((~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(6005,plain,
% 1.44/1.67 (~r(z, s(s(z)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[6004, 6002, 666])).
% 1.44/1.67 tff(6006,plain,
% 1.44/1.67 (b(z, s(s(z)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[729, 6005])).
% 1.44/1.67 tff(6007,plain,
% 1.44/1.67 (r(elem!1, s(elem!1)) <=> r(s(z), s(s(z)))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[2969, 2967])).
% 1.44/1.67 tff(6008,plain,
% 1.44/1.67 (r(s(z), s(s(z))) <=> r(elem!1, s(elem!1))),
% 1.44/1.67 inference(symmetry,[status(thm)],[6007])).
% 1.44/1.67 tff(6009,plain,
% 1.44/1.67 (~b(s(z), s(s(z)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[5317, 1, 817, 687])).
% 1.44/1.67 tff(6010,plain,
% 1.44/1.67 (r(s(z), s(s(z)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[685, 6009])).
% 1.44/1.67 tff(6011,plain,
% 1.44/1.67 (r(elem!1, s(elem!1))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[6010, 6008])).
% 1.44/1.67 tff(6012,plain,
% 1.44/1.67 (r(s(s(s(s(elem!1)))), s(elem!1)) <=> r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[2967])).
% 1.44/1.67 tff(6013,plain,
% 1.44/1.67 (r(s(s(s(s(elem!1)))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.44/1.67 inference(symmetry,[status(thm)],[6012])).
% 1.44/1.67 tff(6014,plain,
% 1.44/1.67 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[2971])).
% 1.44/1.67 tff(6015,plain,
% 1.44/1.67 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.44/1.67 inference(symmetry,[status(thm)],[6014])).
% 1.44/1.67 tff(6016,plain,
% 1.44/1.67 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[6015, 2979])).
% 1.44/1.67 tff(6017,plain,
% 1.44/1.67 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[6016, 1324])).
% 1.44/1.67 tff(6018,plain,
% 1.44/1.67 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.44/1.67 inference(symmetry,[status(thm)],[6017])).
% 1.44/1.67 tff(6019,plain,
% 1.44/1.67 ((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(s(z))))) = s(s(s(s(z))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[6018])).
% 1.44/1.67 tff(6020,plain,
% 1.44/1.67 (~(s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[99, 6019])).
% 1.44/1.67 tff(6021,plain,
% 1.44/1.67 (r(s(s(s(s(s(z))))), z) <=> r(s(s(s(s(elem!1)))), z)),
% 1.44/1.67 inference(monotonicity,[status(thm)],[6015])).
% 1.44/1.68 tff(6022,plain,
% 1.44/1.68 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(s(s(s(z))))), z)),
% 1.44/1.68 inference(symmetry,[status(thm)],[6021])).
% 1.44/1.68 tff(6023,plain,
% 1.44/1.68 ((~r(s(s(s(s(elem!1)))), z)) <=> (~r(s(s(s(s(s(z))))), z))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[6022])).
% 1.44/1.68 tff(6024,plain,
% 1.44/1.68 (~r(s(s(s(s(s(z))))), z)),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[4944, 6023])).
% 1.44/1.68 tff(6025,plain,
% 1.44/1.68 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(z))))) = z))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(6026,plain,
% 1.44/1.68 (~(s(s(s(s(s(z))))) = z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[6025, 26])).
% 1.44/1.68 tff(6027,plain,
% 1.44/1.68 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = z) | b(s(s(s(s(s(z))))), z) | r(s(s(s(s(s(z))))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = z) | b(s(s(s(s(s(z))))), z) | r(s(s(s(s(s(z))))), z))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(6028,plain,
% 1.44/1.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = z) | b(s(s(s(s(s(z))))), z) | r(s(s(s(s(s(z))))), z))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(6029,plain,
% 1.44/1.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = z) | b(s(s(s(s(s(z))))), z) | r(s(s(s(s(s(z))))), z)),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[6028, 6027])).
% 1.44/1.68 tff(6030,plain,
% 1.44/1.68 (b(s(s(s(s(s(z))))), z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[6029, 51, 6026, 6024])).
% 1.44/1.68 tff(6031,plain,
% 1.44/1.68 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(z)))), z)),
% 1.44/1.68 inference(monotonicity,[status(thm)],[2971])).
% 1.44/1.68 tff(6032,plain,
% 1.44/1.68 (b(s(s(s(s(z)))), z)),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[3882, 6031])).
% 1.44/1.68 tff(6033,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(6034,plain,
% 1.44/1.68 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(6035,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[6034])).
% 1.44/1.68 tff(6036,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.44/1.68 inference(transitivity,[status(thm)],[6035, 6033])).
% 1.44/1.68 tff(6037,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(6038,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[6037, 6036])).
% 1.44/1.68 tff(6039,plain,
% 1.44/1.68 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[6038, 319, 711, 6032, 6030])).
% 1.44/1.68 tff(6040,plain,
% 1.44/1.68 (r(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[6015, 2979])).
% 1.44/1.68 tff(6041,plain,
% 1.44/1.68 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.44/1.68 inference(symmetry,[status(thm)],[6040])).
% 1.44/1.68 tff(6042,plain,
% 1.44/1.68 ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[6041])).
% 1.44/1.68 tff(6043,plain,
% 1.44/1.68 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1340, 984, 335])).
% 1.44/1.68 tff(6044,plain,
% 1.44/1.68 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[6043, 6042])).
% 1.44/1.68 tff(6045,plain,
% 1.44/1.68 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(6046,plain,
% 1.44/1.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(6047,plain,
% 1.44/1.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[6046, 6045])).
% 1.44/1.68 tff(6048,plain,
% 1.44/1.68 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[6047, 51, 6044])).
% 1.44/1.68 tff(6049,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[6048, 6039, 6020])).
% 1.44/1.68 tff(6050,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(z)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~(s(elem!1) = s(s(z)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(6051,plain,
% 1.44/1.68 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[6050, 2967, 99, 711, 335, 70])).
% 1.44/1.68 tff(6052,plain,
% 1.44/1.68 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[4681, 3121])).
% 1.44/1.68 tff(6053,plain,
% 1.44/1.68 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[571, 6052, 6051])).
% 1.44/1.68 tff(6054,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(6055,plain,
% 1.44/1.68 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(6056,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z))))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[6055])).
% 1.44/1.68 tff(6057,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[6056, 6054])).
% 1.44/1.68 tff(6058,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(6059,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[6058, 6057])).
% 1.44/1.68 tff(6060,plain,
% 1.44/1.68 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[6059, 319, 1, 687, 6053])).
% 1.44/1.68 tff(6061,plain,
% 1.44/1.68 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[4991, 51, 2140, 6060])).
% 1.44/1.68 tff(6062,plain,
% 1.44/1.68 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[6061, 6013])).
% 1.44/1.68 tff(6063,plain,
% 1.44/1.68 (r(elem!1, s(s(s(s(elem!1))))) <=> r(s(z), s(s(s(s(elem!1)))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[2969])).
% 1.44/1.68 tff(6064,plain,
% 1.44/1.68 (r(s(z), s(s(s(s(elem!1))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 1.44/1.68 inference(symmetry,[status(thm)],[6063])).
% 1.44/1.68 tff(6065,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(6066,plain,
% 1.44/1.68 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1))))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(6067,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[6066])).
% 1.44/1.68 tff(6068,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[6067, 6065])).
% 1.44/1.68 tff(6069,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(6070,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[6069, 6068])).
% 1.44/1.68 tff(6071,plain,
% 1.44/1.68 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[6070, 319, 1, 817, 6053])).
% 1.44/1.68 tff(6072,plain,
% 1.44/1.68 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(elem!1))))) | b(s(z), s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(elem!1))))) | b(s(z), s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(6073,plain,
% 1.44/1.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(elem!1))))) | b(s(z), s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1))))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(6074,plain,
% 1.44/1.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(elem!1))))) | b(s(z), s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1)))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[6073, 6072])).
% 1.44/1.68 tff(6075,plain,
% 1.44/1.68 (r(s(z), s(s(s(s(elem!1)))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[6074, 51, 2212, 6071])).
% 1.44/1.68 tff(6076,plain,
% 1.44/1.68 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[6075, 6064])).
% 1.44/1.68 tff(6077,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[629, 6076, 6062, 6011])).
% 1.44/1.68 tff(6078,plain,((~(s(elem!1) = s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(6079,plain,
% 1.44/1.68 (~(s(elem!1) = s(s(z)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[6078, 1, 6000, 687, 99, 6006, 335, 70])).
% 1.44/1.68 tff(6080,plain,
% 1.44/1.68 (~b(s(elem!1), s(s(elem!1)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2656, 6079, 687, 1, 136, 6002])).
% 1.44/1.68 tff(6081,plain,
% 1.44/1.68 (r(s(elem!1), s(s(elem!1)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[807, 6080, 2142])).
% 1.44/1.68 tff(6082,plain,
% 1.44/1.68 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[343, 6081, 335])).
% 1.44/1.68 tff(6083,plain,
% 1.44/1.68 (~r(s(s(z)), z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[708, 1, 666, 687])).
% 1.44/1.68 tff(6084,plain,
% 1.44/1.68 (~(s(elem!1) = s(s(z)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3179, 731, 3176])).
% 1.44/1.68 tff(6085,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2656, 5834, 6084, 687, 1, 136, 903])).
% 1.44/1.68 tff(6086,plain,((~r(s(elem!1), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (s(z) = s(elem!1)) | (~r(s(z), s(s(z)))) | (s(elem!1) = s(s(elem!1))) | r(s(s(z)), z) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(6087,plain,
% 1.44/1.68 (~r(s(elem!1), z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[6086, 1, 687, 136, 6002, 2142, 6083, 70])).
% 1.44/1.68 tff(6088,plain,
% 1.44/1.68 (b(s(elem!1), z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2602, 6087])).
% 1.44/1.68 tff(6089,plain,
% 1.44/1.68 (~r(z, s(elem!1))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[4120, 6081, 70])).
% 1.44/1.68 tff(6090,plain,
% 1.44/1.68 (b(z, s(elem!1))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[4804, 6089])).
% 1.44/1.68 tff(6091,plain,
% 1.44/1.68 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[5278, 319, 6090, 6088, 3882])).
% 1.44/1.68 tff(6092,plain,
% 1.44/1.68 (s(elem!1) = s(s(s(elem!1)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[434, 6091, 6082])).
% 1.44/1.68 tff(6093,plain,
% 1.44/1.68 ((s(s(s(z))) = s(elem!1)) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[6092])).
% 1.44/1.68 tff(6094,plain,
% 1.44/1.68 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(elem!1))),
% 1.44/1.68 inference(symmetry,[status(thm)],[6093])).
% 1.44/1.68 tff(6095,plain,
% 1.44/1.68 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[6094])).
% 1.44/1.68 tff(6096,plain,
% 1.44/1.68 (~(s(s(s(z))) = s(elem!1))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[3739, 6095])).
% 1.44/1.68 tff(6097,assumption,(s(s(elem!1)) = s(s(s(s(z))))), introduced(assumption)).
% 1.44/1.68 tff(6098,plain,
% 1.44/1.68 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.44/1.68 inference(symmetry,[status(thm)],[6097])).
% 1.44/1.68 tff(6099,plain,
% 1.44/1.68 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[6098])).
% 1.44/1.68 tff(6100,plain,
% 1.44/1.68 (s(s(s(z))) = s(elem!1)),
% 1.44/1.68 inference(transitivity,[status(thm)],[2297, 6099, 118])).
% 1.44/1.68 tff(6101,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[4479, 6100])).
% 1.44/1.68 tff(6102,plain,((~(s(s(elem!1)) = s(s(s(s(z)))))) | (s(s(s(z))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(6103,plain,
% 1.44/1.68 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[6102, 6096])).
% 1.44/1.68 tff(6104,plain,
% 1.44/1.68 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[343, 197, 335])).
% 1.44/1.68 tff(6105,plain,
% 1.44/1.68 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[5851, 319, 6006, 786, 3882])).
% 1.44/1.68 tff(6106,plain,
% 1.44/1.68 (s(elem!1) = s(s(s(elem!1)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[434, 6105, 6104])).
% 1.44/1.68 tff(6107,plain,
% 1.44/1.68 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[267])).
% 1.44/1.68 tff(6108,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[560, 6107])).
% 1.44/1.68 tff(6109,plain,((~(s(elem!1) = s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(6110,plain,
% 1.44/1.68 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[6109, 6106])).
% 1.44/1.68 tff(6111,plain,
% 1.44/1.68 (elem!1 = s(s(s(s(elem!1))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[4681, 6110])).
% 1.44/1.68 tff(6112,plain,
% 1.44/1.68 (s(s(s(s(elem!1)))) = elem!1),
% 1.44/1.68 inference(symmetry,[status(thm)],[6111])).
% 1.44/1.68 tff(6113,plain,
% 1.44/1.68 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 1.44/1.68 inference(symmetry,[status(thm)],[6110])).
% 1.44/1.68 tff(6114,plain,
% 1.44/1.68 (s(s(elem!1)) = elem!1),
% 1.44/1.68 inference(transitivity,[status(thm)],[6113, 6112])).
% 1.44/1.68 tff(6115,plain,
% 1.44/1.68 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), elem!1)),
% 1.44/1.68 inference(monotonicity,[status(thm)],[6114])).
% 1.44/1.68 tff(6116,plain,
% 1.44/1.68 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.44/1.68 inference(symmetry,[status(thm)],[6115])).
% 1.44/1.68 tff(6117,plain,
% 1.44/1.68 ((s(s(s(s(z)))) = elem!1) <=> (elem!1 = s(s(s(s(z)))))),
% 1.44/1.68 inference(commutativity,[status(thm)],[])).
% 1.44/1.68 tff(6118,plain,
% 1.44/1.68 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.44/1.68 inference(symmetry,[status(thm)],[6117])).
% 1.44/1.68 tff(6119,plain,
% 1.44/1.68 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.44/1.68 inference(monotonicity,[status(thm)],[6114])).
% 1.44/1.68 tff(6120,plain,
% 1.44/1.68 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (elem!1 = s(s(s(s(z)))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[6119, 6117])).
% 1.44/1.68 tff(6121,plain,
% 1.44/1.68 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 1.44/1.68 inference(commutativity,[status(thm)],[])).
% 1.44/1.68 tff(6122,plain,
% 1.44/1.68 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.44/1.68 inference(transitivity,[status(thm)],[6121, 6120, 6118])).
% 1.44/1.68 tff(6123,plain,
% 1.44/1.68 ((~(s(s(elem!1)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[6122])).
% 1.44/1.68 tff(6124,plain,
% 1.44/1.68 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(elem!1)))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[6110])).
% 1.44/1.68 tff(6125,plain,
% 1.44/1.68 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 1.44/1.68 inference(symmetry,[status(thm)],[6124])).
% 1.44/1.68 tff(6126,plain,
% 1.44/1.68 (s(elem!1) = s(s(s(elem!1)))),
% 1.44/1.68 inference(transitivity,[status(thm)],[206, 6125, 88])).
% 1.44/1.68 tff(6127,plain,
% 1.44/1.68 ((s(s(s(z))) = s(elem!1)) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[6126])).
% 1.44/1.68 tff(6128,plain,
% 1.44/1.68 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(elem!1))),
% 1.44/1.68 inference(symmetry,[status(thm)],[6127])).
% 1.44/1.68 tff(6129,plain,
% 1.44/1.68 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[6128])).
% 1.44/1.68 tff(6130,plain,
% 1.44/1.68 (~(s(s(s(z))) = s(elem!1))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[3739, 6129])).
% 1.44/1.68 tff(6131,plain,
% 1.44/1.68 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[6102, 6130])).
% 1.44/1.68 tff(6132,plain,
% 1.44/1.68 (~(s(s(s(s(z)))) = elem!1)),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[6131, 6123])).
% 1.44/1.68 tff(6133,plain,
% 1.44/1.68 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), elem!1)),
% 1.44/1.68 inference(monotonicity,[status(thm)],[6114])).
% 1.44/1.68 tff(6134,plain,
% 1.44/1.68 ((~b(s(s(s(s(z)))), s(s(elem!1)))) <=> (~b(s(s(s(s(z)))), elem!1))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[6133])).
% 1.44/1.68 tff(6135,plain,
% 1.44/1.68 (~b(s(s(z)), s(z))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[5145, 319, 1, 687, 6000])).
% 1.44/1.68 tff(6136,plain,
% 1.44/1.68 (r(s(s(z)), s(z))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[4102, 6135])).
% 1.44/1.68 tff(6137,assumption,(~(s(s(elem!1)) = s(s(s(s(z)))))), introduced(assumption)).
% 1.44/1.68 tff(6138,plain,
% 1.44/1.68 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2475, 2467, 115])).
% 1.44/1.68 tff(6139,plain,
% 1.44/1.68 (((~![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))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(6140,plain,
% 1.44/1.68 ((~![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))))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(6141,plain,
% 1.44/1.68 ((~![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)))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[6140, 6139])).
% 1.44/1.68 tff(6142,plain,
% 1.44/1.68 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[6141, 51, 6138, 6137])).
% 1.44/1.68 tff(6143,plain,
% 1.44/1.68 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(6144,plain,
% 1.44/1.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(6145,plain,
% 1.44/1.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[6144, 6143])).
% 1.44/1.68 tff(6146,plain,
% 1.44/1.68 (~r(s(s(s(s(z)))), s(z))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[6145, 297, 666, 2467])).
% 1.44/1.68 tff(6147,plain,
% 1.44/1.68 (b(s(s(s(s(z)))), s(z))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2461, 6146])).
% 1.44/1.68 tff(6148,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(6149,plain,
% 1.44/1.68 (((~b(s(z), s(s(elem!1)))) | (~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(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(6150,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~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(s(s(z)))), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[6149])).
% 1.44/1.68 tff(6151,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~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(s(s(z)))), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[6150, 6148])).
% 1.44/1.68 tff(6152,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~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(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(6153,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[6152, 6151])).
% 1.44/1.68 tff(6154,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[6153, 319, 1, 817, 6147, 6142])).
% 1.44/1.68 tff(6155,plain,((~r(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(6156,plain,
% 1.44/1.68 (~r(s(s(s(s(z)))), z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[6155, 6131, 6000, 1, 666, 115])).
% 1.44/1.68 tff(6157,plain,
% 1.44/1.68 (b(s(s(s(s(z)))), z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2482, 6156])).
% 1.44/1.68 tff(6158,assumption,(b(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 1.44/1.68 tff(6159,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(6160,plain,
% 1.44/1.69 (((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(6161,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[6160])).
% 1.44/1.69 tff(6162,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 1.44/1.69 inference(transitivity,[status(thm)],[6161, 6159])).
% 1.44/1.69 tff(6163,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(6164,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[6163, 6162])).
% 1.44/1.69 tff(6165,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[6164, 319, 711, 687, 3756, 6158])).
% 1.44/1.69 tff(6166,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(6167,plain,
% 1.44/1.69 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[6166, 6157, 687, 6006])).
% 1.44/1.69 tff(6168,assumption,(s(s(s(s(z)))) = s(s(z))), introduced(assumption)).
% 1.44/1.69 tff(6169,plain,
% 1.44/1.69 (inj_0(s(s(s(s(z))))) = inj_0(s(s(z)))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[6168])).
% 1.44/1.69 tff(6170,plain,
% 1.44/1.69 (s(s(s(z))) = s(z)),
% 1.44/1.69 inference(transitivity,[status(thm)],[2297, 6169, 126])).
% 1.44/1.69 tff(6171,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[30, 6170])).
% 1.44/1.69 tff(6172,plain,(~(s(s(s(s(z)))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(6173,plain,
% 1.44/1.69 ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z)))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3001, 51])).
% 1.44/1.69 tff(6174,plain,
% 1.44/1.69 (b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z)))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[6173, 6172])).
% 1.44/1.69 tff(6175,plain,
% 1.44/1.69 (r(s(s(s(s(z)))), s(s(z)))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[6174, 6167])).
% 1.44/1.69 tff(6176,plain,
% 1.44/1.69 (~r(s(s(s(s(z)))), s(z))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3009, 6175, 6136])).
% 1.44/1.69 tff(6177,plain,
% 1.44/1.69 (b(s(s(s(s(z)))), s(z))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2461, 6176])).
% 1.44/1.69 tff(6178,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(6179,plain,
% 1.44/1.69 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(6180,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[6179])).
% 1.44/1.69 tff(6181,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.44/1.69 inference(transitivity,[status(thm)],[6180, 6178])).
% 1.44/1.69 tff(6182,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(6183,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[6182, 6181])).
% 1.44/1.69 tff(6184,plain,
% 1.44/1.69 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[6183, 319, 1, 6000, 6177])).
% 1.44/1.69 tff(6185,plain,
% 1.44/1.69 (~b(s(s(s(s(z)))), elem!1)),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[6184, 6134])).
% 1.44/1.69 tff(6186,plain,
% 1.44/1.69 (((~![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))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(6187,plain,
% 1.44/1.69 ((~![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))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(6188,plain,
% 1.44/1.69 ((~![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)),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[6187, 6186])).
% 1.44/1.69 tff(6189,plain,
% 1.44/1.69 ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[6188, 51])).
% 1.44/1.69 tff(6190,plain,
% 1.44/1.69 (r(s(s(s(s(z)))), elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[6189, 6185, 6132])).
% 1.44/1.69 tff(6191,plain,
% 1.44/1.69 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[6190, 6116])).
% 1.44/1.69 tff(6192,plain,
% 1.44/1.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(6193,plain,
% 1.44/1.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(6194,plain,
% 1.44/1.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[6193, 6192])).
% 1.44/1.69 tff(6195,plain,
% 1.44/1.69 ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[6194, 297, 197])).
% 1.44/1.69 tff(6196,plain,
% 1.44/1.69 (~r(s(s(s(s(z)))), s(elem!1))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[6195, 6191])).
% 1.44/1.69 tff(6197,plain,
% 1.44/1.69 (~r(z, s(elem!1))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[4120, 197, 70])).
% 1.44/1.69 tff(6198,plain,
% 1.44/1.69 (b(z, s(elem!1))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[4804, 6197])).
% 1.44/1.69 tff(6199,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(6200,plain,
% 1.44/1.69 (((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(6201,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[6200])).
% 1.44/1.69 tff(6202,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.44/1.69 inference(transitivity,[status(thm)],[6201, 6199])).
% 1.44/1.69 tff(6203,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(6204,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[6203, 6202])).
% 1.44/1.69 tff(6205,plain,
% 1.44/1.69 (~b(s(s(s(s(z)))), s(elem!1))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[6204, 319, 6198, 786, 6157])).
% 1.44/1.69 tff(6206,plain,
% 1.44/1.69 (((~![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)))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(6207,plain,
% 1.44/1.69 ((~![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)))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(6208,plain,
% 1.44/1.69 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[6207, 6206])).
% 1.44/1.69 tff(6209,plain,
% 1.44/1.69 ((s(s(s(s(z)))) = s(elem!1)) | r(s(s(s(s(z)))), s(elem!1))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[6208, 51, 6205])).
% 1.44/1.69 tff(6210,plain,
% 1.44/1.69 (s(s(s(s(z)))) = s(elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[6209, 6196])).
% 1.44/1.69 tff(6211,plain,
% 1.44/1.69 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[6210])).
% 1.44/1.69 tff(6212,plain,
% 1.44/1.69 (s(s(s(z))) = s(s(elem!1))),
% 1.44/1.69 inference(transitivity,[status(thm)],[2297, 6211, 141, 6111, 6110])).
% 1.44/1.69 tff(6213,plain,
% 1.44/1.69 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2827, 6106])).
% 1.44/1.69 tff(6214,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[6213, 6212])).
% 1.44/1.69 tff(6215,plain,((~r(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(6216,plain,
% 1.44/1.69 (~r(s(elem!1), s(s(elem!1)))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[6215, 786, 687, 1, 666, 115, 3739, 335, 70])).
% 1.44/1.69 tff(6217,plain,
% 1.44/1.69 (b(s(elem!1), s(s(elem!1)))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[807, 6216, 2142])).
% 1.44/1.69 tff(6218,plain,
% 1.44/1.69 (s(elem!1) = s(s(z))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2656, 6217, 687, 1, 136, 6002])).
% 1.44/1.69 tff(6219,plain,
% 1.44/1.69 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(s(z)))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[6218])).
% 1.44/1.69 tff(6220,plain,
% 1.44/1.69 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.69 inference(symmetry,[status(thm)],[6219])).
% 1.44/1.69 tff(6221,plain,
% 1.44/1.69 (s(elem!1) = s(s(z))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2656, 785, 687, 1, 136, 6010])).
% 1.44/1.69 tff(6222,plain,
% 1.44/1.69 (s(s(z)) = s(elem!1)),
% 1.44/1.69 inference(symmetry,[status(thm)],[6221])).
% 1.44/1.69 tff(6223,plain,
% 1.44/1.69 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[6222])).
% 1.44/1.69 tff(6224,plain,
% 1.44/1.69 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[6223])).
% 1.44/1.69 tff(6225,plain,
% 1.44/1.69 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[2140, 6224])).
% 1.44/1.69 tff(6226,plain,
% 1.44/1.69 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(s(z)))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[6221])).
% 1.44/1.69 tff(6227,plain,
% 1.44/1.69 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(elem!1)), s(elem!1))),
% 1.44/1.69 inference(symmetry,[status(thm)],[6226])).
% 1.44/1.69 tff(6228,plain,
% 1.44/1.69 (s(s(elem!1)) = s(s(s(z)))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[6221])).
% 1.44/1.69 tff(6229,plain,
% 1.44/1.69 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(s(z))), s(s(z)))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[6228])).
% 1.44/1.69 tff(6230,plain,
% 1.44/1.69 (b(s(s(s(z))), s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 1.44/1.69 inference(symmetry,[status(thm)],[6229])).
% 1.44/1.69 tff(6231,plain,
% 1.44/1.69 (b(s(s(s(z))), s(s(z))) <=> b(s(s(elem!1)), s(elem!1))),
% 1.44/1.69 inference(transitivity,[status(thm)],[6230, 6227])).
% 1.44/1.69 tff(6232,plain,
% 1.44/1.69 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[6228])).
% 1.44/1.69 tff(6233,plain,
% 1.44/1.69 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(z)))), z)),
% 1.44/1.69 inference(monotonicity,[status(thm)],[6232])).
% 1.44/1.69 tff(6234,plain,
% 1.44/1.69 (b(s(s(s(s(z)))), z)),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[3882, 6233])).
% 1.44/1.69 tff(6235,plain,
% 1.44/1.69 (b(s(s(z)), z)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3187, 6221, 786])).
% 1.44/1.69 tff(6236,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(6237,plain,
% 1.44/1.69 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(6238,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[6237])).
% 1.44/1.69 tff(6239,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.44/1.69 inference(transitivity,[status(thm)],[6238, 6236])).
% 1.44/1.69 tff(6240,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(6241,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[6240, 6239])).
% 1.44/1.69 tff(6242,plain,
% 1.44/1.69 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[6241, 319, 711, 6235, 6234])).
% 1.44/1.69 tff(6243,plain,
% 1.44/1.69 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(z))))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[2233])).
% 1.44/1.69 tff(6244,plain,
% 1.44/1.69 (~(s(s(z)) = s(s(s(s(z)))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[6172, 6243])).
% 1.44/1.69 tff(6245,plain,
% 1.44/1.69 (((~![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))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(6246,plain,
% 1.44/1.69 ((~![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))))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(6247,plain,
% 1.44/1.69 ((~![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)))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[6246, 6245])).
% 1.44/1.70 tff(6248,plain,
% 1.44/1.70 ((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)))))),
% 1.44/1.70 inference(unit_resolution,[status(thm)],[6247, 51])).
% 1.44/1.70 tff(6249,plain,
% 1.44/1.70 (b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.70 inference(unit_resolution,[status(thm)],[6248, 6244])).
% 1.44/1.70 tff(6250,plain,
% 1.44/1.70 (r(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.70 inference(unit_resolution,[status(thm)],[6249, 6242])).
% 1.44/1.70 tff(6251,plain,
% 1.44/1.70 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(z))), s(z))),
% 1.44/1.70 inference(monotonicity,[status(thm)],[6228])).
% 1.44/1.70 tff(6252,plain,
% 1.44/1.70 (b(s(s(s(z))), s(z))),
% 1.44/1.70 inference(modus_ponens,[status(thm)],[1, 6251])).
% 1.44/1.70 tff(6253,plain,
% 1.44/1.70 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 1.44/1.70 inference(monotonicity,[status(thm)],[6232])).
% 1.44/1.70 tff(6254,plain,
% 1.44/1.70 (b(s(s(s(s(z)))), s(z))),
% 1.44/1.70 inference(modus_ponens,[status(thm)],[4727, 6253])).
% 1.44/1.70 tff(6255,plain,
% 1.44/1.70 (s(s(s(z))) = s(s(elem!1))),
% 1.44/1.70 inference(symmetry,[status(thm)],[6228])).
% 1.44/1.70 tff(6256,plain,
% 1.44/1.70 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(elem!1)))),
% 1.44/1.70 inference(monotonicity,[status(thm)],[6255])).
% 1.44/1.70 tff(6257,plain,
% 1.44/1.70 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(z))))),
% 1.44/1.70 inference(symmetry,[status(thm)],[6256])).
% 1.44/1.70 tff(6258,plain,
% 1.44/1.70 (b(s(z), s(s(s(z))))),
% 1.44/1.70 inference(modus_ponens,[status(thm)],[817, 6257])).
% 1.44/1.70 tff(6259,plain,
% 1.44/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))), s(s(s(s(z)))))))),
% 1.44/1.70 inference(rewrite,[status(thm)],[])).
% 1.44/1.70 tff(6260,plain,
% 1.44/1.70 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.44/1.70 inference(rewrite,[status(thm)],[])).
% 1.44/1.70 tff(6261,plain,
% 1.44/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))), s(s(s(s(z))))))))),
% 1.44/1.70 inference(monotonicity,[status(thm)],[6260])).
% 1.44/1.70 tff(6262,plain,
% 1.44/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))), s(s(s(s(z)))))))),
% 1.44/1.70 inference(transitivity,[status(thm)],[6261, 6259])).
% 1.44/1.70 tff(6263,plain,
% 1.44/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.44/1.70 inference(quant_inst,[status(thm)],[])).
% 1.44/1.70 tff(6264,plain,
% 1.44/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))), s(s(s(s(z))))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[6263, 6262])).
% 1.54/1.70 tff(6265,plain,
% 1.54/1.70 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[6264, 319, 6258, 6254, 6252])).
% 1.54/1.70 tff(6266,plain,
% 1.54/1.70 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2281, 6265])).
% 1.54/1.70 tff(6267,plain,
% 1.54/1.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(6268,plain,
% 1.54/1.70 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(6269,plain,
% 1.54/1.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[6268])).
% 1.54/1.70 tff(6270,plain,
% 1.54/1.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[6269, 6267])).
% 1.54/1.70 tff(6271,plain,
% 1.54/1.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(6272,plain,
% 1.54/1.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[6271, 6270])).
% 1.54/1.70 tff(6273,plain,
% 1.54/1.70 (~r(s(s(s(z))), s(s(z)))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[6272, 297, 6266, 6250])).
% 1.54/1.70 tff(6274,plain,
% 1.54/1.70 (b(s(s(s(z))), s(s(z)))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2920, 6273])).
% 1.54/1.70 tff(6275,plain,
% 1.54/1.70 (b(s(s(elem!1)), s(elem!1))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[6274, 6231])).
% 1.54/1.70 tff(6276,plain,
% 1.54/1.70 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3120, 6221])).
% 1.54/1.70 tff(6277,plain,
% 1.54/1.70 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[4681, 6276])).
% 1.54/1.70 tff(6278,plain,
% 1.54/1.70 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[6050, 6221, 99, 711, 335, 70])).
% 1.54/1.70 tff(6279,plain,
% 1.54/1.70 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[571, 6278, 6277])).
% 1.54/1.70 tff(6280,plain,
% 1.54/1.70 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[1839, 6279, 6275, 785])).
% 1.54/1.70 tff(6281,plain,
% 1.54/1.70 ((~(elem!1 = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[598])).
% 1.54/1.70 tff(6282,plain,
% 1.54/1.70 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[6276, 6281])).
% 1.54/1.70 tff(6283,plain,
% 1.54/1.70 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[6221])).
% 1.54/1.70 tff(6284,plain,
% 1.54/1.70 (elem!1 = s(z)),
% 1.54/1.70 inference(transitivity,[status(thm)],[258, 6283, 126])).
% 1.54/1.70 tff(6285,plain,
% 1.54/1.70 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(z))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[6284])).
% 1.54/1.70 tff(6286,plain,
% 1.54/1.70 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 1.54/1.70 inference(symmetry,[status(thm)],[6285])).
% 1.54/1.70 tff(6287,plain,
% 1.54/1.70 (b(s(s(elem!1)), elem!1)),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[1, 6286])).
% 1.54/1.70 tff(6288,plain,
% 1.54/1.70 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[1225, 6279, 6287, 6282, 6276, 1209, 785, 6275])).
% 1.54/1.70 tff(6289,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[595, 6288, 6280, 6225])).
% 1.54/1.70 tff(6290,plain,((~b(s(elem!1), s(s(elem!1)))) | (elem!1 = s(elem!1)) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), z)) | (~b(s(s(z)), s(s(elem!1)))) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(6291,plain,
% 1.54/1.70 (~b(s(s(s(elem!1))), s(z))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[6290, 6217, 99, 6006, 335, 70, 2168, 6000, 1, 786, 687, 136])).
% 1.54/1.70 tff(6292,plain,
% 1.54/1.70 (r(s(s(s(elem!1))), s(z))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[4750, 6291])).
% 1.54/1.70 tff(6293,plain,
% 1.54/1.70 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[4784, 6292, 6002])).
% 1.54/1.70 tff(6294,plain,
% 1.54/1.70 (b(s(s(s(elem!1))), s(s(z)))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[5676, 6293])).
% 1.54/1.70 tff(6295,plain,
% 1.54/1.70 (b(s(s(s(elem!1))), s(elem!1))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[6294, 6220])).
% 1.54/1.70 tff(6296,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(6297,plain,
% 1.54/1.70 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(6298,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[6297])).
% 1.54/1.70 tff(6299,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)))),
% 1.54/1.70 inference(transitivity,[status(thm)],[6298, 6296])).
% 1.54/1.70 tff(6300,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(6301,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[6300, 6299])).
% 1.54/1.70 tff(6302,plain,
% 1.54/1.70 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[6301, 319, 6006, 786, 3882])).
% 1.54/1.70 tff(6303,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[6302, 6295])).
% 1.54/1.70 tff(6304,plain,((~b(s(elem!1), z)) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (s(z) = s(elem!1)) | (s(elem!1) = s(s(elem!1))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (s(s(s(z))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(6305,plain,
% 1.54/1.70 (~r(s(s(elem!1)), z)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[6304, 6088, 335, 70, 1, 687, 136, 2142, 666, 99, 3739])).
% 1.54/1.70 tff(6306,plain,
% 1.54/1.70 (b(s(s(elem!1)), z)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[75, 6305])).
% 1.54/1.70 tff(6307,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2771, 319, 711, 2543, 687, 496])).
% 1.54/1.70 tff(6308,plain,((~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(6309,plain,
% 1.54/1.70 (~b(s(s(elem!1)), s(s(z)))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[6308, 6006, 687, 6306])).
% 1.54/1.70 tff(6310,plain,
% 1.54/1.70 (r(s(s(elem!1)), s(s(z)))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[5327, 6309, 2542])).
% 1.54/1.70 tff(6311,plain,
% 1.54/1.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(6312,plain,
% 1.54/1.70 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(6313,plain,
% 1.54/1.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[6312])).
% 1.54/1.70 tff(6314,plain,
% 1.54/1.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[6313, 6311])).
% 1.54/1.70 tff(6315,plain,
% 1.54/1.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(6316,plain,
% 1.54/1.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[6315, 6314])).
% 1.54/1.70 tff(6317,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[6316, 297, 2557, 3004, 2443])).
% 1.54/1.70 tff(6318,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(6319,plain,
% 1.54/1.70 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[6318, 2443, 2557])).
% 1.54/1.70 tff(6320,plain,
% 1.54/1.70 (b(s(s(s(s(z)))), s(s(z)))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[6174, 6319])).
% 1.54/1.70 tff(6321,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(6322,plain,
% 1.54/1.70 (((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(6323,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[6322])).
% 1.54/1.70 tff(6324,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[6323, 6321])).
% 1.54/1.70 tff(6325,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(6326,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[6325, 6324])).
% 1.54/1.70 tff(6327,plain,
% 1.54/1.70 (~b(z, s(s(s(s(z)))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[6326, 319, 711, 687, 6320])).
% 1.54/1.70 tff(6328,plain,
% 1.54/1.70 ((z = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = z)),
% 1.54/1.70 inference(commutativity,[status(thm)],[])).
% 1.54/1.70 tff(6329,plain,
% 1.54/1.70 ((s(s(s(s(z)))) = z) <=> (z = s(s(s(s(z)))))),
% 1.54/1.70 inference(symmetry,[status(thm)],[6328])).
% 1.54/1.70 tff(6330,plain,
% 1.54/1.70 ((~(s(s(s(s(z)))) = z)) <=> (~(z = s(s(s(s(z))))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[6329])).
% 1.54/1.70 tff(6331,plain,
% 1.54/1.70 (~(z = s(s(s(s(z)))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[2478, 6330])).
% 1.54/1.70 tff(6332,plain,
% 1.54/1.70 (((~![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))))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(6333,plain,
% 1.54/1.70 ((~![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))))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(6334,plain,
% 1.54/1.70 ((~![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)))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[6333, 6332])).
% 1.54/1.70 tff(6335,plain,
% 1.54/1.70 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[6334, 51])).
% 1.54/1.70 tff(6336,plain,
% 1.54/1.70 (b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[6335, 6331])).
% 1.54/1.70 tff(6337,plain,
% 1.54/1.70 (r(z, s(s(s(s(z)))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[6336, 6327])).
% 1.54/1.70 tff(6338,plain,
% 1.54/1.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(6339,plain,
% 1.54/1.70 (((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(6340,plain,
% 1.54/1.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[6339])).
% 1.54/1.70 tff(6341,plain,
% 1.54/1.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[6340, 6338])).
% 1.54/1.70 tff(6342,plain,
% 1.54/1.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(elem!1)))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(6343,plain,
% 1.54/1.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[6342, 6341])).
% 1.54/1.70 tff(6344,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[6343, 297, 70, 6337, 2443])).
% 1.54/1.70 tff(6345,plain,((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(6346,plain,
% 1.54/1.70 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[6345, 6006, 70, 687, 6310])).
% 1.54/1.70 tff(6347,assumption,(~b(s(s(elem!1)), s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.70 tff(6348,assumption,(~r(s(s(elem!1)), s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.70 tff(6349,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[6141, 51, 6348, 6137, 6347])).
% 1.54/1.70 tff(6350,plain,(r(s(s(elem!1)), s(s(s(s(z))))) | (s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(6351,plain,
% 1.54/1.70 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[6350, 6346, 6103])).
% 1.54/1.70 tff(6352,assumption,(b(s(s(elem!1)), s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.70 tff(6353,plain,
% 1.54/1.70 (~r(z, s(s(z)))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[6004, 6010, 666])).
% 1.54/1.70 tff(6354,plain,
% 1.54/1.70 (b(z, s(s(z)))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[729, 6353])).
% 1.54/1.70 tff(6355,plain,
% 1.54/1.70 (~b(s(s(s(s(z)))), z)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[6166, 6158, 687, 6354])).
% 1.54/1.70 tff(6356,plain,
% 1.54/1.70 (r(s(s(s(s(z)))), z)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2482, 6355])).
% 1.54/1.70 tff(6357,plain,
% 1.54/1.70 (~r(s(s(s(s(z)))), s(z))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[6145, 297, 666, 6356])).
% 1.54/1.70 tff(6358,plain,
% 1.54/1.70 (b(s(s(s(s(z)))), s(z))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2461, 6357])).
% 1.54/1.70 tff(6359,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(6360,plain,
% 1.54/1.71 (((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(6361,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[6360])).
% 1.54/1.71 tff(6362,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[6361, 6359])).
% 1.54/1.71 tff(6363,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(6364,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[6363, 6362])).
% 1.54/1.71 tff(6365,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[6364, 319, 1, 687, 817, 6358, 6158, 6352])).
% 1.54/1.71 tff(6366,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(6367,plain,
% 1.54/1.71 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[6366, 1, 687, 6000, 6351, 666])).
% 1.54/1.71 tff(6368,plain,
% 1.54/1.71 (r(s(s(s(s(z)))), s(s(z)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[6174, 6367])).
% 1.54/1.71 tff(6369,plain,
% 1.54/1.71 (~r(s(s(s(s(z)))), s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3009, 6368, 6136])).
% 1.54/1.71 tff(6370,plain,
% 1.54/1.71 (b(s(s(s(s(z)))), s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2461, 6369])).
% 1.54/1.71 tff(6371,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[6153, 319, 1, 6000, 6370, 6351])).
% 1.54/1.71 tff(6372,plain,((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (s(s(elem!1)) = s(s(z))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | (s(z) = s(elem!1)) | (s(s(s(elem!1))) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(6373,plain,
% 1.54/1.71 (~b(s(s(elem!1)), s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[6372, 335, 666, 70, 2522, 2510, 687, 2142, 2504, 99])).
% 1.54/1.71 tff(6374,plain,
% 1.54/1.71 (r(s(s(elem!1)), s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[871, 6373])).
% 1.54/1.71 tff(6375,plain,
% 1.54/1.71 (~r(s(s(elem!1)), z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[5094, 6374, 666])).
% 1.54/1.71 tff(6376,plain,
% 1.54/1.71 (b(s(s(elem!1)), z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[75, 6375])).
% 1.54/1.71 tff(6377,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(6378,plain,
% 1.54/1.71 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(6379,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[6378])).
% 1.54/1.71 tff(6380,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[6379, 6377])).
% 1.54/1.71 tff(6381,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(6382,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z)))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[6381, 6380])).
% 1.54/1.71 tff(6383,plain,
% 1.54/1.71 (~b(s(s(s(elem!1))), s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[6382, 319, 711, 3882, 2493])).
% 1.54/1.71 tff(6384,plain,
% 1.54/1.71 (r(s(s(s(elem!1))), s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[4750, 6383])).
% 1.54/1.71 tff(6385,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[5496, 297, 2169, 335, 6384])).
% 1.54/1.71 tff(6386,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(6387,plain,
% 1.54/1.71 (~b(s(z), z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[6386, 335, 711, 2169, 70])).
% 1.54/1.71 tff(6388,plain,
% 1.54/1.71 (r(s(z), z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[67, 6387])).
% 1.54/1.71 tff(6389,plain,
% 1.54/1.71 (~r(s(s(elem!1)), z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[5094, 6388, 2169])).
% 1.54/1.71 tff(6390,plain,
% 1.54/1.71 (b(s(s(elem!1)), z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[75, 6389])).
% 1.54/1.71 tff(6391,plain,
% 1.54/1.71 (b(s(s(z)), s(s(elem!1)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[122, 5737, 772])).
% 1.54/1.71 tff(6392,plain,
% 1.54/1.71 (b(z, s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1099, 5752])).
% 1.54/1.71 tff(6393,plain,
% 1.54/1.71 (~r(s(s(z)), s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2565, 2557, 2169])).
% 1.54/1.71 tff(6394,plain,
% 1.54/1.71 (b(s(s(z)), s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[4102, 6393])).
% 1.54/1.71 tff(6395,plain,
% 1.54/1.71 (~b(s(z), s(s(z)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[4795, 6394, 711, 2706])).
% 1.54/1.71 tff(6396,plain,
% 1.54/1.71 (r(s(z), s(s(z)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[685, 6395])).
% 1.54/1.71 tff(6397,plain,
% 1.54/1.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(6398,plain,
% 1.54/1.71 (((~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(6399,plain,
% 1.54/1.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z))))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[6398])).
% 1.54/1.71 tff(6400,plain,
% 1.54/1.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[6399, 6397])).
% 1.54/1.71 tff(6401,plain,
% 1.54/1.71 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(z))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(6402,plain,
% 1.54/1.71 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[6401, 6400])).
% 1.54/1.71 tff(6403,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[6402, 297, 2169, 6396, 2557])).
% 1.54/1.71 tff(6404,plain,((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~b(z, s(s(z)))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(6405,plain,
% 1.54/1.71 (~r(s(s(elem!1)), s(s(z)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[6404, 6392, 711, 2169])).
% 1.54/1.71 tff(6406,plain,
% 1.54/1.71 (b(s(s(elem!1)), s(s(z)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[5327, 6405, 2522])).
% 1.54/1.71 tff(6407,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2771, 319, 711, 6406, 6391, 6390])).
% 1.54/1.71 tff(6408,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (s(s(z)) = s(s(elem!1))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(6409,plain,
% 1.54/1.71 (~b(z, s(s(z)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[6408, 6374, 335, 772, 70])).
% 1.54/1.71 tff(6410,plain,
% 1.54/1.71 (r(z, s(s(z)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[729, 6409])).
% 1.54/1.71 tff(6411,plain,
% 1.54/1.71 (~r(s(z), s(s(z)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[6004, 6410, 666])).
% 1.54/1.71 tff(6412,plain,
% 1.54/1.71 (b(s(z), s(s(z)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[685, 6411])).
% 1.54/1.71 tff(6413,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(6414,plain,
% 1.54/1.71 (((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(6415,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z))))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[6414])).
% 1.54/1.71 tff(6416,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[6415, 6413])).
% 1.54/1.71 tff(6417,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(z)))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(6418,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[6417, 6416])).
% 1.54/1.71 tff(6419,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[6418, 319, 687, 6000, 6412, 6376])).
% 1.54/1.71 tff(6420,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~r(s(z), z)) | (s(s(z)) = s(s(elem!1))) | (~r(z, s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | (s(s(s(elem!1))) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(6421,plain,
% 1.54/1.71 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[6420, 772, 666, 687, 70, 114, 93])).
% 1.54/1.71 tff(6422,plain,
% 1.54/1.71 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[348, 6421, 58])).
% 1.54/1.71 tff(6423,plain,
% 1.54/1.71 (~r(s(s(z)), s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3357, 6422, 687, 6000, 2522])).
% 1.54/1.71 tff(6424,plain,
% 1.54/1.71 (b(s(s(z)), s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[4102, 6423])).
% 1.54/1.71 tff(6425,plain,
% 1.54/1.71 (~r(s(z), s(s(z)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[6004, 732, 666])).
% 1.54/1.71 tff(6426,plain,
% 1.54/1.71 (b(s(z), s(s(z)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[685, 6425])).
% 1.54/1.71 tff(6427,plain,
% 1.54/1.71 (~b(s(s(elem!1)), s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[5317, 6426, 6000, 687])).
% 1.54/1.71 tff(6428,plain,
% 1.54/1.71 (r(s(s(elem!1)), s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[871, 6427])).
% 1.54/1.71 tff(6429,plain,
% 1.54/1.71 (~r(z, s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2177, 6428, 70])).
% 1.54/1.71 tff(6430,plain,
% 1.54/1.71 (b(z, s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1099, 6429])).
% 1.54/1.71 tff(6431,plain,
% 1.54/1.71 (~r(s(s(elem!1)), z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[5094, 6428, 666])).
% 1.54/1.71 tff(6432,plain,
% 1.54/1.71 (b(s(s(elem!1)), z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[75, 6431])).
% 1.54/1.71 tff(6433,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[5662, 6432, 6430, 687, 116, 732])).
% 1.54/1.71 tff(6434,plain,((~r(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), z)) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(6435,plain,
% 1.54/1.71 (~r(z, s(s(z)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[6434, 6422, 687, 666, 70])).
% 1.54/1.71 tff(6436,plain,
% 1.54/1.71 (b(z, s(s(z)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[729, 6435])).
% 1.54/1.71 tff(6437,plain,
% 1.54/1.71 (~b(z, s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[5828, 6436, 6424, 6000])).
% 1.54/1.71 tff(6438,plain,
% 1.54/1.71 (r(z, s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1099, 6437])).
% 1.54/1.71 tff(6439,plain,
% 1.54/1.71 (~r(s(s(elem!1)), s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2177, 6438, 70])).
% 1.54/1.71 tff(6440,plain,
% 1.54/1.71 (b(s(s(elem!1)), s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[871, 6439])).
% 1.54/1.71 tff(6441,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[5145, 319, 6440, 6424, 687, 6000])).
% 1.54/1.71 tff(6442,plain,((s(s(z)) = s(s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(6443,plain,
% 1.54/1.71 (s(s(z)) = s(s(elem!1))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[6442, 5998, 57, 5734, 58])).
% 1.54/1.71 tff(6444,plain,
% 1.54/1.71 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(elem!1)), s(s(elem!1)))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[6443])).
% 1.54/1.71 tff(6445,plain,
% 1.54/1.71 (b(s(s(elem!1)), s(s(elem!1))) <=> b(s(s(z)), s(s(elem!1)))),
% 1.54/1.71 inference(symmetry,[status(thm)],[6444])).
% 1.54/1.71 tff(6446,plain,
% 1.54/1.71 ((~b(s(s(elem!1)), s(s(elem!1)))) <=> (~b(s(s(z)), s(s(elem!1))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[6445])).
% 1.54/1.71 tff(6447,plain,
% 1.54/1.71 (~b(s(s(z)), s(s(elem!1)))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[5044, 6446])).
% 1.54/1.71 tff(6448,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[5998, 6447])).
% 1.54/1.71 tff(6449,plain,((s(s(s(elem!1))) = s(s(elem!1))) | b(z, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(6450,plain,
% 1.54/1.71 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[6449, 35])).
% 1.54/1.71 tff(6451,plain,
% 1.54/1.71 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 1.54/1.71 inference(symmetry,[status(thm)],[6121])).
% 1.54/1.71 tff(6452,plain,
% 1.54/1.71 (s(s(s(elem!1))) = elem!1),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[5346, 5177])).
% 1.54/1.71 tff(6453,plain,
% 1.54/1.71 (elem!1 = s(s(s(elem!1)))),
% 1.54/1.71 inference(symmetry,[status(thm)],[6452])).
% 1.54/1.71 tff(6454,plain,
% 1.54/1.71 (elem!1 = s(s(elem!1))),
% 1.54/1.71 inference(transitivity,[status(thm)],[6453, 5177])).
% 1.54/1.71 tff(6455,plain,
% 1.54/1.71 ((elem!1 = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[6454])).
% 1.54/1.71 tff(6456,plain,
% 1.54/1.71 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 1.54/1.71 inference(transitivity,[status(thm)],[6455, 6121])).
% 1.54/1.71 tff(6457,plain,
% 1.54/1.71 ((elem!1 = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[6456, 6451])).
% 1.54/1.71 tff(6458,plain,
% 1.54/1.71 ((~(elem!1 = s(s(s(s(z)))))) <=> (~(s(s(elem!1)) = s(s(s(s(z))))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[6457])).
% 1.54/1.71 tff(6459,plain,
% 1.54/1.71 (s(elem!1) = s(s(elem!1))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[5182, 5177])).
% 1.54/1.71 tff(6460,assumption,(elem!1 = s(s(s(s(z))))), introduced(assumption)).
% 1.54/1.71 tff(6461,plain,
% 1.54/1.71 (s(s(s(s(z)))) = elem!1),
% 1.54/1.71 inference(symmetry,[status(thm)],[6460])).
% 1.54/1.71 tff(6462,plain,
% 1.54/1.71 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.54/1.71 inference(transitivity,[status(thm)],[6461, 6453, 5177])).
% 1.54/1.71 tff(6463,plain,
% 1.54/1.71 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[6462])).
% 1.54/1.71 tff(6464,plain,
% 1.54/1.71 (s(s(s(z))) = s(s(elem!1))),
% 1.54/1.71 inference(transitivity,[status(thm)],[2297, 6463, 118, 6459])).
% 1.54/1.71 tff(6465,plain,
% 1.54/1.71 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(elem!1)) = s(elem!1))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[5177])).
% 1.54/1.71 tff(6466,plain,
% 1.54/1.71 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(elem!1)))),
% 1.54/1.71 inference(transitivity,[status(thm)],[6465, 2494])).
% 1.54/1.71 tff(6467,plain,
% 1.54/1.71 ((s(elem!1) = s(s(elem!1))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.54/1.71 inference(symmetry,[status(thm)],[6466])).
% 1.54/1.71 tff(6468,plain,
% 1.54/1.71 ((s(elem!1) = s(s(elem!1))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[6467, 277])).
% 1.54/1.71 tff(6469,plain,
% 1.54/1.71 (s(elem!1) = s(s(s(elem!1)))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[6459, 6468])).
% 1.54/1.71 tff(6470,plain,
% 1.54/1.71 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2827, 6469])).
% 1.54/1.71 tff(6471,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[6470, 6464])).
% 1.54/1.71 tff(6472,plain,((~(elem!1 = s(s(s(s(z)))))) | (~(s(s(s(elem!1))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(6473,plain,
% 1.54/1.71 (~(elem!1 = s(s(s(s(z)))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[6472, 5177])).
% 1.54/1.71 tff(6474,plain,
% 1.54/1.71 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[6473, 6458])).
% 1.54/1.71 tff(6475,plain,
% 1.54/1.71 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = s(s(elem!1)))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[5177])).
% 1.54/1.71 tff(6476,plain,
% 1.54/1.71 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(z)))),
% 1.54/1.71 inference(transitivity,[status(thm)],[6475, 5124])).
% 1.54/1.71 tff(6477,plain,
% 1.54/1.71 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(elem!1)) = s(s(z))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[6476])).
% 1.54/1.71 tff(6478,plain,
% 1.54/1.71 (~(s(s(elem!1)) = s(s(z)))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[231, 6477])).
% 1.54/1.71 tff(6479,plain,
% 1.54/1.71 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[5177])).
% 1.54/1.71 tff(6480,plain,
% 1.54/1.71 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(z)) = s(s(elem!1))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[6475])).
% 1.54/1.71 tff(6481,plain,
% 1.54/1.71 (~(s(s(z)) = s(s(elem!1)))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[231, 6480])).
% 1.54/1.71 tff(6482,plain,
% 1.54/1.71 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2509, 6481])).
% 1.54/1.71 tff(6483,plain,
% 1.54/1.71 (b(s(z), elem!1) <=> b(s(z), s(s(elem!1)))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[6454])).
% 1.54/1.71 tff(6484,plain,
% 1.54/1.71 (b(s(z), s(s(elem!1))) <=> b(s(z), elem!1)),
% 1.54/1.71 inference(symmetry,[status(thm)],[6483])).
% 1.54/1.71 tff(6485,plain,
% 1.54/1.71 (b(s(z), z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[67, 2617])).
% 1.54/1.71 tff(6486,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2588, 297, 444, 70, 917])).
% 1.54/1.71 tff(6487,plain,((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(6488,plain,
% 1.54/1.71 (~r(z, s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[6487, 444, 70])).
% 1.54/1.71 tff(6489,plain,
% 1.54/1.71 (b(z, s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1099, 6488])).
% 1.54/1.71 tff(6490,plain,
% 1.54/1.71 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(elem!1)))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[5177])).
% 1.54/1.71 tff(6491,plain,
% 1.54/1.71 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(elem!1))))),
% 1.54/1.71 inference(symmetry,[status(thm)],[6490])).
% 1.54/1.71 tff(6492,plain,
% 1.54/1.71 (r(s(z), s(s(s(elem!1))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[444, 6491])).
% 1.54/1.71 tff(6493,plain,
% 1.54/1.71 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[5178])).
% 1.54/1.71 tff(6494,plain,
% 1.54/1.71 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 1.54/1.71 inference(symmetry,[status(thm)],[6493])).
% 1.54/1.71 tff(6495,plain,
% 1.54/1.71 (r(s(s(s(z))), s(s(elem!1)))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[4878, 6494])).
% 1.54/1.71 tff(6496,plain,
% 1.54/1.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(6497,plain,
% 1.54/1.71 (((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(6498,plain,
% 1.54/1.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1))))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[6497])).
% 1.54/1.72 tff(6499,plain,
% 1.54/1.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[6498, 6496])).
% 1.54/1.72 tff(6500,plain,
% 1.54/1.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(6501,plain,
% 1.54/1.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[6500, 6499])).
% 1.54/1.72 tff(6502,plain,
% 1.54/1.72 ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[6501, 297, 70])).
% 1.54/1.72 tff(6503,plain,
% 1.54/1.72 (~r(s(s(s(z))), z)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[6502, 6495])).
% 1.54/1.72 tff(6504,plain,
% 1.54/1.72 (b(s(s(s(z))), z)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[4584, 6503])).
% 1.54/1.72 tff(6505,plain,
% 1.54/1.72 (~r(s(s(s(z))), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[4886, 4878, 4877])).
% 1.54/1.72 tff(6506,plain,
% 1.54/1.72 (b(s(s(s(z))), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[4549, 6505])).
% 1.54/1.72 tff(6507,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(6508,plain,
% 1.54/1.72 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(6509,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z)))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[6508])).
% 1.54/1.72 tff(6510,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[6509, 6507])).
% 1.54/1.72 tff(6511,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(6512,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z)))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[6511, 6510])).
% 1.54/1.72 tff(6513,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[6512, 319, 2706, 2493, 6506, 6504])).
% 1.54/1.72 tff(6514,plain,((~r(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(z, s(s(elem!1)))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(6515,plain,
% 1.54/1.72 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[6514, 6492, 70, 5177, 6489, 6485])).
% 1.54/1.72 tff(6516,plain,
% 1.54/1.72 (b(s(s(s(z))), s(s(s(elem!1))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3794, 6515, 6482])).
% 1.54/1.72 tff(6517,plain,
% 1.54/1.72 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[5177])).
% 1.54/1.72 tff(6518,plain,
% 1.54/1.72 (b(s(s(s(z))), s(s(elem!1)))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[4561, 6517])).
% 1.54/1.72 tff(6519,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[4063, 6518])).
% 1.54/1.72 tff(6520,plain,((~b(s(s(s(z))), s(s(s(elem!1))))) | b(s(s(s(z))), s(s(elem!1))) | (~(s(s(s(elem!1))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(6521,plain,
% 1.54/1.72 (b(s(s(s(z))), s(s(elem!1)))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[6520, 6516, 5177])).
% 1.54/1.72 tff(6522,plain,
% 1.54/1.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(6523,plain,
% 1.54/1.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(6524,plain,
% 1.54/1.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(z))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[6523, 6522])).
% 1.54/1.72 tff(6525,plain,
% 1.54/1.72 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[6524, 297, 2578, 889])).
% 1.54/1.72 tff(6526,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[6525, 6495])).
% 1.54/1.72 tff(6527,plain,((~r(s(s(s(z))), s(s(s(elem!1))))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(6528,plain,
% 1.54/1.72 (~r(s(s(s(z))), s(s(z)))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[6527, 2578, 4878, 5177])).
% 1.54/1.72 tff(6529,plain,
% 1.54/1.72 (b(s(s(s(z))), s(s(z)))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2920, 6528])).
% 1.54/1.72 tff(6530,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(6531,plain,
% 1.54/1.72 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(6532,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[6531])).
% 1.54/1.72 tff(6533,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)))),
% 1.54/1.72 inference(transitivity,[status(thm)],[6532, 6530])).
% 1.54/1.72 tff(6534,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(6535,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[6534, 6533])).
% 1.54/1.72 tff(6536,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[6535, 319, 3884, 6529, 3877, 6504])).
% 1.54/1.72 tff(6537,plain,((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~(s(s(s(elem!1))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(6538,plain,
% 1.54/1.72 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[6537, 2578, 70, 5177])).
% 1.54/1.72 tff(6539,plain,
% 1.54/1.72 (b(s(s(s(z))), s(s(s(elem!1))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3794, 6538, 6482])).
% 1.54/1.72 tff(6540,plain,
% 1.54/1.72 (b(s(s(s(z))), s(s(elem!1)))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[6520, 6539, 5177])).
% 1.54/1.72 tff(6541,plain,
% 1.54/1.72 (~r(s(z), s(s(elem!1)))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[5702, 2578, 70])).
% 1.54/1.72 tff(6542,plain,
% 1.54/1.72 (b(s(z), s(s(elem!1)))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1047, 6541])).
% 1.54/1.72 tff(6543,plain,
% 1.54/1.72 (~r(s(s(z)), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[4108, 2169, 2578])).
% 1.54/1.72 tff(6544,plain,
% 1.54/1.72 (b(s(s(z)), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[4102, 6543])).
% 1.54/1.72 tff(6545,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[5828, 6544, 6392, 3884, 6542])).
% 1.54/1.72 tff(6546,plain,((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(6547,plain,
% 1.54/1.72 (~r(s(s(elem!1)), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[6546, 2578, 70])).
% 1.54/1.72 tff(6548,plain,
% 1.54/1.72 (b(s(s(elem!1)), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[871, 6547])).
% 1.54/1.72 tff(6549,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(6550,plain,
% 1.54/1.72 (((~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(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(6551,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[6550])).
% 1.54/1.72 tff(6552,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[6551, 6549])).
% 1.54/1.72 tff(6553,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(6554,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[6553, 6552])).
% 1.54/1.72 tff(6555,plain,
% 1.54/1.72 (~b(s(z), s(s(s(z))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[6554, 319, 6548, 6542, 6540])).
% 1.54/1.72 tff(6556,plain,
% 1.54/1.72 (((~![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)))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(6557,plain,
% 1.54/1.72 ((~![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)))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(6558,plain,
% 1.54/1.72 ((~![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))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[6557, 6556])).
% 1.54/1.72 tff(6559,plain,
% 1.54/1.72 (r(s(z), s(s(s(z))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[6558, 51, 6555, 32])).
% 1.54/1.72 tff(6560,plain,
% 1.54/1.72 (((~b(s(s(elem!1)), 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(elem!1)))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(6561,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z))), s(s(elem!1)))) | (~b(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[6560])).
% 1.54/1.72 tff(6562,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z))), s(s(elem!1)))) | (~b(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[6561, 4552])).
% 1.54/1.72 tff(6563,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(6564,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[6563, 6562])).
% 1.54/1.72 tff(6565,plain,
% 1.54/1.72 (~b(s(s(s(z))), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[6564, 319, 1, 817, 4230])).
% 1.54/1.72 tff(6566,plain,
% 1.54/1.72 (r(s(s(s(z))), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[4549, 6565])).
% 1.54/1.72 tff(6567,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[6153, 319, 1, 817, 3154, 6352])).
% 1.54/1.72 tff(6568,plain,((~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(elem!1)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(6569,plain,
% 1.54/1.72 (~b(s(s(s(s(z)))), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[6568, 6352, 817, 1])).
% 1.54/1.72 tff(6570,plain,
% 1.54/1.72 (r(s(s(s(s(z)))), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2461, 6569])).
% 1.54/1.72 tff(6571,plain,
% 1.54/1.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(6572,plain,
% 1.54/1.72 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(6573,plain,
% 1.54/1.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[6572])).
% 1.54/1.72 tff(6574,plain,
% 1.54/1.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[6573, 6571])).
% 1.54/1.72 tff(6575,plain,
% 1.54/1.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(6576,plain,
% 1.54/1.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[6575, 6574])).
% 1.54/1.72 tff(6577,plain,
% 1.54/1.72 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[6576, 297, 6570, 6566])).
% 1.54/1.72 tff(6578,plain,
% 1.54/1.72 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2281, 6577])).
% 1.54/1.72 tff(6579,plain,
% 1.54/1.72 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3620, 297, 6570, 6566])).
% 1.54/1.72 tff(6580,plain,
% 1.54/1.72 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2252, 6579])).
% 1.54/1.72 tff(6581,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(6582,plain,
% 1.54/1.72 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(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(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(6583,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[6582])).
% 1.54/1.72 tff(6584,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[6583, 6581])).
% 1.54/1.72 tff(6585,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(6586,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[6585, 6584])).
% 1.54/1.72 tff(6587,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[6586, 319, 4230, 6580, 6578, 6352])).
% 1.54/1.72 tff(6588,plain,((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(6589,plain,
% 1.54/1.72 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[6588, 6540, 6542, 6548])).
% 1.54/1.72 tff(6590,plain,
% 1.54/1.72 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[6350, 6589, 6474])).
% 1.54/1.72 tff(6591,assumption,(r(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.72 tff(6592,plain,
% 1.54/1.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(6593,plain,
% 1.54/1.73 (((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(elem!1))))) <=> ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(6594,plain,
% 1.54/1.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[6593])).
% 1.54/1.73 tff(6595,plain,
% 1.54/1.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[6594, 6592])).
% 1.54/1.73 tff(6596,plain,
% 1.54/1.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(6597,plain,
% 1.54/1.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[6596, 6595])).
% 1.54/1.73 tff(6598,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[6597, 297, 2578, 6591, 2443])).
% 1.54/1.73 tff(6599,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(6600,plain,
% 1.54/1.73 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[6599, 2578, 6590])).
% 1.54/1.73 tff(6601,plain,
% 1.54/1.73 (b(s(s(z)), s(s(s(s(z)))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[6249, 6600])).
% 1.54/1.73 tff(6602,assumption,(b(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.73 tff(6603,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[6241, 319, 711, 3204, 3756, 6602])).
% 1.54/1.73 tff(6604,plain,((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(6605,plain,
% 1.54/1.73 (~b(s(s(s(s(z)))), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[6604, 3884, 3877, 6601])).
% 1.54/1.73 tff(6606,plain,
% 1.54/1.73 (r(s(s(s(s(z)))), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2482, 6605])).
% 1.54/1.73 tff(6607,plain,
% 1.54/1.73 (~r(s(s(elem!1)), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2475, 6606, 6590])).
% 1.54/1.73 tff(6608,plain,
% 1.54/1.73 (b(s(s(elem!1)), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[75, 6607])).
% 1.54/1.73 tff(6609,plain,
% 1.54/1.73 (~b(s(z), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[5714, 6608, 6542, 3884])).
% 1.54/1.73 tff(6610,plain,
% 1.54/1.73 (r(s(z), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[67, 6609])).
% 1.54/1.73 tff(6611,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(6612,plain,
% 1.54/1.73 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(6613,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[6612])).
% 1.54/1.73 tff(6614,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[6613, 6611])).
% 1.54/1.73 tff(6615,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(6616,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[6615, 6614])).
% 1.54/1.73 tff(6617,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[6616, 319, 711, 496, 4230, 3585])).
% 1.54/1.73 tff(6618,plain,((~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(6619,plain,
% 1.54/1.73 (~b(s(s(s(z))), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[6618, 6608, 3884, 6540])).
% 1.54/1.73 tff(6620,plain,
% 1.54/1.73 (r(s(s(s(z))), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4584, 6619])).
% 1.54/1.73 tff(6621,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[5986, 6620, 6610, 6559])).
% 1.54/1.73 tff(6622,plain,((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~(s(s(s(elem!1))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(6623,plain,
% 1.54/1.73 (~r(s(s(z)), s(s(elem!1)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[6622, 70, 5177])).
% 1.54/1.73 tff(6624,plain,
% 1.54/1.73 (b(s(s(z)), s(s(elem!1)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[122, 6623, 6481])).
% 1.54/1.73 tff(6625,plain,
% 1.54/1.73 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[113, 109])).
% 1.54/1.73 tff(6626,plain,
% 1.54/1.73 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = s(s(elem!1)))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[6625])).
% 1.54/1.73 tff(6627,plain,
% 1.54/1.73 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(z)))),
% 1.54/1.73 inference(transitivity,[status(thm)],[6626, 5124])).
% 1.54/1.73 tff(6628,plain,
% 1.54/1.73 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(elem!1)) = s(s(z))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[6627])).
% 1.54/1.73 tff(6629,plain,
% 1.54/1.73 (~(s(s(elem!1)) = s(s(z)))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[231, 6628])).
% 1.54/1.73 tff(6630,plain,
% 1.54/1.73 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(z)) = s(s(elem!1))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[6626])).
% 1.54/1.73 tff(6631,plain,
% 1.54/1.73 (~(s(s(z)) = s(s(elem!1)))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[231, 6630])).
% 1.54/1.73 tff(6632,plain,
% 1.54/1.73 (b(s(s(elem!1)), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[5175, 109, 786])).
% 1.54/1.73 tff(6633,plain,
% 1.54/1.73 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[109])).
% 1.54/1.73 tff(6634,plain,
% 1.54/1.73 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.54/1.73 inference(symmetry,[status(thm)],[6633])).
% 1.54/1.73 tff(6635,plain,
% 1.54/1.73 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[6634, 277])).
% 1.54/1.73 tff(6636,plain,
% 1.54/1.73 (s(elem!1) = s(s(s(elem!1)))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[6625, 6635])).
% 1.54/1.73 tff(6637,plain,
% 1.54/1.73 (s(s(s(elem!1))) = elem!1),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[5346, 6625])).
% 1.54/1.73 tff(6638,plain,
% 1.54/1.73 (elem!1 = s(s(s(elem!1)))),
% 1.54/1.73 inference(symmetry,[status(thm)],[6637])).
% 1.54/1.73 tff(6639,plain,
% 1.54/1.73 (elem!1 = s(s(elem!1))),
% 1.54/1.73 inference(transitivity,[status(thm)],[6638, 6625])).
% 1.54/1.73 tff(6640,plain,
% 1.54/1.73 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(elem!1)))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[6639])).
% 1.54/1.73 tff(6641,plain,
% 1.54/1.73 ((s(s(z)) = s(s(elem!1))) <=> (s(s(z)) = elem!1)),
% 1.54/1.73 inference(symmetry,[status(thm)],[6640])).
% 1.54/1.73 tff(6642,plain,
% 1.54/1.73 ((~(s(s(z)) = s(s(elem!1)))) <=> (~(s(s(z)) = elem!1))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[6641])).
% 1.54/1.73 tff(6643,plain,
% 1.54/1.73 (~(s(s(z)) = elem!1)),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[6631, 6642])).
% 1.54/1.73 tff(6644,plain,
% 1.54/1.73 (~(s(s(s(z))) = s(elem!1))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2759, 6643])).
% 1.54/1.73 tff(6645,plain,
% 1.54/1.73 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4481, 6644, 6636])).
% 1.54/1.73 tff(6646,plain,
% 1.54/1.73 ((s(elem!1) = s(s(z))) <=> (s(s(elem!1)) = s(s(z)))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[109])).
% 1.54/1.73 tff(6647,plain,
% 1.54/1.73 ((s(elem!1) = s(s(z))) <=> (s(s(z)) = s(s(elem!1)))),
% 1.54/1.73 inference(transitivity,[status(thm)],[6646, 2517])).
% 1.54/1.73 tff(6648,plain,
% 1.54/1.73 ((s(s(z)) = s(s(elem!1))) <=> (s(elem!1) = s(s(z)))),
% 1.54/1.73 inference(symmetry,[status(thm)],[6647])).
% 1.54/1.73 tff(6649,plain,
% 1.54/1.73 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(z)))),
% 1.54/1.73 inference(transitivity,[status(thm)],[6626, 6648])).
% 1.54/1.73 tff(6650,plain,
% 1.54/1.73 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(elem!1) = s(s(z))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[6649])).
% 1.54/1.73 tff(6651,plain,
% 1.54/1.73 (~(s(elem!1) = s(s(z)))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[231, 6650])).
% 1.54/1.73 tff(6652,plain,
% 1.54/1.73 (r(s(elem!1), s(z))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[2169, 797])).
% 1.54/1.73 tff(6653,plain,
% 1.54/1.73 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(z)))),
% 1.54/1.73 inference(commutativity,[status(thm)],[])).
% 1.54/1.73 tff(6654,plain,
% 1.54/1.73 ((s(s(s(z))) = s(s(z))) <=> (s(s(z)) = s(s(s(z))))),
% 1.54/1.73 inference(symmetry,[status(thm)],[6653])).
% 1.54/1.73 tff(6655,plain,
% 1.54/1.73 ((~(s(s(s(z))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(z)))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[6654])).
% 1.54/1.73 tff(6656,plain,
% 1.54/1.73 (~(s(s(z)) = s(s(s(z))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[2248, 6655])).
% 1.54/1.73 tff(6657,plain,
% 1.54/1.73 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[6514, 2618, 5177, 70, 2706, 6492])).
% 1.54/1.73 tff(6658,plain,
% 1.54/1.73 (b(s(s(s(z))), s(s(s(elem!1))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3794, 6657, 3739])).
% 1.54/1.73 tff(6659,plain,
% 1.54/1.73 (b(s(s(s(z))), s(s(elem!1)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[6520, 6658, 5177])).
% 1.54/1.73 tff(6660,plain,
% 1.54/1.73 (~r(s(s(z)), s(s(elem!1)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[5702, 444, 70])).
% 1.54/1.73 tff(6661,plain,
% 1.54/1.73 (b(s(s(z)), s(s(elem!1)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[122, 6660, 6481])).
% 1.54/1.73 tff(6662,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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(z)), s(s(s(z))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(6663,plain,
% 1.54/1.73 (((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(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(z)), s(s(s(z))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(6664,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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(z)), s(s(s(z)))))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[6663])).
% 1.54/1.73 tff(6665,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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(z)), s(s(s(z))))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[6664, 6662])).
% 1.54/1.73 tff(6666,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(6667,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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(z)), s(s(s(z)))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[6666, 6665])).
% 1.54/1.73 tff(6668,plain,
% 1.54/1.73 (~b(s(s(z)), s(s(s(z))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[6667, 319, 6661, 496, 6659])).
% 1.54/1.73 tff(6669,plain,
% 1.54/1.73 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z)))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(6670,plain,
% 1.54/1.73 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z)))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(6671,plain,
% 1.54/1.73 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[6670, 6669])).
% 1.54/1.73 tff(6672,plain,
% 1.54/1.73 ((s(s(z)) = s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[6671, 51, 6668])).
% 1.54/1.73 tff(6673,plain,
% 1.54/1.73 (r(s(s(z)), s(s(s(z))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[6672, 6656])).
% 1.54/1.73 tff(6674,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(6675,plain,
% 1.54/1.73 (((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(6676,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[6675])).
% 1.54/1.73 tff(6677,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[6676, 6674])).
% 1.54/1.73 tff(6678,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(6679,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[6678, 6677])).
% 1.54/1.73 tff(6680,plain,
% 1.54/1.73 (~b(s(s(s(z))), s(s(z)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[6679, 319, 6661, 496, 6659])).
% 1.54/1.73 tff(6681,plain,
% 1.54/1.73 (r(s(s(s(z))), s(s(z)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2920, 6680])).
% 1.54/1.73 tff(6682,plain,
% 1.54/1.73 (~b(s(s(s(z))), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[5550, 6659, 496, 2706])).
% 1.54/1.73 tff(6683,plain,
% 1.54/1.73 (r(s(s(s(z))), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4584, 6682])).
% 1.54/1.73 tff(6684,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[895, 297, 732, 889, 5978])).
% 1.54/1.73 tff(6685,plain,((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(6686,plain,
% 1.54/1.73 (~r(z, s(s(z)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[6685, 6683, 6681])).
% 1.54/1.73 tff(6687,plain,
% 1.54/1.73 (b(z, s(s(z)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[729, 6686])).
% 1.54/1.73 tff(6688,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(6689,plain,
% 1.54/1.73 (((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z))) <=> ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(6690,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[6689])).
% 1.54/1.73 tff(6691,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)))),
% 1.54/1.73 inference(transitivity,[status(thm)],[6690, 6688])).
% 1.54/1.73 tff(6692,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(6693,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[6692, 6691])).
% 1.54/1.73 tff(6694,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[6693, 319, 3926, 711, 786, 687])).
% 1.54/1.73 tff(6695,plain,((~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)) | (~b(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(6696,plain,
% 1.54/1.73 (~b(s(elem!1), s(s(z)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[6695, 6687, 786, 6661])).
% 1.54/1.73 tff(6697,plain,
% 1.54/1.73 (r(s(elem!1), s(s(z)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2529, 6696, 2523])).
% 1.54/1.73 tff(6698,plain,
% 1.54/1.73 (~r(s(s(z)), s(z))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2538, 6697, 800])).
% 1.54/1.73 tff(6699,plain,
% 1.54/1.73 (b(s(s(z)), s(z))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4102, 6698])).
% 1.54/1.73 tff(6700,plain,
% 1.54/1.73 (~b(s(s(z)), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[5730, 6699, 2618, 6687])).
% 1.54/1.73 tff(6701,plain,
% 1.54/1.73 ((z = s(s(s(z)))) <=> (s(s(s(z))) = z)),
% 1.54/1.73 inference(commutativity,[status(thm)],[])).
% 1.54/1.73 tff(6702,plain,
% 1.54/1.73 ((s(s(s(z))) = z) <=> (z = s(s(s(z))))),
% 1.54/1.73 inference(symmetry,[status(thm)],[6701])).
% 1.54/1.73 tff(6703,plain,
% 1.54/1.73 ((~(s(s(s(z))) = z)) <=> (~(z = s(s(s(z)))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[6702])).
% 1.54/1.73 tff(6704,plain,
% 1.54/1.73 (~(z = s(s(s(z))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[898, 6703])).
% 1.54/1.73 tff(6705,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(6706,plain,
% 1.54/1.73 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(6707,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z)))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[6706])).
% 1.54/1.73 tff(6708,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[6707, 6705])).
% 1.54/1.74 tff(6709,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(6710,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z)))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[6709, 6708])).
% 1.54/1.74 tff(6711,plain,
% 1.54/1.74 (~b(z, s(s(s(z))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[6710, 319, 2706, 2493, 2965])).
% 1.54/1.74 tff(6712,plain,
% 1.54/1.74 (((~![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)))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(6713,plain,
% 1.54/1.74 ((~![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)))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(6714,plain,
% 1.54/1.74 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[6713, 6712])).
% 1.54/1.74 tff(6715,plain,
% 1.54/1.74 ((z = s(s(s(z)))) | r(z, s(s(s(z))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[6714, 51, 6711])).
% 1.54/1.74 tff(6716,plain,
% 1.54/1.74 (r(z, s(s(s(z))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[6715, 6704])).
% 1.54/1.74 tff(6717,plain,
% 1.54/1.74 (~r(s(s(z)), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3508, 6716, 3502])).
% 1.54/1.74 tff(6718,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[663, 51, 28, 2604, 6717])).
% 1.54/1.74 tff(6719,plain,(b(s(s(z)), z) | (~r(s(s(z)), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(6720,plain,
% 1.54/1.74 (~b(s(s(s(z))), s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[6719, 6700, 2706, 2618, 6673])).
% 1.54/1.74 tff(6721,plain,
% 1.54/1.74 (r(s(s(s(z))), s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4549, 6720])).
% 1.54/1.74 tff(6722,plain,
% 1.54/1.74 (~b(s(z), s(s(z)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4795, 6699, 6687, 2706])).
% 1.54/1.74 tff(6723,plain,
% 1.54/1.74 (r(s(z), s(s(z)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[685, 6722])).
% 1.54/1.74 tff(6724,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[906, 297, 6723, 6681, 6721])).
% 1.54/1.74 tff(6725,plain,((~r(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~r(s(elem!1), s(z))) | (s(elem!1) = s(s(z))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(6726,plain,
% 1.54/1.74 (~r(s(z), s(s(elem!1)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[6725, 6392, 6652, 6651, 786, 6632, 6625, 6645, 70])).
% 1.54/1.74 tff(6727,plain,
% 1.54/1.74 (b(s(z), s(s(elem!1)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1047, 6726])).
% 1.54/1.74 tff(6728,plain,
% 1.54/1.74 (~b(s(z), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[5526, 6392, 6727, 6632])).
% 1.54/1.74 tff(6729,plain,
% 1.54/1.74 (r(s(z), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[65, 51, 62, 6728])).
% 1.54/1.74 tff(6730,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(6731,plain,
% 1.54/1.74 (((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(6732,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[6731])).
% 1.54/1.74 tff(6733,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[6732, 6730])).
% 1.54/1.74 tff(6734,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(6735,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[6734, 6733])).
% 1.54/1.74 tff(6736,plain,
% 1.54/1.74 (~b(s(s(z)), s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[6735, 319, 687, 817, 496])).
% 1.54/1.74 tff(6737,plain,
% 1.54/1.74 (r(s(s(z)), s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4102, 6736])).
% 1.54/1.74 tff(6738,plain,
% 1.54/1.74 (~r(s(elem!1), s(s(z)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2538, 6737, 800])).
% 1.54/1.74 tff(6739,plain,
% 1.54/1.74 (b(s(elem!1), s(s(z)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2529, 6738, 2523])).
% 1.54/1.74 tff(6740,plain,
% 1.54/1.74 (~b(z, s(s(z)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[6695, 6739, 786, 687])).
% 1.54/1.74 tff(6741,plain,
% 1.54/1.74 (r(z, s(s(z)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[729, 6740])).
% 1.54/1.74 tff(6742,plain,
% 1.54/1.74 (~b(s(z), s(s(z)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[6418, 319, 687, 817, 496])).
% 1.54/1.74 tff(6743,plain,
% 1.54/1.74 (r(s(z), s(s(z)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[685, 6742])).
% 1.54/1.74 tff(6744,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[839, 297, 666, 6743, 6741])).
% 1.54/1.74 tff(6745,plain,((~b(s(s(z)), s(s(elem!1)))) | (~r(s(z), z)) | (~b(s(elem!1), z)) | (s(elem!1) = s(s(z))) | (~r(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(6746,plain,
% 1.54/1.74 (~b(s(s(z)), s(s(elem!1)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[6745, 6729, 786, 6651, 6652, 6727, 6632])).
% 1.54/1.74 tff(6747,plain,
% 1.54/1.74 (r(s(s(z)), s(s(elem!1)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[122, 6746, 6631])).
% 1.54/1.74 tff(6748,plain,
% 1.54/1.74 (~r(s(s(z)), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3875, 297, 6747, 70])).
% 1.54/1.74 tff(6749,plain,
% 1.54/1.74 (b(s(s(z)), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[663, 51, 28, 6748])).
% 1.54/1.74 tff(6750,plain,
% 1.54/1.74 (~r(z, s(s(z)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3463, 6747, 70])).
% 1.54/1.74 tff(6751,plain,
% 1.54/1.74 (b(z, s(s(z)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[729, 6750])).
% 1.54/1.74 tff(6752,plain,
% 1.54/1.74 (~b(s(s(elem!1)), s(s(z)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4213, 319, 6751, 6632, 6749])).
% 1.54/1.74 tff(6753,plain,
% 1.54/1.74 (r(s(s(elem!1)), s(s(z)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2555, 51, 6752, 6629])).
% 1.54/1.74 tff(6754,plain,
% 1.54/1.74 (~r(s(s(z)), s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4108, 6747, 2169])).
% 1.54/1.74 tff(6755,plain,
% 1.54/1.74 (b(s(s(z)), s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4102, 6754])).
% 1.54/1.74 tff(6756,plain,
% 1.54/1.74 (~b(s(z), s(s(z)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4795, 6755, 6751, 6392])).
% 1.54/1.74 tff(6757,plain,
% 1.54/1.74 (r(s(z), s(s(z)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[685, 6756])).
% 1.54/1.74 tff(6758,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[6402, 297, 2169, 6757, 6753])).
% 1.54/1.74 tff(6759,plain,((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~(s(elem!1) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(6760,plain,
% 1.54/1.74 (~b(s(elem!1), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[6759, 2169, 6459, 70])).
% 1.54/1.74 tff(6761,plain,
% 1.54/1.74 (b(s(elem!1), z) <=> b(s(s(elem!1)), z)),
% 1.54/1.74 inference(monotonicity,[status(thm)],[5180])).
% 1.54/1.74 tff(6762,plain,
% 1.54/1.74 (b(s(s(elem!1)), z) <=> b(s(elem!1), z)),
% 1.54/1.74 inference(symmetry,[status(thm)],[6761])).
% 1.54/1.74 tff(6763,plain,
% 1.54/1.74 (b(s(elem!1), z)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[496, 6762])).
% 1.54/1.74 tff(6764,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1174, 6763])).
% 1.54/1.74 tff(6765,plain,((~(s(s(s(elem!1))) = s(s(elem!1)))) | b(s(elem!1), z) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(6766,plain,
% 1.54/1.74 (~b(s(s(elem!1)), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[6765, 6760, 5177])).
% 1.54/1.74 tff(6767,plain,
% 1.54/1.74 (r(s(s(elem!1)), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[75, 6766])).
% 1.54/1.74 tff(6768,plain,
% 1.54/1.74 (~r(s(s(elem!1)), s(s(z)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4014, 6767, 732])).
% 1.54/1.74 tff(6769,plain,
% 1.54/1.74 (b(s(s(elem!1)), s(s(z)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[5327, 6768, 6478])).
% 1.54/1.74 tff(6770,plain,
% 1.54/1.74 (s(s(elem!1)) = elem!1),
% 1.54/1.74 inference(transitivity,[status(thm)],[5178, 6452])).
% 1.54/1.74 tff(6771,plain,
% 1.54/1.74 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[6770])).
% 1.54/1.74 tff(6772,plain,
% 1.54/1.74 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.54/1.74 inference(symmetry,[status(thm)],[6771])).
% 1.54/1.74 tff(6773,plain,
% 1.54/1.74 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[3799, 6772])).
% 1.54/1.74 tff(6774,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[6348, 6773])).
% 1.54/1.74 tff(6775,plain,(r(s(s(elem!1)), s(s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))) | (~(s(s(s(elem!1))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(6776,plain,
% 1.54/1.74 (~r(elem!1, s(s(s(s(z)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[6775, 6348, 5177])).
% 1.54/1.74 tff(6777,plain,
% 1.54/1.74 (b(elem!1, s(s(s(s(z)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3036, 6776, 6473])).
% 1.54/1.74 tff(6778,plain,
% 1.54/1.74 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[6770])).
% 1.54/1.74 tff(6779,plain,
% 1.54/1.74 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.54/1.74 inference(symmetry,[status(thm)],[6778])).
% 1.54/1.74 tff(6780,assumption,(b(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.74 tff(6781,plain,
% 1.54/1.74 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[6780, 6779])).
% 1.54/1.74 tff(6782,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(6783,plain,
% 1.54/1.74 (((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(6784,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[6783])).
% 1.54/1.74 tff(6785,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[6784, 6782])).
% 1.54/1.74 tff(6786,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(6787,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[6786, 6785])).
% 1.54/1.74 tff(6788,plain,
% 1.54/1.74 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[6787, 319, 687, 3138, 4230])).
% 1.54/1.74 tff(6789,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[6788, 6781])).
% 1.54/1.74 tff(6790,plain,((~b(elem!1, s(s(s(s(z)))))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(6791,plain,
% 1.54/1.74 (~b(s(s(s(z))), s(s(z)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[6790, 6777, 5177, 687, 4230])).
% 1.54/1.74 tff(6792,plain,
% 1.54/1.74 (r(s(s(s(z))), s(s(z)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2920, 6791])).
% 1.54/1.74 tff(6793,plain,
% 1.54/1.74 (~r(s(s(s(z))), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[6685, 6792, 732])).
% 1.54/1.74 tff(6794,plain,
% 1.54/1.74 (b(s(s(s(z))), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4584, 6793])).
% 1.54/1.74 tff(6795,plain,
% 1.54/1.74 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[6350, 6348, 6474])).
% 1.54/1.74 tff(6796,plain,
% 1.54/1.74 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(6797,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z)))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[6796])).
% 1.54/1.74 tff(6798,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[6797, 6507])).
% 1.54/1.74 tff(6799,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(6800,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z)))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[6799, 6798])).
% 1.54/1.74 tff(6801,plain,
% 1.54/1.74 (~b(s(s(s(z))), s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[6800, 319, 2706, 2493, 6794])).
% 1.54/1.74 tff(6802,plain,
% 1.54/1.74 (r(s(s(s(z))), s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4549, 6801])).
% 1.54/1.74 tff(6803,plain,
% 1.54/1.74 (~r(s(s(z)), s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4544, 6802, 6792])).
% 1.54/1.74 tff(6804,plain,
% 1.54/1.74 (b(s(s(z)), s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4102, 6803])).
% 1.54/1.74 tff(6805,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(z)))), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(6806,plain,
% 1.54/1.74 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(6807,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(z)))), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[6806])).
% 1.54/1.74 tff(6808,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(z)))), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[6807, 6805])).
% 1.54/1.74 tff(6809,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(6810,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[6809, 6808])).
% 1.54/1.74 tff(6811,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[6810, 319, 3390, 2543, 6158, 6352])).
% 1.54/1.74 tff(6812,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(6813,plain,
% 1.54/1.74 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[6812, 6804, 2543, 6795])).
% 1.54/1.74 tff(6814,plain,
% 1.54/1.74 (r(s(s(s(s(z)))), s(s(z)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[6174, 6813])).
% 1.54/1.74 tff(6815,plain,
% 1.54/1.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(6816,plain,
% 1.54/1.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(6817,plain,
% 1.54/1.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[6816, 6815])).
% 1.54/1.74 tff(6818,plain,
% 1.54/1.74 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[6817, 297, 6792, 6814])).
% 1.54/1.74 tff(6819,plain,
% 1.54/1.74 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2252, 6818])).
% 1.54/1.74 tff(6820,plain,
% 1.54/1.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(6821,plain,
% 1.54/1.74 (((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(6822,plain,
% 1.54/1.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[6821])).
% 1.54/1.74 tff(6823,plain,
% 1.54/1.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[6822, 6820])).
% 1.54/1.74 tff(6824,plain,
% 1.54/1.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(6825,plain,
% 1.54/1.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[6824, 6823])).
% 1.54/1.75 tff(6826,plain,
% 1.54/1.75 (~r(s(s(s(s(z)))), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6825, 297, 732, 6814])).
% 1.54/1.75 tff(6827,plain,
% 1.54/1.75 (b(s(s(s(s(z)))), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2482, 6826])).
% 1.54/1.75 tff(6828,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(6829,plain,
% 1.54/1.75 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(6830,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[6829])).
% 1.54/1.75 tff(6831,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.54/1.75 inference(transitivity,[status(thm)],[6830, 6828])).
% 1.54/1.75 tff(6832,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(6833,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[6832, 6831])).
% 1.54/1.75 tff(6834,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6833, 319, 2706, 6827, 6819, 6794])).
% 1.54/1.75 tff(6835,plain,(r(s(s(elem!1)), s(s(s(s(z))))) | (~b(z, s(z))) | (~r(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), z)) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(6836,plain,
% 1.54/1.75 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6835, 6769, 732, 2706, 2493, 5177, 6624, 4230])).
% 1.54/1.75 tff(6837,plain,
% 1.54/1.75 (~r(s(s(s(s(z)))), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2452, 6836, 2169])).
% 1.54/1.75 tff(6838,plain,
% 1.54/1.75 (b(s(s(s(s(z)))), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2461, 6837])).
% 1.54/1.75 tff(6839,plain,
% 1.54/1.75 (~r(s(s(s(s(z)))), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2475, 6836, 6767])).
% 1.54/1.75 tff(6840,plain,
% 1.54/1.75 (b(s(s(s(s(z)))), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2482, 6839])).
% 1.54/1.75 tff(6841,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(6842,plain,
% 1.54/1.75 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(6843,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[6842])).
% 1.54/1.75 tff(6844,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)))),
% 1.54/1.75 inference(transitivity,[status(thm)],[6843, 6841])).
% 1.54/1.75 tff(6845,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(6846,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[6845, 6844])).
% 1.54/1.75 tff(6847,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6846, 319, 2706, 2493, 6840, 6838])).
% 1.54/1.75 tff(6848,plain,((~r(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(z, s(s(z)))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(6849,plain,
% 1.54/1.75 (~r(s(s(elem!1)), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6848, 6489, 6485, 732, 5177, 6521, 70])).
% 1.54/1.75 tff(6850,plain,
% 1.54/1.75 (b(s(s(elem!1)), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[871, 6849])).
% 1.54/1.75 tff(6851,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(6852,plain,
% 1.54/1.75 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(6853,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[6852])).
% 1.54/1.75 tff(6854,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[6853, 6851])).
% 1.54/1.75 tff(6855,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(6856,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[6855, 6854])).
% 1.54/1.75 tff(6857,plain,
% 1.54/1.75 (~b(s(s(s(z))), s(s(z)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6856, 319, 6850, 6624, 6521])).
% 1.54/1.75 tff(6858,plain,
% 1.54/1.75 (r(s(s(s(z))), s(s(z)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2920, 6857])).
% 1.54/1.75 tff(6859,plain,
% 1.54/1.75 (~r(s(s(s(z))), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6685, 6858, 732])).
% 1.54/1.75 tff(6860,plain,
% 1.54/1.75 (b(s(s(s(z))), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4584, 6859])).
% 1.54/1.75 tff(6861,plain,
% 1.54/1.75 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[5177])).
% 1.54/1.75 tff(6862,plain,
% 1.54/1.75 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.54/1.75 inference(symmetry,[status(thm)],[6861])).
% 1.54/1.75 tff(6863,plain,
% 1.54/1.75 (b(s(s(s(elem!1))), s(z))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[6850, 6862])).
% 1.54/1.75 tff(6864,plain,
% 1.54/1.75 (~b(s(s(z)), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4745, 6863, 6489, 6485])).
% 1.54/1.75 tff(6865,plain,
% 1.54/1.75 (r(s(s(z)), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4102, 6864])).
% 1.54/1.75 tff(6866,plain,
% 1.54/1.75 (~r(s(s(s(z))), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4544, 6865, 6858])).
% 1.54/1.75 tff(6867,plain,
% 1.54/1.75 (b(s(s(s(z))), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4549, 6866])).
% 1.54/1.75 tff(6868,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6800, 319, 6489, 6485, 6867, 6860])).
% 1.54/1.75 tff(6869,plain,((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(6870,plain,
% 1.54/1.75 (~r(s(z), s(s(elem!1)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6869, 732, 5177, 70])).
% 1.54/1.75 tff(6871,plain,
% 1.54/1.75 (b(s(z), s(s(elem!1)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1047, 6870])).
% 1.54/1.75 tff(6872,plain,
% 1.54/1.75 (b(s(z), elem!1)),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[6871, 6484])).
% 1.54/1.75 tff(6873,plain,
% 1.54/1.75 (~r(s(z), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[5094, 6767, 2169])).
% 1.54/1.75 tff(6874,plain,
% 1.54/1.75 (b(s(z), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[67, 6873])).
% 1.54/1.75 tff(6875,plain,
% 1.54/1.75 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6848, 6874, 2169, 732, 5177, 6392, 70])).
% 1.54/1.75 tff(6876,plain,
% 1.54/1.75 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6520, 6875, 5177])).
% 1.54/1.75 tff(6877,plain,
% 1.54/1.75 (r(s(s(s(z))), s(s(s(elem!1))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3794, 6876, 6482])).
% 1.54/1.75 tff(6878,plain,
% 1.54/1.75 (r(s(s(s(z))), s(s(elem!1)))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[6877, 6479])).
% 1.54/1.75 tff(6879,plain,
% 1.54/1.75 (~r(s(s(s(z))), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6501, 297, 70, 6878])).
% 1.54/1.75 tff(6880,plain,
% 1.54/1.75 (b(s(s(s(z))), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4584, 6879])).
% 1.54/1.75 tff(6881,assumption,(r(s(s(s(z))), s(s(elem!1)))), introduced(assumption)).
% 1.54/1.75 tff(6882,plain,
% 1.54/1.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(6883,plain,
% 1.54/1.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(6884,plain,
% 1.54/1.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[6883, 6882])).
% 1.54/1.75 tff(6885,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6884, 297, 2169, 4539, 6881])).
% 1.54/1.75 tff(6886,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(6887,plain,
% 1.54/1.75 (~r(s(s(s(z))), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6886, 2169, 6878])).
% 1.54/1.75 tff(6888,plain,
% 1.54/1.75 (b(s(s(s(z))), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4549, 6887])).
% 1.54/1.75 tff(6889,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6800, 319, 6392, 6874, 6888, 6880])).
% 1.54/1.75 tff(6890,plain,((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(6891,plain,
% 1.54/1.75 (~r(s(s(elem!1)), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6890, 732, 5177, 70])).
% 1.54/1.75 tff(6892,plain,
% 1.54/1.75 (b(s(s(elem!1)), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[871, 6891])).
% 1.54/1.75 tff(6893,plain,
% 1.54/1.75 (~b(s(z), s(s(z)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[5317, 6892, 6624, 6871])).
% 1.54/1.75 tff(6894,plain,
% 1.54/1.75 (r(s(z), s(s(z)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[685, 6893])).
% 1.54/1.75 tff(6895,plain,
% 1.54/1.75 (~r(s(s(s(z))), s(s(z)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[935, 6894, 732, 6872])).
% 1.54/1.75 tff(6896,plain,
% 1.54/1.75 (b(s(s(s(z))), s(s(z)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2920, 6895])).
% 1.54/1.75 tff(6897,plain,
% 1.54/1.75 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(elem!1)))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[5177])).
% 1.54/1.75 tff(6898,plain,
% 1.54/1.75 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 1.54/1.75 inference(symmetry,[status(thm)],[6897])).
% 1.54/1.75 tff(6899,plain,
% 1.54/1.75 (b(s(s(z)), s(s(s(elem!1))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[6624, 6898])).
% 1.54/1.75 tff(6900,plain,
% 1.54/1.75 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[5177])).
% 1.54/1.75 tff(6901,plain,
% 1.54/1.75 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 1.54/1.75 inference(symmetry,[status(thm)],[6900])).
% 1.54/1.75 tff(6902,plain,
% 1.54/1.75 (~r(z, s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[922, 6894, 732])).
% 1.54/1.75 tff(6903,plain,
% 1.54/1.75 (b(z, s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1099, 6902])).
% 1.54/1.75 tff(6904,plain,
% 1.54/1.75 (~r(s(z), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6004, 6894, 732])).
% 1.54/1.75 tff(6905,plain,
% 1.54/1.75 (b(s(z), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[67, 6904])).
% 1.54/1.75 tff(6906,plain,
% 1.54/1.75 (~b(s(s(elem!1)), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[5526, 6905, 6871, 6903])).
% 1.54/1.75 tff(6907,plain,
% 1.54/1.75 (r(s(s(elem!1)), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[75, 6906])).
% 1.54/1.75 tff(6908,plain,
% 1.54/1.75 (~r(s(s(elem!1)), s(s(z)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4014, 6907, 732])).
% 1.54/1.75 tff(6909,plain,
% 1.54/1.75 (b(s(s(elem!1)), s(s(z)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[5327, 6908, 6478])).
% 1.54/1.75 tff(6910,plain,
% 1.54/1.75 (b(s(s(s(elem!1))), s(s(z)))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[6909, 6901])).
% 1.54/1.75 tff(6911,plain,
% 1.54/1.75 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4571, 6910, 6899, 6896])).
% 1.54/1.75 tff(6912,plain,
% 1.54/1.75 (r(s(s(s(z))), s(s(s(elem!1))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3794, 6911, 6482])).
% 1.54/1.75 tff(6913,plain,
% 1.54/1.75 (r(s(s(s(z))), s(s(elem!1)))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[6912, 6479])).
% 1.54/1.75 tff(6914,plain,
% 1.54/1.75 (~r(s(s(s(z))), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6501, 297, 70, 6913])).
% 1.54/1.75 tff(6915,plain,
% 1.54/1.75 (b(s(s(s(z))), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4584, 6914])).
% 1.54/1.75 tff(6916,plain,
% 1.54/1.75 ((s(z) = s(elem!1)) <=> (s(z) = s(s(elem!1)))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[6459])).
% 1.54/1.75 tff(6917,plain,
% 1.54/1.75 ((s(z) = s(elem!1)) <=> (s(s(elem!1)) = s(z))),
% 1.54/1.75 inference(transitivity,[status(thm)],[6916, 809])).
% 1.54/1.75 tff(6918,plain,
% 1.54/1.75 ((s(s(elem!1)) = s(z)) <=> (s(z) = s(elem!1))),
% 1.54/1.75 inference(symmetry,[status(thm)],[6917])).
% 1.54/1.75 tff(6919,plain,
% 1.54/1.75 ((s(s(elem!1)) = s(z)) <=> (s(elem!1) = s(z))),
% 1.54/1.75 inference(transitivity,[status(thm)],[6918, 2500])).
% 1.54/1.75 tff(6920,plain,
% 1.54/1.75 ((~(s(s(elem!1)) = s(z))) <=> (~(s(elem!1) = s(z)))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[6919])).
% 1.54/1.75 tff(6921,plain,
% 1.54/1.75 (~(s(elem!1) = s(z))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[209, 6920])).
% 1.54/1.75 tff(6922,plain,
% 1.54/1.75 (~r(s(elem!1), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[802, 6891, 6459])).
% 1.54/1.75 tff(6923,plain,
% 1.54/1.75 (b(s(elem!1), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[783, 6922, 6921])).
% 1.54/1.75 tff(6924,plain,
% 1.54/1.75 (r(s(z), s(elem!1)) <=> r(s(z), s(s(elem!1)))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[6459])).
% 1.54/1.75 tff(6925,plain,
% 1.54/1.75 (r(s(z), s(s(elem!1))) <=> r(s(z), s(elem!1))),
% 1.54/1.75 inference(symmetry,[status(thm)],[6924])).
% 1.54/1.75 tff(6926,plain,
% 1.54/1.75 ((~r(s(z), s(s(elem!1)))) <=> (~r(s(z), s(elem!1)))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[6925])).
% 1.54/1.75 tff(6927,plain,
% 1.54/1.75 (~r(s(z), s(elem!1))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[6870, 6926])).
% 1.54/1.75 tff(6928,plain,
% 1.54/1.75 (~b(s(elem!1), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[5175, 6906, 6459])).
% 1.54/1.75 tff(6929,plain,
% 1.54/1.75 (r(s(elem!1), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2602, 6928])).
% 1.54/1.75 tff(6930,plain,
% 1.54/1.75 (~r(s(elem!1), s(s(z)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[740, 6929, 732])).
% 1.54/1.75 tff(6931,plain,
% 1.54/1.75 ((elem!1 = z) <=> (z = elem!1)),
% 1.54/1.75 inference(commutativity,[status(thm)],[])).
% 1.54/1.75 tff(6932,assumption,(s(s(s(elem!1))) = elem!1), introduced(assumption)).
% 1.54/1.75 tff(6933,plain,
% 1.54/1.75 ((s(s(s(elem!1))) = z) <=> (elem!1 = z)),
% 1.54/1.75 inference(monotonicity,[status(thm)],[6932])).
% 1.54/1.75 tff(6934,plain,
% 1.54/1.75 ((s(s(s(elem!1))) = z) <=> (z = elem!1)),
% 1.54/1.75 inference(transitivity,[status(thm)],[6933, 6931])).
% 1.54/1.75 tff(6935,plain,
% 1.54/1.75 ((~(s(s(s(elem!1))) = z)) <=> (~(z = elem!1))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[6934])).
% 1.54/1.75 tff(6936,plain,
% 1.54/1.75 (~(z = elem!1)),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[160, 6935])).
% 1.54/1.75 tff(6937,plain,
% 1.54/1.75 (~(s(z) = s(elem!1))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[148, 6936])).
% 1.54/1.75 tff(6938,plain,
% 1.54/1.75 ((s(z) = s(elem!1)) | b(s(z), s(elem!1))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2638, 51, 4814])).
% 1.54/1.75 tff(6939,plain,
% 1.54/1.75 (b(s(z), s(elem!1))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6938, 6937])).
% 1.54/1.75 tff(6940,plain,
% 1.54/1.75 ((elem!1 = s(z)) <=> (s(z) = elem!1)),
% 1.54/1.75 inference(commutativity,[status(thm)],[])).
% 1.54/1.75 tff(6941,plain,
% 1.54/1.75 ((s(s(s(elem!1))) = s(z)) <=> (elem!1 = s(z))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[6932])).
% 1.54/1.75 tff(6942,plain,
% 1.54/1.75 ((s(s(s(elem!1))) = s(z)) <=> (s(z) = elem!1)),
% 1.54/1.75 inference(transitivity,[status(thm)],[6941, 6940])).
% 1.54/1.75 tff(6943,plain,
% 1.54/1.75 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(z) = elem!1))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[6942])).
% 1.54/1.75 tff(6944,plain,
% 1.54/1.75 (~(s(z) = elem!1)),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[171, 6943])).
% 1.54/1.75 tff(6945,plain,
% 1.54/1.75 (~(s(elem!1) = s(s(z)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3419, 6944])).
% 1.54/1.75 tff(6946,plain,
% 1.54/1.75 (b(s(elem!1), s(s(z)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2529, 6945, 2524])).
% 1.54/1.75 tff(6947,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(z))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(6948,plain,
% 1.54/1.75 (((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(z))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(6949,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(z)))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[6948])).
% 1.54/1.75 tff(6950,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(z))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[6949, 6947])).
% 1.54/1.75 tff(6951,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(6952,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(z)))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[6951, 6950])).
% 1.54/1.75 tff(6953,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6952, 319, 3390, 6946, 2541, 6939])).
% 1.54/1.75 tff(6954,plain,((~(s(s(s(elem!1))) = elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | r(s(elem!1), s(s(z))) | r(s(z), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(6955,plain,
% 1.54/1.75 (~b(s(s(z)), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6954, 6930, 6452, 6927, 6923])).
% 1.54/1.75 tff(6956,plain,
% 1.54/1.75 (r(s(s(z)), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4102, 6955])).
% 1.54/1.75 tff(6957,plain,
% 1.54/1.75 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3009, 6570, 2511])).
% 1.54/1.75 tff(6958,plain,
% 1.54/1.75 (b(s(s(s(s(z)))), s(s(z)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6174, 6957])).
% 1.54/1.75 tff(6959,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(z)))), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(6960,plain,
% 1.54/1.75 (((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(6961,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(z)))), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[6960])).
% 1.54/1.75 tff(6962,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(z)))), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[6961, 6959])).
% 1.54/1.75 tff(6963,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(6964,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[6963, 6962])).
% 1.54/1.75 tff(6965,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6964, 319, 2543, 687, 6958, 6352])).
% 1.54/1.75 tff(6966,plain,((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(6967,plain,
% 1.54/1.75 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6966, 6909, 6624, 6956, 6871, 6892])).
% 1.54/1.75 tff(6968,plain,
% 1.54/1.75 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6350, 6967, 6474])).
% 1.54/1.75 tff(6969,plain,
% 1.54/1.75 (~r(s(s(s(s(z)))), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2475, 6968, 6907])).
% 1.54/1.75 tff(6970,plain,
% 1.54/1.75 (b(s(s(s(s(z)))), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2482, 6969])).
% 1.54/1.75 tff(6971,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(6972,plain,
% 1.54/1.75 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(6973,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[6972])).
% 1.54/1.76 tff(6974,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[6973, 6971])).
% 1.54/1.76 tff(6975,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(6976,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[6975, 6974])).
% 1.54/1.76 tff(6977,plain,
% 1.54/1.76 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[6976, 319, 6903, 6970, 6915])).
% 1.54/1.76 tff(6978,plain,
% 1.54/1.76 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2281, 6977])).
% 1.54/1.76 tff(6979,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(6980,plain,
% 1.54/1.76 (((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(6981,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z)))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[6980])).
% 1.54/1.76 tff(6982,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[6981, 6979])).
% 1.54/1.76 tff(6983,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(6984,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[6983, 6982])).
% 1.54/1.76 tff(6985,plain,
% 1.54/1.76 (~b(s(s(s(z))), s(z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[6984, 319, 6892, 6903, 6871, 6905, 6915])).
% 1.54/1.76 tff(6986,plain,
% 1.54/1.76 (r(s(s(s(z))), s(z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4549, 6985])).
% 1.54/1.76 tff(6987,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(6988,plain,
% 1.54/1.76 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(6989,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[6988])).
% 1.54/1.76 tff(6990,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.54/1.76 inference(transitivity,[status(thm)],[6989, 6987])).
% 1.54/1.76 tff(6991,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(6992,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[6991, 6990])).
% 1.54/1.76 tff(6993,plain,
% 1.54/1.76 (~b(s(z), s(s(s(s(z)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[6992, 319, 6903, 6905, 6970])).
% 1.54/1.76 tff(6994,plain,
% 1.54/1.76 (r(s(z), s(s(s(s(z)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2301, 6993])).
% 1.54/1.76 tff(6995,plain,
% 1.54/1.76 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(6996,plain,
% 1.54/1.76 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(6997,plain,
% 1.54/1.76 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[6996])).
% 1.54/1.76 tff(6998,plain,
% 1.54/1.76 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[6997, 6995])).
% 1.54/1.76 tff(6999,plain,
% 1.54/1.76 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(7000,plain,
% 1.54/1.76 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[6999, 6998])).
% 1.54/1.76 tff(7001,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[7000, 297, 6994, 6986, 6978])).
% 1.54/1.76 tff(7002,plain,((~r(z, s(s(z)))) | (~r(z, s(s(elem!1)))) | (~(s(s(s(elem!1))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(7003,plain,
% 1.54/1.76 (~r(z, s(s(z)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[7002, 70, 5177])).
% 1.54/1.76 tff(7004,plain,
% 1.54/1.76 (b(z, s(s(z)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[729, 7003])).
% 1.54/1.76 tff(7005,plain,
% 1.54/1.76 (~r(s(z), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[5094, 115, 2169])).
% 1.54/1.76 tff(7006,plain,
% 1.54/1.76 (b(s(z), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[67, 7005])).
% 1.54/1.76 tff(7007,plain,
% 1.54/1.76 (~r(s(s(s(s(z)))), s(z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2452, 2443, 2169])).
% 1.54/1.76 tff(7008,plain,
% 1.54/1.76 (b(s(s(s(s(z)))), s(z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2461, 7007])).
% 1.54/1.76 tff(7009,plain,
% 1.54/1.76 (~r(s(s(s(s(z)))), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2475, 2443, 115])).
% 1.54/1.76 tff(7010,plain,
% 1.54/1.76 (b(s(s(s(s(z)))), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2482, 7009])).
% 1.54/1.76 tff(7011,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(7012,plain,
% 1.54/1.76 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(7013,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[7012])).
% 1.54/1.76 tff(7014,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.54/1.76 inference(transitivity,[status(thm)],[7013, 7011])).
% 1.54/1.76 tff(7015,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(7016,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[7015, 7014])).
% 1.54/1.76 tff(7017,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[7016, 319, 711, 2493, 7010, 7008])).
% 1.54/1.76 tff(7018,plain,((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(7019,plain,
% 1.54/1.76 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[7018, 7006, 711, 2169, 115])).
% 1.54/1.76 tff(7020,plain,
% 1.54/1.76 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[6350, 7019, 6474])).
% 1.54/1.76 tff(7021,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(7022,plain,
% 1.54/1.76 (((~b(s(s(elem!1)), s(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(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(7023,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(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(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[7022])).
% 1.54/1.76 tff(7024,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(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(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[7023, 7021])).
% 1.54/1.76 tff(7025,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(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(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(7026,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[7025, 7024])).
% 1.54/1.76 tff(7027,plain,
% 1.54/1.76 (~b(s(s(z)), s(s(s(z))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[7026, 319, 687, 4230, 7020])).
% 1.54/1.76 tff(7028,plain,
% 1.54/1.76 ((s(s(z)) = s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[6671, 51, 7027])).
% 1.54/1.76 tff(7029,plain,
% 1.54/1.76 (r(s(s(z)), s(s(s(z))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[7028, 6656])).
% 1.54/1.76 tff(7030,plain,
% 1.54/1.76 (b(s(s(z)), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[6719, 2965, 7006, 7029, 2706])).
% 1.54/1.76 tff(7031,plain,
% 1.54/1.76 (~r(s(s(elem!1)), s(s(z)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[6404, 2706, 711, 2169])).
% 1.54/1.76 tff(7032,plain,
% 1.54/1.76 (b(s(s(elem!1)), s(s(z)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[5327, 7031, 6478])).
% 1.54/1.76 tff(7033,plain,
% 1.54/1.76 (~r(elem!1, s(s(s(s(z)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[6775, 7019, 5177])).
% 1.54/1.76 tff(7034,plain,
% 1.54/1.76 (b(elem!1, s(s(s(s(z)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3036, 7033, 6473])).
% 1.54/1.76 tff(7035,plain,
% 1.54/1.76 (~b(s(s(s(z))), s(s(z)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[6790, 4230, 5177, 687, 7034])).
% 1.54/1.76 tff(7036,plain,
% 1.54/1.76 (r(s(s(s(z))), s(s(z)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2920, 7035])).
% 1.54/1.76 tff(7037,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(7038,plain,
% 1.54/1.76 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(7039,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[7038])).
% 1.54/1.76 tff(7040,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[7039, 7037])).
% 1.54/1.76 tff(7041,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(7042,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[7041, 7040])).
% 1.54/1.77 tff(7043,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[7042, 319, 711, 4787, 3204, 2493])).
% 1.54/1.77 tff(7044,plain,((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(7045,plain,
% 1.54/1.77 (~b(s(z), s(s(z)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[7044, 7030, 711, 7006])).
% 1.54/1.77 tff(7046,plain,
% 1.54/1.77 (r(s(z), s(s(z)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[685, 7045])).
% 1.54/1.77 tff(7047,plain,
% 1.54/1.77 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(7048,plain,
% 1.54/1.77 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(7049,plain,
% 1.54/1.77 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z)))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[7048])).
% 1.54/1.77 tff(7050,plain,
% 1.54/1.77 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[7049, 7047])).
% 1.54/1.77 tff(7051,plain,
% 1.54/1.77 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(7052,plain,
% 1.54/1.77 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z)))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[7051, 7050])).
% 1.54/1.77 tff(7053,plain,
% 1.54/1.77 (~r(s(z), s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[7052, 297, 7046, 7036])).
% 1.54/1.77 tff(7054,plain,
% 1.54/1.77 (b(s(z), s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[6558, 51, 7053, 32])).
% 1.54/1.77 tff(7055,plain,
% 1.54/1.77 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[5177])).
% 1.54/1.77 tff(7056,assumption,(s(s(s(elem!1))) = s(s(s(z)))), introduced(assumption)).
% 1.54/1.77 tff(7057,plain,
% 1.54/1.77 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[7056, 3395])).
% 1.54/1.77 tff(7058,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3739, 7057])).
% 1.54/1.77 tff(7059,plain,((~(s(s(s(elem!1))) = s(s(s(z))))) | (s(s(s(z))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(7060,plain,
% 1.54/1.77 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[7059, 6482])).
% 1.54/1.77 tff(7061,plain,
% 1.54/1.77 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[5177])).
% 1.54/1.77 tff(7062,plain,
% 1.54/1.77 (r(s(s(elem!1)), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 1.54/1.77 inference(symmetry,[status(thm)],[7061])).
% 1.54/1.77 tff(7063,plain,
% 1.54/1.77 ((~r(s(s(elem!1)), s(s(s(z))))) <=> (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[7062])).
% 1.54/1.77 tff(7064,plain,
% 1.54/1.77 (~b(s(s(s(z))), z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4307, 319, 2706, 7054, 2965])).
% 1.54/1.77 tff(7065,plain,
% 1.54/1.77 (r(s(s(s(z))), z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4584, 7064])).
% 1.54/1.77 tff(7066,plain,
% 1.54/1.77 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(7067,plain,
% 1.54/1.77 (((~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(z)))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(7068,plain,
% 1.54/1.77 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[7067])).
% 1.54/1.77 tff(7069,plain,
% 1.54/1.77 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[7068, 7066])).
% 1.54/1.77 tff(7070,plain,
% 1.54/1.77 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(7071,plain,
% 1.54/1.77 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[7070, 7069])).
% 1.54/1.77 tff(7072,plain,
% 1.54/1.77 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[7071, 297, 115, 7065])).
% 1.54/1.77 tff(7073,plain,
% 1.54/1.77 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[7072, 7063])).
% 1.54/1.77 tff(7074,plain,
% 1.54/1.77 (b(s(s(s(elem!1))), s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3600, 7073, 7060])).
% 1.54/1.77 tff(7075,plain,
% 1.54/1.77 (b(s(s(elem!1)), s(s(s(z))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[7074, 7055])).
% 1.54/1.77 tff(7076,plain,
% 1.54/1.77 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), elem!1)),
% 1.54/1.77 inference(monotonicity,[status(thm)],[6770])).
% 1.54/1.77 tff(7077,plain,
% 1.54/1.77 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.54/1.77 inference(symmetry,[status(thm)],[7076])).
% 1.54/1.77 tff(7078,plain,
% 1.54/1.77 ((~(elem!1 = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[6118])).
% 1.54/1.77 tff(7079,plain,
% 1.54/1.77 (~(s(s(s(s(z)))) = elem!1)),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[6473, 7078])).
% 1.54/1.77 tff(7080,plain,
% 1.54/1.77 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), elem!1)),
% 1.54/1.77 inference(monotonicity,[status(thm)],[6770])).
% 1.54/1.77 tff(7081,plain,
% 1.54/1.77 ((~b(s(s(s(s(z)))), s(s(elem!1)))) <=> (~b(s(s(s(s(z)))), elem!1))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[7080])).
% 1.54/1.77 tff(7082,assumption,(b(s(s(elem!1)), s(s(s(z))))), introduced(assumption)).
% 1.54/1.77 tff(7083,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~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)))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(7084,plain,
% 1.54/1.77 (((~b(s(s(s(z))), s(s(elem!1)))) | (~b(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(elem!1)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~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)))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(7085,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(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(elem!1)), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~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))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[7084])).
% 1.54/1.77 tff(7086,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(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(elem!1)), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~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)))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[7085, 7083])).
% 1.54/1.77 tff(7087,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(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(elem!1)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(7088,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~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))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[7087, 7086])).
% 1.54/1.77 tff(7089,plain,
% 1.54/1.77 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[7088, 319, 2543, 687, 4230, 2966, 7082])).
% 1.54/1.77 tff(7090,plain,
% 1.54/1.77 (~b(s(s(s(s(z)))), elem!1)),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[7089, 7081])).
% 1.54/1.77 tff(7091,plain,
% 1.54/1.77 (r(s(s(s(s(z)))), elem!1)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[6189, 7090, 7079])).
% 1.54/1.77 tff(7092,plain,
% 1.54/1.77 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[7091, 7077])).
% 1.54/1.77 tff(7093,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(7094,plain,
% 1.54/1.77 (((~b(s(s(s(z))), s(s(elem!1)))) | (~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(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(7095,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~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(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[7094])).
% 1.54/1.77 tff(7096,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~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(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[7095, 7093])).
% 1.54/1.77 tff(7097,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~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(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(7098,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[7097, 7096])).
% 1.54/1.77 tff(7099,plain,
% 1.54/1.77 (~b(s(s(s(s(z)))), s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[7098, 319, 4230, 3540, 2966])).
% 1.54/1.77 tff(7100,plain,
% 1.54/1.77 (r(s(s(s(s(z)))), s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2460, 7099, 2456])).
% 1.54/1.77 tff(7101,plain,
% 1.54/1.77 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(7102,plain,
% 1.54/1.77 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(7103,plain,
% 1.54/1.77 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[7102, 7101])).
% 1.54/1.77 tff(7104,plain,
% 1.54/1.77 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[7103, 297, 2169, 7100])).
% 1.54/1.77 tff(7105,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[7104, 7092])).
% 1.54/1.77 tff(7106,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~r(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(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(7107,plain,
% 1.54/1.77 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[7106, 7075, 2169, 4230, 7054, 7032, 687, 5177])).
% 1.54/1.77 tff(7108,plain,
% 1.54/1.77 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2252, 7107])).
% 1.54/1.77 tff(7109,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(z))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(7110,plain,
% 1.54/1.77 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(7111,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(z)))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[7110])).
% 1.54/1.77 tff(7112,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(z))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[7111, 7109])).
% 1.54/1.77 tff(7113,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(7114,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(z)))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[7113, 7112])).
% 1.54/1.77 tff(7115,plain,
% 1.54/1.77 (~b(z, s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[7114, 319, 2706, 7054, 2965])).
% 1.54/1.77 tff(7116,plain,
% 1.54/1.77 ((z = s(s(s(z)))) | r(z, s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[6714, 51, 7115])).
% 1.54/1.77 tff(7117,plain,
% 1.54/1.77 (r(z, s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[7116, 6704])).
% 1.54/1.77 tff(7118,plain,
% 1.54/1.77 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(7119,plain,
% 1.54/1.77 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(7120,plain,
% 1.54/1.77 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[7119])).
% 1.54/1.77 tff(7121,plain,
% 1.54/1.77 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[7120, 7118])).
% 1.54/1.77 tff(7122,plain,
% 1.54/1.77 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(7123,plain,
% 1.54/1.77 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[7122, 7121])).
% 1.54/1.77 tff(7124,plain,
% 1.54/1.77 (~r(s(s(s(s(z)))), z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[7123, 297, 7117, 7108])).
% 1.54/1.77 tff(7125,plain,
% 1.54/1.77 (b(s(s(s(s(z)))), z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2482, 7124])).
% 1.54/1.77 tff(7126,plain,
% 1.54/1.77 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3693, 297, 7029, 7108])).
% 1.54/1.77 tff(7127,plain,
% 1.54/1.77 (b(s(s(z)), s(s(s(s(z)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[6249, 7126])).
% 1.54/1.77 tff(7128,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[6604, 7127, 7125, 711, 7030])).
% 1.54/1.77 tff(7129,plain,((~b(s(s(s(z))), s(z))) | (~b(z, s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(7130,plain,
% 1.54/1.77 (~b(s(s(s(z))), s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[7129, 4230, 2169, 711, 687, 5177, 115, 2706])).
% 1.54/1.77 tff(7131,plain,
% 1.54/1.77 (r(s(s(s(z))), s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4549, 7130])).
% 1.54/1.77 tff(7132,plain,
% 1.54/1.77 (~r(s(s(z)), s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4544, 7131, 7036])).
% 1.54/1.77 tff(7133,plain,
% 1.54/1.77 (b(s(s(z)), s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4102, 7132])).
% 1.54/1.77 tff(7134,plain,
% 1.54/1.77 (~b(s(z), s(s(z)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4795, 7133, 711, 2706])).
% 1.54/1.77 tff(7135,plain,
% 1.54/1.77 (r(s(z), s(s(z)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[685, 7134])).
% 1.54/1.77 tff(7136,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[906, 297, 7135, 7036, 7131])).
% 1.54/1.77 tff(7137,plain,((~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(7138,plain,
% 1.54/1.77 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[7137, 6392, 7004, 2169, 6624, 5177, 6767])).
% 1.54/1.77 tff(7139,plain,
% 1.54/1.77 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[6520, 7138, 5177])).
% 1.54/1.77 tff(7140,plain,
% 1.54/1.77 (r(s(s(s(z))), s(s(s(elem!1))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3794, 7139, 6482])).
% 1.54/1.77 tff(7141,plain,
% 1.54/1.77 (r(s(s(s(z))), s(s(elem!1)))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[7140, 6479])).
% 1.54/1.77 tff(7142,plain,
% 1.54/1.77 (~r(s(s(s(z))), z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[6501, 297, 70, 7141])).
% 1.54/1.77 tff(7143,plain,
% 1.54/1.77 (b(s(s(s(z))), z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4584, 7142])).
% 1.54/1.77 tff(7144,plain,
% 1.54/1.77 (~r(s(s(s(z))), s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[6886, 7141, 2169])).
% 1.54/1.77 tff(7145,plain,
% 1.54/1.77 (b(s(s(s(z))), s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4549, 7144])).
% 1.54/1.77 tff(7146,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(7147,plain,
% 1.54/1.78 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(7148,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z)))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[7147])).
% 1.54/1.78 tff(7149,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[7148, 7146])).
% 1.54/1.78 tff(7150,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(7151,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z)))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[7150, 7149])).
% 1.54/1.78 tff(7152,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[7151, 319, 7004, 6874, 7145, 7143])).
% 1.54/1.78 tff(7153,plain,((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~(s(s(s(elem!1))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(7154,plain,
% 1.54/1.78 (~r(s(s(elem!1)), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[7153, 70, 5177])).
% 1.54/1.78 tff(7155,plain,
% 1.54/1.78 (b(s(s(elem!1)), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[871, 7154])).
% 1.54/1.78 tff(7156,plain,
% 1.54/1.78 (~b(s(s(z)), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[5145, 319, 1, 687, 817])).
% 1.54/1.78 tff(7157,plain,
% 1.54/1.78 (r(s(s(z)), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4102, 7156])).
% 1.54/1.78 tff(7158,plain,
% 1.54/1.78 (~b(s(s(elem!1)), s(s(z)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[6308, 496, 687, 711])).
% 1.54/1.78 tff(7159,plain,
% 1.54/1.78 (r(s(s(elem!1)), s(s(z)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[5327, 7158, 2542])).
% 1.54/1.78 tff(7160,plain,
% 1.54/1.78 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[6345, 7159, 70, 687, 711])).
% 1.54/1.78 tff(7161,plain,
% 1.54/1.78 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[6350, 7160, 6137])).
% 1.54/1.78 tff(7162,plain,
% 1.54/1.78 (~b(s(s(s(s(z)))), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[6568, 7161, 817, 1])).
% 1.54/1.78 tff(7163,plain,
% 1.54/1.78 (r(s(s(s(s(z)))), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[2461, 7162])).
% 1.54/1.78 tff(7164,plain,
% 1.54/1.78 (~b(s(z), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[5714, 496, 711, 817])).
% 1.54/1.78 tff(7165,plain,
% 1.54/1.78 (r(s(z), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[67, 7164])).
% 1.54/1.78 tff(7166,plain,
% 1.54/1.78 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[6366, 7161, 687, 817, 7165, 1])).
% 1.54/1.78 tff(7167,plain,
% 1.54/1.78 (r(s(s(s(s(z)))), s(s(z)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[6174, 7166])).
% 1.54/1.78 tff(7168,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3009, 7167, 7163, 7157])).
% 1.54/1.78 tff(7169,plain,((~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (s(s(elem!1)) = s(s(s(s(z))))) | (~r(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (s(s(elem!1)) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(7170,plain,
% 1.54/1.78 (~b(s(s(elem!1)), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[7169, 817, 6624, 7155, 6474, 70, 7004, 6478])).
% 1.54/1.78 tff(7171,plain,
% 1.54/1.78 (r(s(s(elem!1)), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[75, 7170])).
% 1.54/1.78 tff(7172,plain,
% 1.54/1.78 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(elem!1)))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[5177])).
% 1.54/1.78 tff(7173,plain,
% 1.54/1.78 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(elem!1))))),
% 1.54/1.78 inference(symmetry,[status(thm)],[7172])).
% 1.54/1.78 tff(7174,plain,
% 1.54/1.78 (b(s(z), s(s(s(elem!1))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[817, 7173])).
% 1.54/1.78 tff(7175,plain,
% 1.54/1.78 (~b(s(s(z)), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[5145, 319, 7155, 6624, 817])).
% 1.54/1.78 tff(7176,plain,
% 1.54/1.78 (r(s(s(z)), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4102, 7175])).
% 1.54/1.78 tff(7177,assumption,(~r(s(s(s(z))), s(s(elem!1)))), introduced(assumption)).
% 1.54/1.78 tff(7178,plain,
% 1.54/1.78 ((s(elem!1) = s(s(elem!1))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[5178])).
% 1.54/1.78 tff(7179,plain,
% 1.54/1.78 ((s(elem!1) = s(s(elem!1))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.54/1.78 inference(transitivity,[status(thm)],[7178, 276])).
% 1.54/1.78 tff(7180,plain,
% 1.54/1.78 ((s(elem!1) = s(s(elem!1))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[7179, 277])).
% 1.54/1.78 tff(7181,plain,
% 1.54/1.78 (s(elem!1) = s(s(s(elem!1)))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[6459, 7180])).
% 1.54/1.78 tff(7182,plain,
% 1.54/1.78 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[2827, 7181])).
% 1.54/1.78 tff(7183,plain,
% 1.54/1.78 (b(s(s(s(z))), s(s(elem!1)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4066, 51, 7182, 7177])).
% 1.54/1.78 tff(7184,assumption,(b(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 1.54/1.78 tff(7185,plain,
% 1.54/1.78 (b(s(s(s(elem!1))), s(z))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[1, 6862])).
% 1.54/1.78 tff(7186,plain,
% 1.54/1.78 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 1.54/1.78 inference(symmetry,[status(thm)],[6479])).
% 1.54/1.78 tff(7187,plain,
% 1.54/1.78 ((~r(s(s(s(z))), s(s(elem!1)))) <=> (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[7186])).
% 1.54/1.78 tff(7188,plain,
% 1.54/1.78 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[7177, 7187])).
% 1.54/1.78 tff(7189,plain,
% 1.54/1.78 (b(s(s(s(z))), s(s(s(elem!1))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3794, 7188, 6482])).
% 1.54/1.78 tff(7190,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(7191,plain,
% 1.54/1.78 (((~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(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(7192,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[7191])).
% 1.54/1.78 tff(7193,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[7192, 7190])).
% 1.54/1.78 tff(7194,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(7195,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[7194, 7193])).
% 1.54/1.78 tff(7196,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[7195, 319, 4561, 2965, 4727, 7184])).
% 1.54/1.78 tff(7197,plain,((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(7198,plain,
% 1.54/1.78 (~b(s(s(s(z))), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[7197, 7189, 7185, 7184])).
% 1.54/1.78 tff(7199,plain,
% 1.54/1.78 (r(s(s(s(z))), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4549, 7198])).
% 1.54/1.78 tff(7200,plain,
% 1.54/1.78 (~r(s(s(s(z))), s(s(z)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4544, 7199, 2511])).
% 1.54/1.78 tff(7201,plain,
% 1.54/1.78 (b(s(s(s(z))), s(s(z)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[2920, 7200])).
% 1.54/1.78 tff(7202,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[6856, 319, 1, 687, 7201, 7183])).
% 1.54/1.78 tff(7203,plain,(r(s(s(s(z))), s(s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~(s(s(s(elem!1))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(7204,plain,
% 1.54/1.78 (r(s(s(s(z))), s(s(elem!1)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[7203, 7176, 6624, 7155, 7174, 5177])).
% 1.54/1.78 tff(7205,plain,
% 1.54/1.78 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[6166, 3756, 687, 711])).
% 1.54/1.78 tff(7206,plain,
% 1.54/1.78 (r(s(s(s(s(z)))), s(s(z)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[6174, 7205])).
% 1.54/1.78 tff(7207,plain,
% 1.54/1.78 (~r(s(s(s(s(z)))), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3009, 7206, 7157])).
% 1.54/1.78 tff(7208,plain,
% 1.54/1.78 (~r(s(s(s(z))), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[6501, 297, 70, 6881])).
% 1.54/1.78 tff(7209,plain,
% 1.54/1.78 (b(s(s(s(z))), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4584, 7208])).
% 1.54/1.78 tff(7210,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(7211,plain,
% 1.54/1.78 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(7212,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[7211])).
% 1.54/1.78 tff(7213,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[7212, 7210])).
% 1.54/1.78 tff(7214,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(7215,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[7214, 7213])).
% 1.54/1.78 tff(7216,plain,
% 1.54/1.78 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[7215, 319, 711, 3756, 7209])).
% 1.54/1.78 tff(7217,plain,
% 1.54/1.78 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[2281, 7216])).
% 1.54/1.78 tff(7218,plain,
% 1.54/1.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(7219,plain,
% 1.54/1.78 (((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(elem!1))))) <=> ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(7220,plain,
% 1.54/1.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[7219])).
% 1.54/1.78 tff(7221,plain,
% 1.54/1.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[7220, 7218])).
% 1.54/1.78 tff(7222,plain,
% 1.54/1.78 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(7223,plain,
% 1.54/1.78 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[7222, 7221])).
% 1.54/1.78 tff(7224,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[7223, 297, 7217, 2443, 6881])).
% 1.54/1.78 tff(7225,plain,((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(7226,plain,
% 1.54/1.78 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[7225, 3756, 711, 6881, 70])).
% 1.54/1.78 tff(7227,plain,
% 1.54/1.78 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[6350, 7226, 6137])).
% 1.54/1.78 tff(7228,plain,
% 1.54/1.78 (~b(s(s(s(s(z)))), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[6568, 7227, 817, 1])).
% 1.54/1.78 tff(7229,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[2461, 7228, 7207])).
% 1.54/1.78 tff(7230,plain,((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (s(s(elem!1)) = s(s(s(s(z))))) | (~b(z, s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(7231,plain,
% 1.54/1.78 (~b(s(s(s(s(z)))), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[7230, 817, 7155, 6474, 7004, 7204, 70, 6624])).
% 1.54/1.78 tff(7232,plain,
% 1.54/1.78 (r(s(s(s(s(z)))), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[2482, 7231])).
% 1.54/1.78 tff(7233,plain,
% 1.54/1.78 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[2475, 7232, 7171])).
% 1.54/1.78 tff(7234,plain,
% 1.54/1.78 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[6350, 7233, 6474])).
% 1.54/1.78 tff(7235,plain,
% 1.54/1.78 (~b(s(s(s(s(z)))), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[6568, 7234, 817, 7155])).
% 1.54/1.78 tff(7236,plain,
% 1.54/1.78 (r(s(s(s(s(z)))), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[2461, 7235])).
% 1.54/1.78 tff(7237,plain,
% 1.54/1.78 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3009, 7236, 7176])).
% 1.54/1.78 tff(7238,plain,
% 1.54/1.78 (b(s(s(s(s(z)))), s(s(z)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[6174, 7237])).
% 1.54/1.78 tff(7239,plain,
% 1.54/1.78 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4345, 297, 7176, 7236])).
% 1.54/1.78 tff(7240,plain,
% 1.54/1.78 (b(s(s(z)), s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[6249, 7239])).
% 1.54/1.78 tff(7241,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(7242,plain,
% 1.54/1.78 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(7243,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[7242])).
% 1.54/1.78 tff(7244,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[7243, 7241])).
% 1.54/1.78 tff(7245,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(7246,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[7245, 7244])).
% 1.54/1.78 tff(7247,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[7246, 319, 6624, 7240, 7238, 7234])).
% 1.54/1.78 tff(7248,plain,((~b(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~(s(s(s(elem!1))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(7249,plain,
% 1.54/1.78 (~b(s(z), s(s(elem!1)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[7248, 57, 6450])).
% 1.54/1.78 tff(7250,plain,
% 1.54/1.78 (r(s(z), s(s(elem!1)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1047, 7249])).
% 1.54/1.78 tff(7251,plain,
% 1.54/1.78 (~r(s(z), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[865, 7250, 57])).
% 1.54/1.78 tff(7252,plain,
% 1.54/1.78 (b(s(z), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[67, 7251])).
% 1.54/1.78 tff(7253,plain,
% 1.54/1.78 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[6450])).
% 1.54/1.78 tff(7254,plain,
% 1.54/1.78 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.54/1.78 inference(symmetry,[status(thm)],[7253])).
% 1.54/1.78 tff(7255,plain,
% 1.54/1.78 (~r(s(s(elem!1)), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[7153, 57, 6450])).
% 1.54/1.78 tff(7256,plain,
% 1.54/1.78 (b(s(s(elem!1)), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[871, 7255])).
% 1.54/1.78 tff(7257,plain,
% 1.54/1.78 (b(s(s(s(elem!1))), s(z))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[7256, 7254])).
% 1.54/1.78 tff(7258,plain,
% 1.54/1.78 (~r(z, s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[6487, 7250, 57])).
% 1.54/1.78 tff(7259,plain,
% 1.54/1.78 (b(z, s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1099, 7258])).
% 1.54/1.78 tff(7260,plain,
% 1.54/1.78 (~b(s(s(z)), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4745, 7259, 7257, 7252])).
% 1.54/1.78 tff(7261,plain,
% 1.54/1.78 (r(s(s(z)), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4102, 7260])).
% 1.54/1.78 tff(7262,plain,
% 1.54/1.78 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = s(s(elem!1)))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[6450])).
% 1.54/1.78 tff(7263,plain,
% 1.54/1.78 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(z)) = s(s(elem!1))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[7262])).
% 1.54/1.78 tff(7264,plain,
% 1.54/1.78 (~(s(s(z)) = s(s(elem!1)))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[231, 7263])).
% 1.54/1.78 tff(7265,plain,
% 1.54/1.78 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[2509, 7264])).
% 1.54/1.78 tff(7266,plain,
% 1.54/1.78 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(elem!1)))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[6450])).
% 1.54/1.78 tff(7267,plain,
% 1.54/1.78 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(elem!1))))),
% 1.54/1.78 inference(symmetry,[status(thm)],[7266])).
% 1.54/1.78 tff(7268,plain,
% 1.54/1.78 (r(s(z), s(s(s(elem!1))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[7250, 7267])).
% 1.54/1.78 tff(7269,plain,
% 1.54/1.78 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[6514, 7268, 57, 6450, 7259, 7252])).
% 1.54/1.78 tff(7270,plain,
% 1.54/1.78 (b(s(s(s(z))), s(s(s(elem!1))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3794, 7269, 7265])).
% 1.54/1.78 tff(7271,plain,
% 1.54/1.78 (b(s(s(s(z))), s(s(elem!1)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[6520, 7270, 6450])).
% 1.54/1.78 tff(7272,plain,
% 1.54/1.78 (~r(s(s(z)), s(s(elem!1)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[6622, 57, 6450])).
% 1.54/1.78 tff(7273,plain,
% 1.54/1.78 (b(s(s(z)), s(s(elem!1)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[122, 7272, 7264])).
% 1.54/1.78 tff(7274,plain,
% 1.54/1.78 (~b(s(s(s(z))), s(s(z)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[6856, 319, 7256, 7273, 7271])).
% 1.54/1.78 tff(7275,plain,
% 1.54/1.78 (r(s(s(s(z))), s(s(z)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[2920, 7274])).
% 1.54/1.78 tff(7276,plain,
% 1.54/1.78 (~r(s(s(s(z))), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4544, 7275, 7261])).
% 1.54/1.78 tff(7277,plain,
% 1.54/1.78 (b(s(s(s(z))), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4549, 7276])).
% 1.54/1.78 tff(7278,plain,
% 1.54/1.78 (~r(z, s(s(z)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[7002, 57, 6450])).
% 1.54/1.78 tff(7279,plain,
% 1.54/1.78 (b(z, s(s(z)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[729, 7278])).
% 1.54/1.78 tff(7280,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(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(z)), s(s(s(z))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(7281,plain,
% 1.54/1.78 (((~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(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(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(z)), s(s(s(z))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(7282,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(z)), s(s(s(z)))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[7281])).
% 1.54/1.78 tff(7283,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(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(z)), s(s(s(z))))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[7282, 7280])).
% 1.54/1.78 tff(7284,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(7285,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(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(z)), s(s(s(z)))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[7284, 7283])).
% 1.54/1.78 tff(7286,plain,
% 1.54/1.78 (~b(s(s(z)), s(s(s(z))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[7285, 319, 7256, 7273, 7271])).
% 1.54/1.78 tff(7287,plain,
% 1.54/1.78 ((s(s(z)) = s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[6671, 51, 7286])).
% 1.54/1.78 tff(7288,plain,
% 1.54/1.78 (r(s(s(z)), s(s(s(z))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[7287, 6656])).
% 1.54/1.79 tff(7289,plain,
% 1.54/1.79 (b(s(s(z)), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[6719, 7288, 7252, 7277, 7259])).
% 1.54/1.79 tff(7290,plain,
% 1.54/1.79 (~b(s(z), s(s(z)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[7044, 7289, 7279, 7252])).
% 1.54/1.79 tff(7291,plain,
% 1.54/1.79 (r(s(z), s(s(z)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[685, 7290])).
% 1.54/1.79 tff(7292,plain,
% 1.54/1.79 (~r(s(z), s(s(s(z))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[7052, 297, 7291, 7275])).
% 1.54/1.79 tff(7293,plain,
% 1.54/1.79 (b(s(z), s(s(s(z))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[6558, 51, 7292, 32])).
% 1.54/1.79 tff(7294,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(7295,plain,
% 1.54/1.79 (((~b(s(z), s(s(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(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))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(7296,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(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(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1)))) | (~b(s(s(elem!1)), s(z)))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[7295])).
% 1.54/1.79 tff(7297,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(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(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[7296, 7294])).
% 1.54/1.79 tff(7298,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(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(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(7299,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[7298, 7297])).
% 1.54/1.79 tff(7300,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[7299, 319, 7256, 7271, 7293, 7277])).
% 1.54/1.79 tff(7301,plain,(b(z, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(7302,plain,
% 1.54/1.79 (b(z, s(s(z)))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[202, 875])).
% 1.54/1.79 tff(7303,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[34, 7302])).
% 1.54/1.79 tff(7304,plain,((~(s(s(z)) = s(s(elem!1)))) | b(z, s(s(z))) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(7305,plain,
% 1.54/1.79 ((~(s(s(z)) = s(s(elem!1)))) | b(z, s(s(z)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[7304, 7301])).
% 1.54/1.79 tff(7306,plain,
% 1.54/1.79 (~(s(s(z)) = s(s(elem!1)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[7305, 34])).
% 1.54/1.79 tff(7307,plain,
% 1.54/1.79 (~(s(elem!1) = s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[774, 7306])).
% 1.54/1.79 tff(7308,plain,
% 1.54/1.79 (r(z, s(s(z)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[729, 34])).
% 1.54/1.79 tff(7309,plain,
% 1.54/1.79 (r(s(s(z)), s(s(elem!1)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[122, 7306, 33])).
% 1.54/1.79 tff(7310,plain,
% 1.54/1.79 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[2509, 7306])).
% 1.54/1.79 tff(7311,plain,
% 1.54/1.79 (~(s(s(z)) = s(s(elem!1)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[7304, 34, 202])).
% 1.54/1.79 tff(7312,plain,
% 1.54/1.79 (~r(s(s(elem!1)), s(s(z)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4014, 732, 115])).
% 1.54/1.79 tff(7313,plain,
% 1.54/1.79 (~r(s(z), s(s(elem!1)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[304, 666, 115])).
% 1.54/1.79 tff(7314,plain,
% 1.54/1.79 (b(s(z), s(s(elem!1)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1047, 7313])).
% 1.54/1.79 tff(7315,plain,
% 1.54/1.79 (~r(s(s(elem!1)), s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[5094, 666, 115])).
% 1.54/1.79 tff(7316,plain,
% 1.54/1.79 (b(s(s(elem!1)), s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[871, 7315])).
% 1.54/1.79 tff(7317,plain,
% 1.54/1.79 (~b(z, s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1095, 319, 7316, 7314, 202])).
% 1.54/1.79 tff(7318,plain,
% 1.54/1.79 (r(z, s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1099, 7317])).
% 1.54/1.79 tff(7319,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4170, 297, 732, 917, 2511])).
% 1.54/1.79 tff(7320,plain,((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(7321,plain,
% 1.54/1.79 (~r(s(s(z)), s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[7320, 7318, 732])).
% 1.54/1.79 tff(7322,plain,
% 1.54/1.79 (b(s(s(z)), s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4102, 7321])).
% 1.54/1.79 tff(7323,plain,
% 1.54/1.79 (~b(s(s(elem!1)), s(s(z)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4000, 319, 7316, 7322, 7314])).
% 1.54/1.79 tff(7324,plain,
% 1.54/1.79 (s(s(elem!1)) = s(s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[2555, 51, 7323, 7312])).
% 1.54/1.79 tff(7325,plain,
% 1.54/1.79 (r(s(s(elem!1)), z) <=> r(s(s(z)), z)),
% 1.54/1.79 inference(monotonicity,[status(thm)],[7324])).
% 1.54/1.79 tff(7326,plain,
% 1.54/1.79 (r(s(s(z)), z) <=> r(s(s(elem!1)), z)),
% 1.54/1.79 inference(symmetry,[status(thm)],[7325])).
% 1.54/1.79 tff(7327,plain,
% 1.54/1.79 ((~r(s(s(z)), z)) <=> (~r(s(s(elem!1)), z))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[7326])).
% 1.54/1.79 tff(7328,plain,
% 1.54/1.79 (~b(s(s(z)), s(s(elem!1)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[841, 7316, 202, 7314])).
% 1.54/1.79 tff(7329,plain,
% 1.54/1.79 (r(s(s(z)), s(s(elem!1)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[2127, 7328, 7315])).
% 1.54/1.79 tff(7330,plain,
% 1.54/1.79 (~r(s(s(z)), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3526, 7329, 115])).
% 1.54/1.79 tff(7331,plain,
% 1.54/1.79 (~r(s(s(elem!1)), z)),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[7330, 7327])).
% 1.54/1.79 tff(7332,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[115, 7331])).
% 1.54/1.79 tff(7333,plain,((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(z)))) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(7334,plain,
% 1.54/1.79 (~r(s(z), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[7333, 7308, 76, 202])).
% 1.54/1.79 tff(7335,plain,
% 1.54/1.79 (b(s(z), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[67, 7334])).
% 1.54/1.79 tff(7336,plain,
% 1.54/1.79 (~r(s(s(elem!1)), s(s(z)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4014, 7308, 76])).
% 1.54/1.79 tff(7337,plain,
% 1.54/1.79 (~(s(s(elem!1)) = s(s(z)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[2521, 7311])).
% 1.54/1.79 tff(7338,plain,
% 1.54/1.79 (b(s(s(elem!1)), s(s(z)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[5327, 7337, 7336])).
% 1.54/1.79 tff(7339,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[831, 319, 1, 817, 202, 2493])).
% 1.54/1.79 tff(7340,plain,((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(7341,plain,
% 1.54/1.79 (~b(s(s(elem!1)), s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[7340, 817, 202, 2493])).
% 1.54/1.79 tff(7342,plain,
% 1.54/1.79 (r(s(s(elem!1)), s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[871, 7341])).
% 1.54/1.79 tff(7343,plain,
% 1.54/1.79 (~r(z, s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3560, 7342, 115])).
% 1.54/1.79 tff(7344,plain,
% 1.54/1.79 (b(z, s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1099, 7343])).
% 1.54/1.79 tff(7345,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(7346,plain,
% 1.54/1.79 (((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(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(s(z)))) | (~b(z, s(z))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(7347,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z)))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[7346])).
% 1.54/1.79 tff(7348,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[7347, 7345])).
% 1.54/1.79 tff(7349,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(7350,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z)))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[7349, 7348])).
% 1.54/1.79 tff(7351,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[7350, 319, 2543, 7344, 817, 202])).
% 1.54/1.79 tff(7352,plain,((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(7353,plain,
% 1.54/1.79 (~b(s(z), s(s(elem!1)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[7352, 7338, 202, 76, 7335])).
% 1.54/1.79 tff(7354,plain,
% 1.54/1.79 (r(s(z), s(s(elem!1)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1047, 7353])).
% 1.54/1.79 tff(7355,plain,
% 1.54/1.79 (~r(s(z), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[7333, 732, 115, 202])).
% 1.54/1.79 tff(7356,plain,
% 1.54/1.79 (b(s(z), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[67, 7355])).
% 1.54/1.79 tff(7357,plain,
% 1.54/1.79 (b(s(s(z)), s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4102, 4099])).
% 1.54/1.79 tff(7358,plain,
% 1.54/1.79 (~r(s(z), s(s(z)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[922, 917, 732])).
% 1.54/1.79 tff(7359,plain,
% 1.54/1.79 (b(s(z), s(s(z)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[685, 7358])).
% 1.54/1.79 tff(7360,plain,
% 1.54/1.79 (~(s(s(elem!1)) = s(s(z)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[5535, 7358, 444])).
% 1.54/1.79 tff(7361,plain,
% 1.54/1.79 (b(s(s(elem!1)), s(s(z)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[5327, 7360, 7312])).
% 1.54/1.79 tff(7362,plain,
% 1.54/1.79 (~r(s(s(elem!1)), s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3560, 917, 115])).
% 1.54/1.79 tff(7363,plain,
% 1.54/1.79 (b(s(s(elem!1)), s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[871, 7362])).
% 1.54/1.79 tff(7364,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(7365,plain,
% 1.54/1.79 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(7366,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[7365])).
% 1.54/1.79 tff(7367,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[7366, 7364])).
% 1.54/1.79 tff(7368,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(7369,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[7368, 7367])).
% 1.54/1.79 tff(7370,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[7369, 319, 7363, 3390, 7361, 7359])).
% 1.54/1.79 tff(7371,plain,((~r(z, s(z))) | (~b(s(s(z)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(7372,plain,
% 1.54/1.79 (~r(z, s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[7371, 7357, 444, 732, 115])).
% 1.54/1.79 tff(7373,plain,
% 1.54/1.79 (b(z, s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1099, 7372])).
% 1.54/1.79 tff(7374,plain,
% 1.54/1.79 (~b(s(s(z)), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4724, 319, 7357, 7373, 7356])).
% 1.54/1.79 tff(7375,plain,
% 1.54/1.79 (r(s(s(z)), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[663, 51, 28, 7374])).
% 1.54/1.79 tff(7376,plain,
% 1.54/1.79 (~r(s(s(z)), s(s(elem!1)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3526, 7375, 115])).
% 1.54/1.79 tff(7377,plain,
% 1.54/1.79 (r(s(s(elem!1)), s(z)) <=> r(s(s(z)), s(z))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[2518])).
% 1.54/1.79 tff(7378,plain,
% 1.54/1.79 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(z))),
% 1.54/1.79 inference(symmetry,[status(thm)],[7377])).
% 1.54/1.79 tff(7379,plain,
% 1.54/1.79 ((~r(s(s(z)), s(z))) <=> (~r(s(s(elem!1)), s(z)))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[7378])).
% 1.54/1.79 tff(7380,plain,
% 1.54/1.79 (~r(s(s(elem!1)), s(z))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[4099, 7379])).
% 1.54/1.79 tff(7381,plain,
% 1.54/1.79 (r(s(elem!1), s(s(elem!1)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1045, 5071, 444])).
% 1.54/1.79 tff(7382,plain,
% 1.54/1.79 (r(s(s(elem!1)), s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1039, 7381, 69, 5071])).
% 1.54/1.79 tff(7383,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[7382, 7380])).
% 1.54/1.79 tff(7384,plain,((~(s(s(elem!1)) = s(s(z)))) | r(s(s(z)), s(z)) | r(s(s(z)), s(s(elem!1))) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(7385,plain,
% 1.54/1.79 (~(s(s(elem!1)) = s(s(z)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[7384, 4099, 7376, 444])).
% 1.54/1.79 tff(7386,plain,
% 1.54/1.79 (b(s(s(elem!1)), s(s(z)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[5327, 7385, 7312])).
% 1.54/1.79 tff(7387,plain,
% 1.54/1.79 (~(s(s(z)) = s(s(elem!1)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[5127, 7385])).
% 1.54/1.79 tff(7388,plain,
% 1.54/1.79 (b(s(s(z)), s(s(elem!1)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[122, 7387, 7376])).
% 1.54/1.79 tff(7389,plain,
% 1.54/1.79 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4657, 7388, 202, 7386])).
% 1.54/1.79 tff(7390,plain,
% 1.54/1.79 (~b(s(s(s(elem!1))), s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4745, 7373, 7356, 7357])).
% 1.54/1.79 tff(7391,plain,
% 1.54/1.79 (r(s(s(s(elem!1))), s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1088, 51, 171, 7390])).
% 1.54/1.79 tff(7392,plain,
% 1.54/1.79 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[5135, 7391, 444])).
% 1.54/1.79 tff(7393,plain,
% 1.54/1.79 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[348, 7392, 7389])).
% 1.54/1.79 tff(7394,plain,
% 1.54/1.79 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(elem!1)))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[7393])).
% 1.54/1.79 tff(7395,plain,
% 1.54/1.79 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(elem!1))))),
% 1.54/1.79 inference(symmetry,[status(thm)],[7394])).
% 1.54/1.79 tff(7396,plain,
% 1.54/1.79 (r(s(z), s(s(s(elem!1))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[444, 7395])).
% 1.54/1.79 tff(7397,plain,
% 1.54/1.79 (s(s(elem!1)) = s(s(s(elem!1)))),
% 1.54/1.79 inference(symmetry,[status(thm)],[7393])).
% 1.54/1.79 tff(7398,plain,
% 1.54/1.79 ((s(elem!1) = s(s(elem!1))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[7397])).
% 1.54/1.79 tff(7399,plain,
% 1.54/1.79 ((s(elem!1) = s(s(elem!1))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.54/1.79 inference(transitivity,[status(thm)],[7398, 276])).
% 1.54/1.79 tff(7400,plain,
% 1.54/1.79 ((s(elem!1) = s(s(elem!1))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[7399, 277])).
% 1.54/1.79 tff(7401,plain,
% 1.54/1.79 (s(elem!1) = s(s(elem!1))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[5182, 7393])).
% 1.54/1.79 tff(7402,plain,
% 1.54/1.79 (s(elem!1) = s(s(s(elem!1)))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[7401, 7400])).
% 1.54/1.79 tff(7403,plain,
% 1.54/1.79 (s(s(s(elem!1))) = elem!1),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[5346, 7393])).
% 1.54/1.79 tff(7404,plain,
% 1.54/1.79 (elem!1 = s(s(s(elem!1)))),
% 1.54/1.79 inference(symmetry,[status(thm)],[7403])).
% 1.54/1.79 tff(7405,plain,
% 1.54/1.79 (elem!1 = s(s(elem!1))),
% 1.54/1.79 inference(transitivity,[status(thm)],[7404, 7393])).
% 1.54/1.79 tff(7406,plain,
% 1.54/1.79 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(elem!1)))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[7405])).
% 1.54/1.79 tff(7407,plain,
% 1.54/1.79 ((s(s(z)) = s(s(elem!1))) <=> (s(s(z)) = elem!1)),
% 1.54/1.79 inference(symmetry,[status(thm)],[7406])).
% 1.54/1.79 tff(7408,plain,
% 1.54/1.79 ((~(s(s(z)) = s(s(elem!1)))) <=> (~(s(s(z)) = elem!1))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[7407])).
% 1.54/1.79 tff(7409,plain,
% 1.54/1.79 (~(s(s(z)) = elem!1)),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[7387, 7408])).
% 1.54/1.79 tff(7410,plain,
% 1.54/1.79 (~(s(s(s(z))) = s(elem!1))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[2759, 7409])).
% 1.54/1.79 tff(7411,plain,
% 1.54/1.79 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4481, 7410, 7402])).
% 1.54/1.79 tff(7412,plain,
% 1.54/1.79 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(elem!1)))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[7393])).
% 1.54/1.79 tff(7413,plain,
% 1.54/1.79 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 1.54/1.79 inference(symmetry,[status(thm)],[7412])).
% 1.54/1.79 tff(7414,plain,
% 1.54/1.79 (b(s(s(z)), s(s(s(elem!1))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[7388, 7413])).
% 1.54/1.79 tff(7415,plain,
% 1.54/1.79 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[7393])).
% 1.54/1.79 tff(7416,plain,
% 1.54/1.79 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 1.54/1.79 inference(symmetry,[status(thm)],[7415])).
% 1.54/1.79 tff(7417,plain,
% 1.54/1.79 (b(s(s(s(elem!1))), s(s(z)))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[7386, 7416])).
% 1.54/1.79 tff(7418,plain,
% 1.54/1.79 (b(s(elem!1), s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[7401])).
% 1.54/1.79 tff(7419,plain,
% 1.54/1.79 (b(s(s(elem!1)), s(s(z))) <=> b(s(elem!1), s(s(z)))),
% 1.54/1.79 inference(symmetry,[status(thm)],[7418])).
% 1.54/1.79 tff(7420,plain,
% 1.54/1.79 (b(s(elem!1), s(s(z)))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[7386, 7419])).
% 1.54/1.79 tff(7421,plain,
% 1.54/1.79 (b(z, s(elem!1)) <=> b(z, s(s(elem!1)))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[7401])).
% 1.54/1.79 tff(7422,plain,
% 1.54/1.79 (b(z, s(s(elem!1))) <=> b(z, s(elem!1))),
% 1.54/1.79 inference(symmetry,[status(thm)],[7421])).
% 1.54/1.79 tff(7423,plain,
% 1.54/1.79 (b(z, s(elem!1))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[202, 7422])).
% 1.54/1.79 tff(7424,plain,
% 1.54/1.79 (~r(s(s(s(z))), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[6685, 4538, 732])).
% 1.54/1.79 tff(7425,plain,
% 1.54/1.79 (b(s(s(s(z))), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4584, 7424])).
% 1.54/1.79 tff(7426,plain,
% 1.54/1.79 (~r(s(s(s(z))), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[895, 297, 732, 4282])).
% 1.54/1.79 tff(7427,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(7428,plain,
% 1.54/1.79 (((~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(7429,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1)))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[7428])).
% 1.54/1.79 tff(7430,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[7429, 7427])).
% 1.54/1.79 tff(7431,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(7432,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1)))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[7431, 7430])).
% 1.54/1.79 tff(7433,plain,
% 1.54/1.79 ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[7432, 319, 3926, 2389])).
% 1.54/1.79 tff(7434,plain,
% 1.54/1.79 (~b(s(s(s(z))), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[7433, 2841])).
% 1.54/1.79 tff(7435,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[901, 51, 898, 7434, 7426])).
% 1.54/1.79 tff(7436,plain,((~b(s(s(s(z))), s(elem!1))) | (~r(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))) | b(s(s(s(z))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(7437,plain,
% 1.54/1.79 (~b(s(s(s(z))), s(elem!1))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[7436, 2915, 732, 2389, 3926])).
% 1.54/1.79 tff(7438,plain,
% 1.54/1.79 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4874, 7437, 266])).
% 1.54/1.79 tff(7439,plain,
% 1.54/1.79 (r(s(s(s(z))), s(s(s(elem!1))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3794, 7438, 3739])).
% 1.54/1.80 tff(7440,plain,
% 1.54/1.80 (~r(s(s(s(z))), s(z))),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[4886, 7439, 4877])).
% 1.54/1.80 tff(7441,plain,
% 1.54/1.80 (b(s(s(s(z))), s(z))),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[4549, 7440])).
% 1.54/1.80 tff(7442,plain,
% 1.54/1.80 ($false),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[6512, 319, 2706, 2493, 7441, 7425])).
% 1.54/1.80 tff(7443,plain,(b(s(s(s(z))), s(s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~(s(elem!1) = s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.80 tff(7444,plain,
% 1.54/1.80 (b(s(s(s(z))), s(s(z)))),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[7443, 7373, 7356, 7396, 7411, 7402, 732, 7423, 7420])).
% 1.54/1.80 tff(7445,plain,
% 1.54/1.80 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[4571, 7444, 7417, 7414])).
% 1.54/1.80 tff(7446,plain,
% 1.54/1.80 (r(s(s(s(z))), s(s(s(elem!1))))),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[3794, 7445, 7411])).
% 1.54/1.80 tff(7447,plain,
% 1.54/1.80 (~r(s(s(s(z))), s(z))),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[4886, 7446, 7396])).
% 1.54/1.80 tff(7448,plain,
% 1.54/1.80 (b(s(s(s(z))), s(z))),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[4549, 7447])).
% 1.54/1.80 tff(7449,plain,
% 1.54/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 1.54/1.80 inference(rewrite,[status(thm)],[])).
% 1.54/1.80 tff(7450,plain,
% 1.54/1.80 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 1.54/1.80 inference(rewrite,[status(thm)],[])).
% 1.54/1.80 tff(7451,plain,
% 1.54/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z)))))),
% 1.54/1.80 inference(monotonicity,[status(thm)],[7450])).
% 1.54/1.80 tff(7452,plain,
% 1.54/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[7451, 7449])).
% 1.64/1.80 tff(7453,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(7454,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z)))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[7453, 7452])).
% 1.64/1.80 tff(7455,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[7454, 319, 7357, 7444, 7356, 7448])).
% 1.64/1.80 tff(7456,plain,(r(s(s(z)), s(z)) | (~r(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.80 tff(7457,plain,
% 1.64/1.80 (r(s(s(z)), s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[7456, 7354, 202, 7308, 76])).
% 1.64/1.80 tff(7458,plain,
% 1.64/1.80 (~r(s(s(z)), s(s(elem!1)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[2583, 7354, 7457])).
% 1.64/1.80 tff(7459,plain,
% 1.64/1.80 (b(s(s(z)), s(s(elem!1)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[122, 7458, 7311])).
% 1.64/1.80 tff(7460,plain,
% 1.64/1.80 (~(s(elem!1) = s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[774, 7311])).
% 1.64/1.80 tff(7461,plain,
% 1.64/1.80 (~(s(z) = s(elem!1))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[2503, 7460])).
% 1.64/1.80 tff(7462,plain,
% 1.64/1.80 (~r(s(elem!1), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[740, 203, 732])).
% 1.64/1.80 tff(7463,plain,
% 1.64/1.80 (b(s(elem!1), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[2602, 7462])).
% 1.64/1.80 tff(7464,plain,
% 1.64/1.80 (~(s(elem!1) = s(s(elem!1)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[5175, 7463, 71])).
% 1.64/1.80 tff(7465,plain,
% 1.64/1.80 (~r(s(z), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[7333, 732, 76, 202])).
% 1.64/1.80 tff(7466,plain,
% 1.64/1.80 (b(s(z), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[67, 7465])).
% 1.64/1.80 tff(7467,plain,
% 1.64/1.80 (~r(z, s(elem!1))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[755, 297, 732, 203])).
% 1.64/1.80 tff(7468,plain,
% 1.64/1.80 (b(z, s(elem!1))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4804, 7467])).
% 1.64/1.80 tff(7469,plain,
% 1.64/1.80 (~b(s(z), s(elem!1))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4811, 319, 7468, 7463, 7466])).
% 1.64/1.80 tff(7470,plain,
% 1.64/1.80 (r(s(z), s(elem!1))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4816, 7469, 136])).
% 1.64/1.80 tff(7471,assumption,(r(s(z), s(elem!1))), introduced(assumption)).
% 1.64/1.80 tff(7472,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3309, 297, 444, 7471, 197])).
% 1.64/1.80 tff(7473,plain,((~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.80 tff(7474,plain,
% 1.64/1.80 (~r(s(elem!1), s(s(elem!1)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[7473, 7470, 444])).
% 1.64/1.80 tff(7475,plain,
% 1.64/1.80 (b(s(elem!1), s(s(elem!1)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[807, 7474, 7464])).
% 1.64/1.80 tff(7476,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(7477,plain,
% 1.64/1.80 (((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(7478,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[7477])).
% 1.64/1.80 tff(7479,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))),
% 1.64/1.80 inference(transitivity,[status(thm)],[7478, 7476])).
% 1.64/1.80 tff(7480,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(7481,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[7480, 7479])).
% 1.64/1.80 tff(7482,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[7481, 319, 7463, 2543, 7475, 202])).
% 1.64/1.80 tff(7483,plain,((~r(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (s(z) = s(elem!1)) | (~r(z, s(s(z)))) | b(s(s(elem!1)), z)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.80 tff(7484,plain,
% 1.64/1.80 (~r(s(elem!1), s(s(z)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[7483, 7354, 202, 7461, 7338, 7308, 71])).
% 1.64/1.80 tff(7485,plain,
% 1.64/1.80 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4657, 7459, 202, 7338])).
% 1.64/1.80 tff(7486,plain,
% 1.64/1.80 (~r(z, s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[7320, 7457, 7308])).
% 1.64/1.80 tff(7487,plain,
% 1.64/1.80 (b(z, s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1099, 7486])).
% 1.64/1.80 tff(7488,plain,
% 1.64/1.80 ((~b(s(s(s(elem!1))), s(s(s(z))))) <=> (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[3533])).
% 1.64/1.80 tff(7489,plain,
% 1.64/1.80 ((~b(s(s(s(elem!1))), s(s(elem!1)))) <=> (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[4285])).
% 1.64/1.80 tff(7490,assumption,(~b(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 1.64/1.80 tff(7491,plain,
% 1.64/1.80 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[7490, 7489])).
% 1.64/1.80 tff(7492,plain,
% 1.64/1.80 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[7491, 7488])).
% 1.64/1.80 tff(7493,plain,
% 1.64/1.80 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[2252, 7492])).
% 1.64/1.80 tff(7494,plain,
% 1.64/1.80 (r(s(s(elem!1)), z) <=> r(s(s(s(z))), z)),
% 1.64/1.80 inference(monotonicity,[status(thm)],[2970])).
% 1.64/1.80 tff(7495,plain,
% 1.64/1.80 (r(s(s(s(z))), z)),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[115, 7494])).
% 1.64/1.80 tff(7496,plain,
% 1.64/1.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(7497,plain,
% 1.64/1.80 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(7498,plain,
% 1.64/1.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[7497])).
% 1.64/1.80 tff(7499,plain,
% 1.64/1.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[7498, 7496])).
% 1.64/1.80 tff(7500,plain,
% 1.64/1.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(7501,plain,
% 1.64/1.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[7500, 7499])).
% 1.64/1.80 tff(7502,plain,
% 1.64/1.80 (~r(s(s(s(s(z)))), s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[7501, 297, 7493, 3126])).
% 1.64/1.80 tff(7503,plain,
% 1.64/1.80 (b(s(s(s(s(z)))), s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[2461, 7502])).
% 1.64/1.80 tff(7504,plain,
% 1.64/1.80 (~b(s(s(s(s(z)))), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[6846, 319, 2706, 2493, 7503])).
% 1.64/1.80 tff(7505,plain,
% 1.64/1.80 (r(s(s(s(s(z)))), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[2482, 7504])).
% 1.64/1.80 tff(7506,plain,
% 1.64/1.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(7507,plain,
% 1.64/1.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(7508,plain,
% 1.64/1.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[7507, 7506])).
% 1.64/1.80 tff(7509,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[7508, 297, 7505, 7495, 7493])).
% 1.64/1.80 tff(7510,plain,((~(s(elem!1) = s(s(z)))) | (~b(z, s(z))) | (~b(s(z), z)) | b(s(s(s(elem!1))), s(s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.80 tff(7511,plain,
% 1.64/1.80 (~(s(elem!1) = s(s(z)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[7510, 7487, 7335, 7485, 76, 7354])).
% 1.64/1.80 tff(7512,plain,
% 1.64/1.80 (b(s(elem!1), s(s(z)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[2529, 7511, 7484])).
% 1.64/1.80 tff(7513,plain,
% 1.64/1.80 (~b(s(elem!1), s(s(elem!1)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4607, 7512, 7338, 7459])).
% 1.64/1.80 tff(7514,plain,
% 1.64/1.80 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[348, 5380, 7490])).
% 1.64/1.80 tff(7515,plain,
% 1.64/1.80 (~r(s(s(s(elem!1))), s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[5135, 7514, 444])).
% 1.64/1.80 tff(7516,plain,
% 1.64/1.80 (b(s(s(s(elem!1))), s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1088, 51, 171, 7515])).
% 1.64/1.80 tff(7517,plain,
% 1.64/1.80 (r(s(elem!1), s(s(elem!1)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[807, 2142, 4687])).
% 1.64/1.80 tff(7518,plain,
% 1.64/1.80 (~r(s(z), s(elem!1))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[7473, 7517, 444])).
% 1.64/1.80 tff(7519,plain,
% 1.64/1.80 (b(s(z), s(elem!1))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4816, 7518, 136])).
% 1.64/1.80 tff(7520,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(7521,plain,
% 1.64/1.80 (((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(7522,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[7521])).
% 1.64/1.80 tff(7523,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[7522, 7520])).
% 1.64/1.80 tff(7524,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(7525,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[7524, 7523])).
% 1.64/1.80 tff(7526,plain,
% 1.64/1.80 (~b(s(s(s(elem!1))), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[7525, 319, 2706, 7519, 7516])).
% 1.64/1.80 tff(7527,plain,
% 1.64/1.80 (r(s(s(s(elem!1))), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1077, 51, 160, 7526])).
% 1.64/1.80 tff(7528,plain,
% 1.64/1.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(7529,plain,
% 1.64/1.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(7530,plain,
% 1.64/1.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[7529, 7528])).
% 1.64/1.80 tff(7531,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[7530, 297, 115, 7514, 7527])).
% 1.64/1.80 tff(7532,plain,((s(elem!1) = s(s(elem!1))) | (~r(s(s(elem!1)), z)) | (~b(z, s(z))) | (s(z) = s(elem!1)) | (~r(s(z), s(s(elem!1)))) | b(s(s(s(elem!1))), s(s(elem!1))) | b(s(elem!1), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.80 tff(7533,plain,
% 1.64/1.80 (s(elem!1) = s(s(elem!1))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[7532, 7487, 76, 7461, 7354, 7485, 7513])).
% 1.64/1.80 tff(7534,plain,
% 1.64/1.80 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[113, 7533])).
% 1.64/1.80 tff(7535,plain,
% 1.64/1.80 (s(s(elem!1)) = s(s(s(elem!1)))),
% 1.64/1.80 inference(symmetry,[status(thm)],[7534])).
% 1.64/1.80 tff(7536,plain,
% 1.64/1.80 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[7535])).
% 1.64/1.80 tff(7537,plain,
% 1.64/1.80 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 1.64/1.80 inference(symmetry,[status(thm)],[7536])).
% 1.64/1.80 tff(7538,plain,
% 1.64/1.80 (s(s(elem!1)) = s(elem!1)),
% 1.64/1.80 inference(symmetry,[status(thm)],[7533])).
% 1.64/1.80 tff(7539,plain,
% 1.64/1.80 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[7538])).
% 1.64/1.80 tff(7540,plain,
% 1.64/1.80 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[7539, 277])).
% 1.64/1.80 tff(7541,plain,
% 1.64/1.80 (s(elem!1) = s(s(s(elem!1)))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[7534, 7540])).
% 1.64/1.80 tff(7542,plain,
% 1.64/1.80 (s(s(s(elem!1))) = elem!1),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[5346, 7534])).
% 1.64/1.80 tff(7543,plain,
% 1.64/1.80 (elem!1 = s(s(s(elem!1)))),
% 1.64/1.80 inference(symmetry,[status(thm)],[7542])).
% 1.64/1.80 tff(7544,plain,
% 1.64/1.80 (elem!1 = s(s(elem!1))),
% 1.64/1.80 inference(transitivity,[status(thm)],[7543, 7534])).
% 1.64/1.80 tff(7545,plain,
% 1.64/1.80 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(elem!1)))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[7544])).
% 1.64/1.80 tff(7546,plain,
% 1.64/1.80 ((s(s(z)) = s(s(elem!1))) <=> (s(s(z)) = elem!1)),
% 1.64/1.80 inference(symmetry,[status(thm)],[7545])).
% 1.64/1.80 tff(7547,plain,
% 1.64/1.80 ((~(s(s(z)) = s(s(elem!1)))) <=> (~(s(s(z)) = elem!1))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[7546])).
% 1.64/1.80 tff(7548,plain,
% 1.64/1.80 (~(s(s(z)) = elem!1)),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[7311, 7547])).
% 1.64/1.80 tff(7549,plain,
% 1.64/1.80 (~(s(s(s(z))) = s(elem!1))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[2759, 7548])).
% 1.64/1.80 tff(7550,plain,
% 1.64/1.80 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4481, 7549, 7541])).
% 1.64/1.80 tff(7551,plain,
% 1.64/1.80 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(elem!1)))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[7534])).
% 1.64/1.80 tff(7552,plain,
% 1.64/1.80 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 1.64/1.80 inference(symmetry,[status(thm)],[7551])).
% 1.64/1.80 tff(7553,plain,
% 1.64/1.80 (b(s(s(z)), s(s(s(elem!1))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[7459, 7552])).
% 1.64/1.80 tff(7554,plain,
% 1.64/1.80 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[7534])).
% 1.64/1.80 tff(7555,plain,
% 1.64/1.80 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 1.64/1.80 inference(symmetry,[status(thm)],[7554])).
% 1.64/1.80 tff(7556,plain,
% 1.64/1.80 (b(s(s(s(elem!1))), s(s(z)))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[7338, 7555])).
% 1.64/1.80 tff(7557,plain,
% 1.64/1.80 (b(z, s(elem!1)) <=> b(z, s(s(elem!1)))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[7533])).
% 1.64/1.80 tff(7558,plain,
% 1.64/1.80 (b(z, s(s(elem!1))) <=> b(z, s(elem!1))),
% 1.64/1.80 inference(symmetry,[status(thm)],[7557])).
% 1.64/1.80 tff(7559,plain,
% 1.64/1.80 (b(z, s(elem!1))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[202, 7558])).
% 1.64/1.80 tff(7560,plain,
% 1.64/1.80 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(elem!1)))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[7534])).
% 1.64/1.80 tff(7561,plain,
% 1.64/1.80 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(elem!1))))),
% 1.64/1.80 inference(symmetry,[status(thm)],[7560])).
% 1.64/1.80 tff(7562,plain,
% 1.64/1.80 (r(s(z), s(s(s(elem!1))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[7354, 7561])).
% 1.64/1.80 tff(7563,plain,
% 1.64/1.80 (b(s(s(s(z))), s(s(z)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[7443, 7550, 7335, 7487, 7562, 7541, 7308, 7559, 7512])).
% 1.64/1.80 tff(7564,plain,
% 1.64/1.80 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4571, 7563, 7556, 7553])).
% 1.64/1.80 tff(7565,plain,
% 1.64/1.80 (r(s(s(s(z))), s(s(s(elem!1))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3794, 7564, 7550])).
% 1.64/1.80 tff(7566,plain,
% 1.64/1.80 (r(s(s(s(z))), s(s(elem!1)))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[7565, 7537])).
% 1.64/1.80 tff(7567,plain,
% 1.64/1.80 (~r(s(s(s(z))), s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4886, 7565, 7562])).
% 1.64/1.80 tff(7568,plain,
% 1.64/1.80 (b(s(s(s(z))), s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4549, 7567])).
% 1.64/1.80 tff(7569,plain,
% 1.64/1.80 (~b(s(s(s(z))), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[6512, 319, 7487, 7335, 7568])).
% 1.64/1.80 tff(7570,plain,
% 1.64/1.80 (r(s(s(s(z))), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4584, 7569])).
% 1.64/1.80 tff(7571,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4865, 297, 76, 7570, 7566])).
% 1.64/1.80 tff(7572,plain,(b(z, s(s(z))) | (~b(z, s(s(elem!1)))) | b(s(s(elem!1)), z)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.80 tff(7573,plain,
% 1.64/1.80 (b(z, s(s(z)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[7572, 71, 202])).
% 1.64/1.80 tff(7574,plain,
% 1.64/1.80 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1105, 872, 202, 817])).
% 1.64/1.80 tff(7575,plain,
% 1.64/1.80 (~b(s(s(z)), s(s(elem!1)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[841, 872, 202, 817])).
% 1.64/1.80 tff(7576,plain,
% 1.64/1.80 (r(s(s(z)), s(s(elem!1)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[2127, 7575, 180])).
% 1.64/1.80 tff(7577,plain,
% 1.64/1.80 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4139, 297, 2578, 335])).
% 1.64/1.80 tff(7578,plain,
% 1.64/1.80 ((s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[2728, 51, 7577])).
% 1.64/1.80 tff(7579,plain,
% 1.64/1.80 (b(s(s(s(elem!1))), s(s(z)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[7578, 2516])).
% 1.64/1.80 tff(7580,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(7581,plain,
% 1.64/1.80 (((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(7582,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[7581])).
% 1.64/1.80 tff(7583,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[7582, 7580])).
% 1.64/1.80 tff(7584,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(7585,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[7584, 7583])).
% 1.64/1.81 tff(7586,plain,
% 1.64/1.81 (~b(s(s(s(elem!1))), z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[7585, 319, 3892, 7579, 711])).
% 1.64/1.81 tff(7587,plain,
% 1.64/1.81 (r(s(s(s(elem!1))), z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1077, 51, 160, 7586])).
% 1.64/1.81 tff(7588,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[7530, 297, 115, 335, 7587])).
% 1.64/1.81 tff(7589,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~r(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(7590,plain,
% 1.64/1.81 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[7589, 7576, 711, 115])).
% 1.64/1.81 tff(7591,plain,
% 1.64/1.81 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[348, 7590, 7574])).
% 1.64/1.81 tff(7592,plain,
% 1.64/1.81 (s(s(elem!1)) = s(s(s(elem!1)))),
% 1.64/1.81 inference(symmetry,[status(thm)],[7591])).
% 1.64/1.81 tff(7593,plain,
% 1.64/1.81 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[7592])).
% 1.64/1.81 tff(7594,plain,
% 1.64/1.81 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 1.64/1.81 inference(symmetry,[status(thm)],[7593])).
% 1.64/1.81 tff(7595,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(7596,plain,
% 1.64/1.81 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(7597,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[7596])).
% 1.64/1.81 tff(7598,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[7597, 7595])).
% 1.64/1.81 tff(7599,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(7600,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[7599, 7598])).
% 1.64/1.81 tff(7601,plain,
% 1.64/1.81 (~b(s(s(s(z))), z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[7600, 319, 1, 202, 4230])).
% 1.64/1.81 tff(7602,plain,
% 1.64/1.81 (r(s(s(s(z))), z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4584, 7601])).
% 1.64/1.81 tff(7603,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4265, 297, 1100, 7602, 6566])).
% 1.64/1.81 tff(7604,plain,((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(7605,plain,
% 1.64/1.81 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[7604, 872, 202, 817])).
% 1.64/1.81 tff(7606,plain,
% 1.64/1.81 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[6520, 7591, 7605])).
% 1.64/1.81 tff(7607,plain,
% 1.64/1.81 ((s(elem!1) = s(s(elem!1))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[7592])).
% 1.64/1.81 tff(7608,plain,
% 1.64/1.81 ((s(elem!1) = s(s(elem!1))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.64/1.81 inference(transitivity,[status(thm)],[7607, 276])).
% 1.64/1.81 tff(7609,plain,
% 1.64/1.81 ((s(elem!1) = s(s(elem!1))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[7608, 277])).
% 1.64/1.81 tff(7610,plain,
% 1.64/1.81 (s(elem!1) = s(s(elem!1))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[5182, 7591])).
% 1.64/1.81 tff(7611,plain,
% 1.64/1.81 (s(elem!1) = s(s(s(elem!1)))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[7610, 7609])).
% 1.64/1.81 tff(7612,plain,
% 1.64/1.81 (s(s(s(elem!1))) = elem!1),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[5346, 7591])).
% 1.64/1.81 tff(7613,plain,
% 1.64/1.81 (elem!1 = s(s(s(elem!1)))),
% 1.64/1.81 inference(symmetry,[status(thm)],[7612])).
% 1.64/1.81 tff(7614,plain,
% 1.64/1.81 (elem!1 = s(s(elem!1))),
% 1.64/1.81 inference(transitivity,[status(thm)],[7613, 7591])).
% 1.64/1.81 tff(7615,plain,
% 1.64/1.81 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(elem!1)))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[7614])).
% 1.64/1.81 tff(7616,plain,
% 1.64/1.81 ((s(s(z)) = s(s(elem!1))) <=> (s(s(z)) = elem!1)),
% 1.64/1.81 inference(symmetry,[status(thm)],[7615])).
% 1.64/1.81 tff(7617,plain,
% 1.64/1.81 ((~(s(s(z)) = s(s(elem!1)))) <=> (~(s(s(z)) = elem!1))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[7616])).
% 1.64/1.81 tff(7618,plain,
% 1.64/1.81 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = s(s(elem!1)))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[7591])).
% 1.64/1.81 tff(7619,plain,
% 1.64/1.81 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(z)) = s(s(elem!1))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[7618])).
% 1.64/1.81 tff(7620,plain,
% 1.64/1.81 (~(s(s(z)) = s(s(elem!1)))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[231, 7619])).
% 1.64/1.81 tff(7621,plain,
% 1.64/1.81 (~(s(s(z)) = elem!1)),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[7620, 7617])).
% 1.64/1.81 tff(7622,plain,
% 1.64/1.81 (~(s(s(s(z))) = s(elem!1))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[2759, 7621])).
% 1.64/1.81 tff(7623,plain,
% 1.64/1.81 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4481, 7622, 7611])).
% 1.64/1.81 tff(7624,plain,
% 1.64/1.81 (r(s(s(s(z))), s(s(s(elem!1))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3794, 7623, 7606])).
% 1.64/1.81 tff(7625,plain,
% 1.64/1.81 (r(s(s(s(z))), s(s(elem!1)))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[7624, 7594])).
% 1.64/1.81 tff(7626,plain,
% 1.64/1.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(7627,plain,
% 1.64/1.81 (((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(7628,plain,
% 1.64/1.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[7627])).
% 1.64/1.81 tff(7629,plain,
% 1.64/1.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[7628, 7626])).
% 1.64/1.81 tff(7630,plain,
% 1.64/1.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(7631,plain,
% 1.64/1.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[7630, 7629])).
% 1.64/1.81 tff(7632,plain,
% 1.64/1.81 ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[7631, 297, 7576])).
% 1.64/1.81 tff(7633,plain,
% 1.64/1.81 (~r(s(s(z)), s(s(s(z))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[7632, 7625])).
% 1.64/1.81 tff(7634,plain,
% 1.64/1.81 ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[6671, 51, 7633])).
% 1.64/1.81 tff(7635,plain,
% 1.64/1.81 (b(s(s(z)), s(s(s(z))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[7634, 6656])).
% 1.64/1.81 tff(7636,plain,
% 1.64/1.81 (~r(s(s(s(z))), s(s(z)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[6527, 7624, 7576, 7591])).
% 1.64/1.81 tff(7637,plain,
% 1.64/1.81 (b(s(s(s(z))), s(s(z)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[2920, 7636])).
% 1.64/1.81 tff(7638,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(7639,plain,
% 1.64/1.81 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(7640,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[7639])).
% 1.64/1.81 tff(7641,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[7640, 7638])).
% 1.64/1.81 tff(7642,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(7643,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[7642, 7641])).
% 1.64/1.81 tff(7644,plain,
% 1.64/1.81 (~b(s(s(s(z))), z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[7643, 319, 711, 7637, 7635])).
% 1.64/1.81 tff(7645,plain,
% 1.64/1.81 (r(s(s(s(z))), z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4584, 7644])).
% 1.64/1.81 tff(7646,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4865, 297, 115, 7645, 7625])).
% 1.64/1.81 tff(7647,plain,(r(s(s(elem!1)), s(z)) | (~r(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(7648,plain,
% 1.64/1.81 (r(s(s(elem!1)), s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[7647, 817, 7573, 202, 76])).
% 1.64/1.81 tff(7649,plain,
% 1.64/1.81 (~r(s(z), z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[5094, 7648, 76])).
% 1.64/1.81 tff(7650,plain,
% 1.64/1.81 (b(s(z), z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[67, 7649])).
% 1.64/1.81 tff(7651,plain,
% 1.64/1.81 (~b(s(s(elem!1)), s(s(z)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[7352, 7650, 202, 76, 817])).
% 1.64/1.81 tff(7652,plain,
% 1.64/1.81 (~r(z, s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3560, 7648, 76])).
% 1.64/1.81 tff(7653,plain,
% 1.64/1.81 (b(z, s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1099, 7652])).
% 1.64/1.81 tff(7654,plain,
% 1.64/1.81 (~r(s(s(elem!1)), s(s(z)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[6404, 7648, 7573, 7653])).
% 1.64/1.81 tff(7655,plain,
% 1.64/1.81 (s(s(elem!1)) = s(s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[5327, 7654, 7651])).
% 1.64/1.81 tff(7656,plain,
% 1.64/1.81 (b(s(s(elem!1)), z) <=> b(s(s(z)), z)),
% 1.64/1.81 inference(monotonicity,[status(thm)],[7655])).
% 1.64/1.81 tff(7657,plain,
% 1.64/1.81 ((~b(s(s(elem!1)), z)) <=> (~b(s(s(z)), z))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[7656])).
% 1.64/1.81 tff(7658,plain,
% 1.64/1.81 (~b(s(s(z)), z)),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[71, 7657])).
% 1.64/1.81 tff(7659,plain,
% 1.64/1.81 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[7655])).
% 1.64/1.81 tff(7660,plain,
% 1.64/1.81 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.64/1.81 inference(symmetry,[status(thm)],[7659])).
% 1.64/1.81 tff(7661,plain,
% 1.64/1.81 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[7660])).
% 1.64/1.81 tff(7662,plain,
% 1.64/1.81 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(z))))),
% 1.64/1.81 inference(symmetry,[status(thm)],[7661])).
% 1.64/1.81 tff(7663,plain,
% 1.64/1.81 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(z))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[7659])).
% 1.64/1.81 tff(7664,plain,
% 1.64/1.81 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 1.64/1.81 inference(symmetry,[status(thm)],[7663])).
% 1.64/1.81 tff(7665,plain,
% 1.64/1.81 ((~b(s(s(z)), s(s(s(z))))) <=> (~b(s(s(z)), s(s(s(elem!1)))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[7664])).
% 1.64/1.81 tff(7666,plain,
% 1.64/1.81 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(z)))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[7655])).
% 1.64/1.81 tff(7667,plain,
% 1.64/1.81 (b(s(z), s(s(z)))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[817, 7666])).
% 1.64/1.81 tff(7668,plain,
% 1.64/1.81 (s(s(z)) = s(s(elem!1))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[2521, 7655])).
% 1.64/1.81 tff(7669,plain,
% 1.64/1.81 (s(z) = s(elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[138, 7668])).
% 1.64/1.81 tff(7670,plain,
% 1.64/1.81 (z = elem!1),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[148, 7669])).
% 1.64/1.81 tff(7671,plain,
% 1.64/1.81 (b(s(z), z) <=> b(s(z), elem!1)),
% 1.64/1.81 inference(monotonicity,[status(thm)],[7670])).
% 1.64/1.81 tff(7672,plain,
% 1.64/1.81 (b(s(z), elem!1)),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[7650, 7671])).
% 1.64/1.81 tff(7673,plain,
% 1.64/1.81 (b(z, s(s(z))) <=> b(elem!1, s(s(z)))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[7670])).
% 1.64/1.81 tff(7674,plain,
% 1.64/1.81 (b(elem!1, s(s(z)))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[7573, 7673])).
% 1.64/1.81 tff(7675,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(7676,plain,
% 1.64/1.81 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1))) <=> ((~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(7677,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(s(s(z)))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[7676])).
% 1.64/1.81 tff(7678,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[7677, 7675])).
% 1.64/1.81 tff(7679,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(7680,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(s(s(z)))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[7679, 7678])).
% 1.64/1.81 tff(7681,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[7680, 319, 240, 912, 4787, 3133])).
% 1.64/1.81 tff(7682,plain,((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(7683,plain,
% 1.64/1.81 (~b(s(s(z)), s(s(s(z))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[7682, 7674, 7672, 7667])).
% 1.64/1.81 tff(7684,plain,
% 1.64/1.81 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[7683, 7665])).
% 1.64/1.81 tff(7685,plain,
% 1.64/1.81 (r(s(s(z)), s(s(s(elem!1))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1571, 7684])).
% 1.64/1.81 tff(7686,plain,
% 1.64/1.81 (r(s(s(z)), s(s(s(z))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[7685, 7662])).
% 1.64/1.81 tff(7687,plain,
% 1.64/1.81 (~b(s(s(s(z))), s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[6719, 7686, 7653, 7650, 7658])).
% 1.64/1.81 tff(7688,plain,
% 1.64/1.81 (r(s(s(elem!1)), s(z)) <=> r(s(s(z)), s(z))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[7655])).
% 1.64/1.81 tff(7689,plain,
% 1.64/1.81 (r(s(s(z)), s(z))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[7648, 7688])).
% 1.64/1.81 tff(7690,plain,
% 1.64/1.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(7691,plain,
% 1.64/1.81 (((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(7692,plain,
% 1.64/1.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[7691])).
% 1.64/1.81 tff(7693,plain,
% 1.64/1.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[7692, 7690])).
% 1.64/1.81 tff(7694,plain,
% 1.64/1.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(7695,plain,
% 1.64/1.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[7694, 7693])).
% 1.64/1.81 tff(7696,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[7695, 297, 2511, 3502, 4539])).
% 1.64/1.81 tff(7697,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(7698,plain,
% 1.64/1.81 (~r(s(s(s(z))), s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[7697, 7686, 7689])).
% 1.64/1.81 tff(7699,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4549, 7698, 7687])).
% 1.64/1.81 tff(7700,plain,((~b(s(z), s(s(elem!1)))) | b(s(s(elem!1)), z) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(7701,plain,
% 1.64/1.81 (~b(s(z), s(s(elem!1)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[7700, 71, 202])).
% 1.64/1.81 tff(7702,plain,
% 1.64/1.81 (r(s(z), s(s(elem!1)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1047, 7701])).
% 1.64/1.81 tff(7703,plain,
% 1.64/1.81 (~r(s(z), z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[304, 7702, 76])).
% 1.64/1.81 tff(7704,plain,
% 1.64/1.81 (b(s(z), z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[67, 7703])).
% 1.64/1.81 tff(7705,plain,
% 1.64/1.81 (~r(s(z), s(s(z)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[5690, 2578, 444])).
% 1.64/1.81 tff(7706,plain,
% 1.64/1.81 (b(s(z), s(s(z)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[685, 7705])).
% 1.64/1.81 tff(7707,plain,
% 1.64/1.81 (~r(s(s(z)), s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[2583, 2578, 444])).
% 1.64/1.81 tff(7708,plain,
% 1.64/1.81 (b(s(s(z)), s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4102, 7707])).
% 1.64/1.81 tff(7709,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[5700, 319, 7708, 711, 7706, 2493])).
% 1.64/1.81 tff(7710,plain,((~r(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(7711,plain,
% 1.64/1.81 (~r(s(s(z)), s(s(elem!1)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[7710, 7573, 7704, 7702])).
% 1.64/1.81 tff(7712,plain,
% 1.64/1.81 (b(s(s(z)), s(s(elem!1)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[2127, 180, 69])).
% 1.64/1.81 tff(7713,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[719, 7712, 872, 202, 711])).
% 1.64/1.81 tff(7714,plain,(r(s(s(elem!1)), s(z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | r(s(s(z)), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(7715,plain,
% 1.64/1.81 (r(s(s(elem!1)), s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[7714, 7573, 202, 7711])).
% 1.64/1.81 tff(7716,plain,
% 1.64/1.81 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[7018, 7573, 7704, 76, 7715])).
% 1.64/1.81 tff(7717,plain,
% 1.64/1.81 (b(s(z), z) <=> b(s(z), elem!1)),
% 1.64/1.81 inference(monotonicity,[status(thm)],[187])).
% 1.64/1.81 tff(7718,plain,
% 1.64/1.81 (b(s(z), elem!1)),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[2493, 7717])).
% 1.64/1.81 tff(7719,plain,
% 1.64/1.81 (b(s(elem!1), elem!1)),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[7718, 886])).
% 1.64/1.81 tff(7720,plain,
% 1.64/1.81 (b(z, s(z)) <=> b(elem!1, s(elem!1))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[187, 135])).
% 1.64/1.81 tff(7721,plain,
% 1.64/1.81 (b(elem!1, s(elem!1))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[5088, 7720])).
% 1.64/1.81 tff(7722,plain,
% 1.64/1.81 (r(s(s(elem!1)), s(s(s(s(elem!1))))) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[961])).
% 1.64/1.82 tff(7723,plain,
% 1.64/1.82 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(symmetry,[status(thm)],[7722])).
% 1.64/1.82 tff(7724,plain,
% 1.64/1.82 ((~r(s(s(elem!1)), s(s(s(s(z)))))) <=> (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[7723])).
% 1.64/1.82 tff(7725,plain,
% 1.64/1.82 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[6348, 7724])).
% 1.64/1.82 tff(7726,plain,
% 1.64/1.82 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1259, 51, 7725, 2330])).
% 1.64/1.82 tff(7727,plain,
% 1.64/1.82 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1002, 319, 275, 449, 1445])).
% 1.64/1.82 tff(7728,plain,
% 1.64/1.82 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[595, 7727, 590])).
% 1.64/1.82 tff(7729,plain,
% 1.64/1.82 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[2395, 7728, 2390])).
% 1.64/1.82 tff(7730,plain,
% 1.64/1.82 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[571, 7729, 560])).
% 1.64/1.82 tff(7731,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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)), s(s(s(s(elem!1)))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(7732,plain,
% 1.64/1.82 (((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(7733,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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)), s(s(s(s(elem!1))))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[7732])).
% 1.64/1.82 tff(7734,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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)), s(s(s(s(elem!1)))))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[7733, 7731])).
% 1.64/1.82 tff(7735,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(7736,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[7735, 7734])).
% 1.64/1.82 tff(7737,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[7736, 319, 1445, 7730, 397, 2336])).
% 1.64/1.82 tff(7738,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(7739,plain,
% 1.64/1.82 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[7738, 1116, 7726, 2202, 5102, 2213, 7721, 7719])).
% 1.64/1.82 tff(7740,plain,
% 1.64/1.82 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[616, 7739, 605])).
% 1.64/1.82 tff(7741,plain,
% 1.64/1.82 (s(s(elem!1)) = s(s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[5127, 133])).
% 1.64/1.82 tff(7742,plain,
% 1.64/1.82 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[5122, 7741, 115, 2169])).
% 1.64/1.82 tff(7743,plain,
% 1.64/1.82 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[348, 232, 7742])).
% 1.64/1.82 tff(7744,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(7745,plain,
% 1.64/1.82 (((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(7746,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[7745])).
% 1.64/1.82 tff(7747,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[7746, 7744])).
% 1.64/1.82 tff(7748,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(7749,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[7748, 7747])).
% 1.64/1.82 tff(7750,plain,
% 1.64/1.82 (~b(s(s(s(elem!1))), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[7749, 319, 7743, 1116, 7726])).
% 1.64/1.82 tff(7751,plain,
% 1.64/1.82 (r(s(s(s(elem!1))), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[361, 7750, 249])).
% 1.64/1.82 tff(7752,plain,
% 1.64/1.82 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1892, 297, 7751, 7740])).
% 1.64/1.82 tff(7753,plain,
% 1.64/1.82 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[1326])).
% 1.64/1.82 tff(7754,plain,
% 1.64/1.82 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[1331, 7753])).
% 1.64/1.82 tff(7755,plain,
% 1.64/1.82 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[558, 51, 7754, 7752])).
% 1.64/1.82 tff(7756,plain,
% 1.64/1.82 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(7757,plain,
% 1.64/1.82 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(7758,plain,
% 1.64/1.82 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[7757, 7756])).
% 1.64/1.82 tff(7759,plain,
% 1.64/1.82 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[7758, 297, 441, 7740])).
% 1.64/1.82 tff(7760,plain,
% 1.64/1.82 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[571, 7759, 2202])).
% 1.64/1.82 tff(7761,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[2434, 319, 7743, 7760, 7726, 7755])).
% 1.64/1.82 tff(7762,plain,((~(s(s(z)) = s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(s(z))))) | (~r(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(7763,plain,
% 1.64/1.82 (~(s(s(z)) = s(s(elem!1)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[7762, 7716, 7715, 7704, 202, 76])).
% 1.64/1.82 tff(7764,plain,
% 1.64/1.82 (b(s(s(z)), s(s(elem!1)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[122, 7763, 7711])).
% 1.64/1.82 tff(7765,plain,
% 1.64/1.82 (~r(z, s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3560, 7715, 76])).
% 1.64/1.82 tff(7766,plain,
% 1.64/1.82 (b(z, s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1099, 7765])).
% 1.64/1.82 tff(7767,plain,
% 1.64/1.82 (~r(s(s(elem!1)), s(s(z)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[6404, 7766, 7573, 7715])).
% 1.64/1.82 tff(7768,plain,
% 1.64/1.82 (~(s(s(elem!1)) = s(s(z)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[2521, 7763])).
% 1.64/1.82 tff(7769,plain,
% 1.64/1.82 (b(s(s(elem!1)), s(s(z)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[5327, 7768, 7767])).
% 1.64/1.82 tff(7770,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(7771,plain,
% 1.64/1.82 (((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(7772,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[7771])).
% 1.64/1.82 tff(7773,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[7772, 7770])).
% 1.64/1.82 tff(7774,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1)))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(7775,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[7774, 7773])).
% 1.64/1.82 tff(7776,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[7775, 319, 7573, 7769, 7764, 202])).
% 1.64/1.82 tff(7777,plain,(b(s(s(elem!1)), z) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(7778,plain,
% 1.64/1.82 (b(s(s(elem!1)), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[7777, 7301])).
% 1.64/1.82 tff(7779,plain,
% 1.64/1.82 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[7059, 3739])).
% 1.64/1.82 tff(7780,plain,
% 1.64/1.82 (~r(s(s(s(elem!1))), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[5133, 297, 444, 335])).
% 1.64/1.82 tff(7781,plain,
% 1.64/1.82 (b(s(s(s(elem!1))), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1088, 51, 171, 7780])).
% 1.64/1.82 tff(7782,plain,
% 1.64/1.82 (~r(s(s(z)), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[2581, 297, 444, 2578])).
% 1.64/1.82 tff(7783,plain,
% 1.64/1.82 (b(s(s(z)), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4102, 7782])).
% 1.64/1.82 tff(7784,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(7785,plain,
% 1.64/1.82 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(7786,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[7785])).
% 1.64/1.82 tff(7787,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[7786, 7784])).
% 1.64/1.82 tff(7788,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(7789,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[7788, 7787])).
% 1.64/1.82 tff(7790,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[7789, 319, 3892, 7783, 5692, 7781])).
% 1.64/1.82 tff(7791,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(7792,plain,
% 1.64/1.82 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[7791, 444, 2578])).
% 1.64/1.82 tff(7793,plain,
% 1.64/1.82 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[348, 7792, 58])).
% 1.64/1.82 tff(7794,plain,
% 1.64/1.82 (r(s(elem!1), s(s(elem!1)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[807, 4687, 2142])).
% 1.64/1.82 tff(7795,plain,
% 1.64/1.82 (~r(s(elem!1), s(s(z)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3361, 7794, 2578])).
% 1.64/1.82 tff(7796,plain,
% 1.64/1.82 (~r(s(elem!1), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[853, 297, 444, 7794])).
% 1.64/1.82 tff(7797,plain,
% 1.64/1.82 (b(s(elem!1), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[783, 7796, 776])).
% 1.64/1.82 tff(7798,plain,
% 1.64/1.82 (~(s(z) = s(elem!1))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[2503, 776])).
% 1.64/1.82 tff(7799,plain,
% 1.64/1.82 (~r(s(z), s(elem!1))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3309, 297, 444, 7794])).
% 1.64/1.82 tff(7800,plain,
% 1.64/1.82 (b(s(z), s(elem!1))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[2638, 51, 7799, 7798])).
% 1.64/1.82 tff(7801,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[6952, 319, 3390, 3926, 2541, 2842])).
% 1.64/1.82 tff(7802,plain,((~b(s(z), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(7803,plain,
% 1.64/1.82 (~b(s(elem!1), s(s(z)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[7802, 7800, 3390, 7797])).
% 1.64/1.82 tff(7804,plain,
% 1.64/1.82 (s(elem!1) = s(s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[2529, 7803, 7795])).
% 1.64/1.82 tff(7805,plain,
% 1.64/1.82 (s(s(elem!1)) = s(s(s(z)))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[7804])).
% 1.64/1.82 tff(7806,plain,
% 1.64/1.82 (b(z, s(s(elem!1))) <=> b(z, s(s(s(z))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[7805])).
% 1.64/1.82 tff(7807,plain,
% 1.64/1.82 (~r(z, s(s(elem!1)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[5702, 444, 2578])).
% 1.64/1.82 tff(7808,plain,
% 1.64/1.82 (b(z, s(s(elem!1)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[56, 7807])).
% 1.64/1.82 tff(7809,plain,
% 1.64/1.82 (b(z, s(s(s(z))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[7808, 7806])).
% 1.64/1.82 tff(7810,plain,
% 1.64/1.82 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[7805])).
% 1.64/1.82 tff(7811,plain,
% 1.64/1.82 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.64/1.82 inference(symmetry,[status(thm)],[7810])).
% 1.64/1.82 tff(7812,plain,
% 1.64/1.82 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[7811])).
% 1.64/1.82 tff(7813,plain,
% 1.64/1.82 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.82 inference(symmetry,[status(thm)],[7812])).
% 1.64/1.82 tff(7814,plain,
% 1.64/1.82 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[7805])).
% 1.64/1.82 tff(7815,plain,
% 1.64/1.82 (b(s(s(s(elem!1))), s(s(s(z))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[116, 7814])).
% 1.64/1.82 tff(7816,plain,
% 1.64/1.82 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[7815, 7813])).
% 1.64/1.82 tff(7817,plain,
% 1.64/1.82 (r(s(s(z)), s(s(s(z))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3496, 7804, 2578])).
% 1.64/1.82 tff(7818,plain,
% 1.64/1.82 ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1))))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3255, 297, 5457])).
% 1.64/1.82 tff(7819,plain,
% 1.64/1.82 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[7818, 3126])).
% 1.64/1.82 tff(7820,plain,
% 1.64/1.82 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[7819, 3123])).
% 1.64/1.82 tff(7821,plain,
% 1.64/1.82 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[634, 7820, 3121])).
% 1.64/1.82 tff(7822,plain,
% 1.64/1.82 (b(s(z), s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[7821, 3113])).
% 1.64/1.82 tff(7823,plain,
% 1.64/1.82 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3671, 297, 5457, 3502])).
% 1.64/1.82 tff(7824,plain,
% 1.64/1.82 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[7823, 3490])).
% 1.64/1.82 tff(7825,plain,
% 1.64/1.82 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[595, 7824, 3200])).
% 1.64/1.82 tff(7826,plain,
% 1.64/1.82 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[7825, 3489])).
% 1.64/1.82 tff(7827,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(7828,plain,
% 1.64/1.82 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1))))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(7829,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[7828])).
% 1.64/1.82 tff(7830,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[7829, 7827])).
% 1.64/1.83 tff(7831,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(7832,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[7831, 7830])).
% 1.64/1.83 tff(7833,plain,
% 1.64/1.83 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[7832, 319, 3390, 4787, 7826])).
% 1.64/1.83 tff(7834,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[7833, 7822])).
% 1.64/1.83 tff(7835,plain,((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~(s(elem!1) = s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(7836,plain,
% 1.64/1.83 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[7835, 7817, 3390, 5692, 444, 7804])).
% 1.64/1.83 tff(7837,plain,
% 1.64/1.83 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(s(s(elem!1)))) = s(s(s(z))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[7805])).
% 1.64/1.83 tff(7838,plain,
% 1.64/1.83 ((~(s(s(s(s(elem!1)))) = s(s(elem!1)))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(z)))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[7837])).
% 1.64/1.83 tff(7839,plain,
% 1.64/1.83 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4690, 4687, 116])).
% 1.64/1.83 tff(7840,plain,
% 1.64/1.83 (~(s(s(s(s(elem!1)))) = s(s(s(z))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[7839, 7838])).
% 1.64/1.83 tff(7841,plain,
% 1.64/1.83 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1346, 7840, 7836])).
% 1.64/1.83 tff(7842,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(7843,plain,
% 1.64/1.83 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(7844,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[7843])).
% 1.64/1.83 tff(7845,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[7844, 7842])).
% 1.64/1.83 tff(7846,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(7847,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[7846, 7845])).
% 1.64/1.83 tff(7848,plain,
% 1.64/1.83 (~b(s(s(s(s(elem!1)))), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[7847, 319, 3203, 3586, 3585])).
% 1.64/1.83 tff(7849,plain,
% 1.64/1.83 (r(s(s(s(s(elem!1)))), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[3268, 51, 604, 7848])).
% 1.64/1.83 tff(7850,plain,
% 1.64/1.83 (~b(s(s(s(s(z)))), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[3592, 319, 2966, 3586, 3585])).
% 1.64/1.83 tff(7851,plain,
% 1.64/1.83 (r(s(s(s(s(z)))), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[2481, 51, 2478, 7850])).
% 1.64/1.83 tff(7852,plain,
% 1.64/1.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(7853,plain,
% 1.64/1.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(7854,plain,
% 1.64/1.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[7853, 7852])).
% 1.64/1.83 tff(7855,plain,
% 1.64/1.83 (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[7854, 297, 7851, 7849])).
% 1.64/1.83 tff(7856,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(7857,plain,
% 1.64/1.83 (((~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(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(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(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(7858,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[7857])).
% 1.64/1.83 tff(7859,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[7858, 7856])).
% 1.64/1.83 tff(7860,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(7861,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[7860, 7859])).
% 1.64/1.83 tff(7862,plain,
% 1.64/1.83 (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[7861, 319, 3203, 2966, 3585])).
% 1.64/1.83 tff(7863,plain,
% 1.64/1.83 ((s(s(s(s(elem!1)))) = s(s(s(s(z))))) | r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[3229, 51, 7862])).
% 1.64/1.83 tff(7864,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[7863, 7855, 3219])).
% 1.64/1.83 tff(7865,plain,((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~(s(elem!1) = 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)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(7866,plain,
% 1.64/1.83 (~b(s(s(s(z))), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[7865, 7841, 7804, 7816, 7809, 99])).
% 1.64/1.83 tff(7867,plain,
% 1.64/1.83 (b(s(s(elem!1)), z) <=> b(s(s(s(z))), z)),
% 1.64/1.83 inference(monotonicity,[status(thm)],[2970])).
% 1.64/1.83 tff(7868,plain,
% 1.64/1.83 (b(s(s(s(z))), z)),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[496, 7867])).
% 1.64/1.83 tff(7869,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4582, 7868])).
% 1.64/1.83 tff(7870,plain,((~b(s(s(elem!1)), z)) | b(s(s(s(z))), z) | (~(s(elem!1) = s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(7871,plain,
% 1.64/1.83 (~b(s(s(elem!1)), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[7870, 7866, 7804])).
% 1.64/1.83 tff(7872,plain,
% 1.64/1.83 (r(s(s(elem!1)), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[75, 7871])).
% 1.64/1.83 tff(7873,plain,
% 1.64/1.83 (~r(s(s(z)), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[3526, 7872, 2578])).
% 1.64/1.83 tff(7874,plain,
% 1.64/1.83 (~r(s(elem!1), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[3179, 7873, 7804])).
% 1.64/1.83 tff(7875,plain,
% 1.64/1.83 (b(s(elem!1), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[2602, 7874])).
% 1.64/1.83 tff(7876,plain,
% 1.64/1.83 (b(s(s(z)), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[3187, 7875, 7804])).
% 1.64/1.83 tff(7877,plain,
% 1.64/1.83 (~b(z, s(s(z)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[5730, 3204, 2493, 3390])).
% 1.64/1.83 tff(7878,plain,
% 1.64/1.83 (r(z, s(s(z)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[729, 7877])).
% 1.64/1.83 tff(7879,plain,
% 1.64/1.83 (~r(z, s(s(elem!1)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[3463, 7878, 2578])).
% 1.64/1.83 tff(7880,plain,
% 1.64/1.83 (b(z, s(s(elem!1)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[56, 7879])).
% 1.64/1.83 tff(7881,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(7882,plain,
% 1.64/1.83 (((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(7883,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[7882])).
% 1.64/1.83 tff(7884,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)))),
% 1.64/1.83 inference(transitivity,[status(thm)],[7883, 7881])).
% 1.64/1.83 tff(7885,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(7886,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[7885, 7884])).
% 1.64/1.83 tff(7887,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[7886, 319, 3390, 7880, 3204, 2493])).
% 1.64/1.83 tff(7888,plain,((~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~r(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(7889,plain,
% 1.64/1.83 (~b(s(z), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[7888, 7876, 3390, 2578])).
% 1.64/1.83 tff(7890,plain,
% 1.64/1.83 (~r(s(z), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[5094, 7872, 2169])).
% 1.64/1.83 tff(7891,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[65, 51, 62, 7890, 7889])).
% 1.64/1.83 tff(7892,plain,(b(s(elem!1), s(s(elem!1))) | (~b(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (s(elem!1) = s(z)) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(7893,plain,
% 1.64/1.83 (b(s(elem!1), s(s(elem!1)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[7892, 7793, 2578, 2169, 93, 444, 6544, 776, 114])).
% 1.64/1.83 tff(7894,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(7895,plain,
% 1.64/1.83 (((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(7896,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[7895])).
% 1.64/1.83 tff(7897,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[7896, 7894])).
% 1.64/1.83 tff(7898,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(7899,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[7898, 7897])).
% 1.64/1.83 tff(7900,plain,
% 1.64/1.83 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[7899, 319, 7893, 7778, 7793])).
% 1.64/1.83 tff(7901,plain,
% 1.64/1.83 (~b(s(elem!1), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[3990, 319, 7893, 7301, 7778])).
% 1.64/1.83 tff(7902,plain,
% 1.64/1.83 (r(s(elem!1), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[2602, 7901])).
% 1.64/1.83 tff(7903,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(7904,plain,
% 1.64/1.83 (((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(7905,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[7904])).
% 1.64/1.83 tff(7906,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[7905, 7903])).
% 1.64/1.83 tff(7907,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(7908,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[7907, 7906])).
% 1.64/1.83 tff(7909,plain,
% 1.64/1.83 (~b(z, s(s(s(elem!1))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[7908, 319, 7301, 7778, 7793])).
% 1.64/1.83 tff(7910,plain,
% 1.64/1.83 (r(z, s(s(s(elem!1))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[416, 7909])).
% 1.64/1.83 tff(7911,plain,
% 1.64/1.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(7912,plain,
% 1.64/1.83 (((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(7913,plain,
% 1.64/1.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1)))))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[7912])).
% 1.64/1.83 tff(7914,plain,
% 1.64/1.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[7913, 7911])).
% 1.64/1.83 tff(7915,plain,
% 1.64/1.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(7916,plain,
% 1.64/1.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1)))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[7915, 7914])).
% 1.64/1.83 tff(7917,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[7916, 297, 731, 5050, 334])).
% 1.64/1.83 tff(7918,plain,((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(7919,plain,
% 1.64/1.83 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[7918, 7910, 7902])).
% 1.64/1.83 tff(7920,plain,
% 1.64/1.83 (s(elem!1) = s(s(s(elem!1)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[434, 7919, 7900])).
% 1.64/1.84 tff(7921,plain,
% 1.64/1.84 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[6109, 7920])).
% 1.64/1.84 tff(7922,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(7923,plain,
% 1.64/1.84 (((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1)))) <=> ((~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(7924,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[7923])).
% 1.64/1.84 tff(7925,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[7924, 7922])).
% 1.64/1.84 tff(7926,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(7927,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[7926, 7925])).
% 1.64/1.84 tff(7928,plain,
% 1.64/1.84 (~b(z, s(elem!1))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[7927, 319, 7893, 7301, 7778])).
% 1.64/1.84 tff(7929,plain,
% 1.64/1.84 (r(z, s(elem!1))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4804, 7928])).
% 1.64/1.84 tff(7930,plain,
% 1.64/1.84 (~r(s(elem!1), s(s(z)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[740, 7902, 732])).
% 1.64/1.84 tff(7931,plain,
% 1.64/1.84 (elem!1 = s(s(s(s(elem!1))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4681, 7921])).
% 1.64/1.84 tff(7932,plain,
% 1.64/1.84 (~(s(elem!1) = s(s(z)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[3120, 7931])).
% 1.64/1.84 tff(7933,plain,
% 1.64/1.84 (b(s(elem!1), s(s(z)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[2529, 7932, 7930])).
% 1.64/1.84 tff(7934,plain,
% 1.64/1.84 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(elem!1)))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[7921])).
% 1.64/1.84 tff(7935,plain,
% 1.64/1.84 (s(s(s(elem!1))) = s(elem!1)),
% 1.64/1.84 inference(transitivity,[status(thm)],[89, 7934, 118])).
% 1.64/1.84 tff(7936,plain,
% 1.64/1.84 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[7935])).
% 1.64/1.84 tff(7937,plain,
% 1.64/1.84 ((~r(s(s(s(elem!1))), s(s(elem!1)))) <=> (~r(s(elem!1), s(s(elem!1))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[7936])).
% 1.64/1.84 tff(7938,plain,
% 1.64/1.84 (~r(s(elem!1), s(s(elem!1)))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[7792, 7937])).
% 1.64/1.84 tff(7939,plain,
% 1.64/1.84 (~(s(s(z)) = s(s(elem!1)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1045, 444, 1042])).
% 1.64/1.84 tff(7940,plain,
% 1.64/1.84 (r(s(s(z)), s(s(elem!1)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[122, 7939, 33])).
% 1.64/1.84 tff(7941,plain,
% 1.64/1.84 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[7791, 7940, 444])).
% 1.64/1.84 tff(7942,plain,
% 1.64/1.84 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[348, 7941, 58])).
% 1.64/1.84 tff(7943,plain,
% 1.64/1.84 (~r(z, s(s(elem!1)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5702, 7940, 444])).
% 1.64/1.84 tff(7944,plain,
% 1.64/1.84 (b(z, s(s(elem!1)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[56, 7943])).
% 1.64/1.84 tff(7945,plain,
% 1.64/1.84 (~(s(elem!1) = s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[774, 7939])).
% 1.64/1.84 tff(7946,plain,
% 1.64/1.84 (~r(s(z), s(s(z)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5690, 7940, 444])).
% 1.64/1.84 tff(7947,plain,
% 1.64/1.84 (b(s(z), s(s(z)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[685, 7946])).
% 1.64/1.84 tff(7948,plain,
% 1.64/1.84 (~r(s(s(z)), s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[2583, 7940, 444])).
% 1.64/1.84 tff(7949,plain,
% 1.64/1.84 (b(s(s(z)), s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4102, 7948])).
% 1.64/1.84 tff(7950,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(z)))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(7951,plain,
% 1.64/1.84 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), s(z)))) <=> ((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(z)))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(7952,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(z))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[7951])).
% 1.64/1.84 tff(7953,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(z)))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[7952, 7950])).
% 1.64/1.84 tff(7954,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), s(z))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(7955,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(z))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[7954, 7953])).
% 1.64/1.84 tff(7956,plain,
% 1.64/1.84 (~b(s(elem!1), s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[7955, 319, 7949, 3926, 7947])).
% 1.64/1.84 tff(7957,plain,
% 1.64/1.84 (r(s(elem!1), s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[783, 7956, 7945])).
% 1.64/1.84 tff(7958,plain,
% 1.64/1.84 (b(s(elem!1), s(s(elem!1)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[807, 1042, 114])).
% 1.64/1.84 tff(7959,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(z), s(s(z)))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(7960,plain,
% 1.64/1.84 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(z), s(elem!1)))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(z), s(s(z)))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(7961,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(z), s(s(z))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[7960])).
% 1.64/1.84 tff(7962,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(z), s(s(z)))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[7961, 7959])).
% 1.64/1.84 tff(7963,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(z), s(elem!1))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(7964,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(z), s(s(z))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[7963, 7962])).
% 1.64/1.84 tff(7965,plain,
% 1.64/1.84 (~b(s(z), s(elem!1))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[7964, 319, 7949, 3926, 7947])).
% 1.64/1.84 tff(7966,plain,
% 1.64/1.84 (~r(z, s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[3992, 2169, 800, 2142, 202])).
% 1.64/1.84 tff(7967,plain,
% 1.64/1.84 (b(z, s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1099, 7966])).
% 1.64/1.84 tff(7968,plain,
% 1.64/1.84 (~b(z, s(s(z)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4795, 7967, 3390, 4787])).
% 1.64/1.84 tff(7969,plain,
% 1.64/1.84 (r(z, s(s(z)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[729, 7968])).
% 1.64/1.84 tff(7970,plain,
% 1.64/1.84 (~r(s(s(s(z))), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[895, 297, 7969, 889])).
% 1.64/1.84 tff(7971,plain,
% 1.64/1.84 (b(s(s(s(z))), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[901, 51, 898, 7970])).
% 1.64/1.84 tff(7972,plain,
% 1.64/1.84 (~r(s(s(elem!1)), s(elem!1))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[3077, 2169, 800])).
% 1.64/1.84 tff(7973,plain,
% 1.64/1.84 ((s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[2780, 51, 7972])).
% 1.64/1.84 tff(7974,plain,
% 1.64/1.84 (b(s(s(elem!1)), s(elem!1))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[7973, 2763])).
% 1.64/1.84 tff(7975,plain,
% 1.64/1.84 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1485, 319, 7974, 785, 116])).
% 1.64/1.84 tff(7976,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(7977,plain,
% 1.64/1.84 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(7978,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[7977])).
% 1.64/1.84 tff(7979,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[7978, 7976])).
% 1.64/1.84 tff(7980,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(7981,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[7980, 7979])).
% 1.64/1.84 tff(7982,plain,
% 1.64/1.84 (~b(s(s(s(elem!1))), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[7981, 319, 7974, 202, 116])).
% 1.64/1.84 tff(7983,plain,
% 1.64/1.84 (r(s(s(s(elem!1))), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1077, 51, 160, 7982])).
% 1.64/1.84 tff(7984,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(7985,plain,
% 1.64/1.84 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(7986,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[7985])).
% 1.64/1.84 tff(7987,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))),
% 1.64/1.84 inference(transitivity,[status(thm)],[7986, 7984])).
% 1.64/1.84 tff(7988,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(7989,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[7988, 7987])).
% 1.64/1.84 tff(7990,plain,
% 1.64/1.84 (~b(s(elem!1), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[7989, 319, 7974, 785, 202])).
% 1.64/1.84 tff(7991,plain,
% 1.64/1.84 (r(s(elem!1), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[2602, 7990])).
% 1.64/1.84 tff(7992,plain,
% 1.64/1.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(7993,plain,
% 1.64/1.84 (((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1)))))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(7994,plain,
% 1.64/1.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[7993])).
% 1.64/1.84 tff(7995,plain,
% 1.64/1.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)))),
% 1.64/1.84 inference(transitivity,[status(thm)],[7994, 7992])).
% 1.64/1.84 tff(7996,plain,
% 1.64/1.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(7997,plain,
% 1.64/1.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[7996, 7995])).
% 1.64/1.84 tff(7998,plain,
% 1.64/1.84 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[7997, 297, 7991, 7983])).
% 1.64/1.84 tff(7999,plain,
% 1.64/1.84 (s(elem!1) = s(s(s(elem!1)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[434, 7998, 7975])).
% 1.64/1.84 tff(8000,plain,
% 1.64/1.84 (s(s(s(elem!1))) = s(elem!1)),
% 1.64/1.84 inference(symmetry,[status(thm)],[7999])).
% 1.64/1.84 tff(8001,plain,
% 1.64/1.84 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(elem!1))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[8000])).
% 1.64/1.84 tff(8002,plain,
% 1.64/1.84 (r(s(z), s(elem!1)) <=> r(s(z), s(s(s(elem!1))))),
% 1.64/1.84 inference(symmetry,[status(thm)],[8001])).
% 1.64/1.84 tff(8003,plain,
% 1.64/1.84 ((s(s(s(elem!1))) = s(z)) <=> (s(elem!1) = s(z))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[8000])).
% 1.64/1.84 tff(8004,plain,
% 1.64/1.84 ((s(s(s(elem!1))) = s(z)) <=> (s(z) = s(elem!1))),
% 1.64/1.84 inference(transitivity,[status(thm)],[8003, 2499])).
% 1.64/1.84 tff(8005,plain,
% 1.64/1.84 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(z) = s(elem!1)))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[8004])).
% 1.64/1.84 tff(8006,plain,
% 1.64/1.84 (~(s(z) = s(elem!1))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[171, 8005])).
% 1.64/1.84 tff(8007,plain,
% 1.64/1.84 ((s(z) = s(elem!1)) | r(s(z), s(elem!1))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[2638, 51, 4813])).
% 1.64/1.84 tff(8008,plain,
% 1.64/1.84 (r(s(z), s(elem!1))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[8007, 8006])).
% 1.64/1.84 tff(8009,plain,
% 1.64/1.84 (r(s(z), s(s(s(elem!1))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[8008, 8002])).
% 1.64/1.84 tff(8010,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(8011,plain,
% 1.64/1.84 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(8012,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[8011])).
% 1.64/1.84 tff(8013,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[8012, 8010])).
% 1.64/1.84 tff(8014,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(8015,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[8014, 8013])).
% 1.64/1.85 tff(8016,plain,
% 1.64/1.85 (~b(z, s(s(s(elem!1))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[8015, 319, 7974, 202, 116])).
% 1.64/1.85 tff(8017,plain,
% 1.64/1.85 (r(z, s(s(s(elem!1))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[416, 8016])).
% 1.64/1.85 tff(8018,plain,
% 1.64/1.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(8019,plain,
% 1.64/1.85 (((~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(8020,plain,
% 1.64/1.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[8019])).
% 1.64/1.85 tff(8021,plain,
% 1.64/1.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[8020, 8018])).
% 1.64/1.85 tff(8022,plain,
% 1.64/1.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(8023,plain,
% 1.64/1.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[8022, 8021])).
% 1.64/1.85 tff(8024,plain,
% 1.64/1.85 ((~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[8023, 297, 8017])).
% 1.64/1.85 tff(8025,plain,
% 1.64/1.85 (~r(s(z), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[8024, 8009])).
% 1.64/1.85 tff(8026,plain,
% 1.64/1.85 (b(s(z), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[65, 51, 62, 8025])).
% 1.64/1.85 tff(8027,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(8028,plain,
% 1.64/1.85 (((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(8029,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z)))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[8028])).
% 1.64/1.85 tff(8030,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[8029, 8027])).
% 1.64/1.85 tff(8031,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(8032,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z)))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[8031, 8030])).
% 1.64/1.85 tff(8033,plain,
% 1.64/1.85 (~b(s(s(s(z))), s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[8032, 319, 3390, 7967, 4787, 8026, 7971])).
% 1.64/1.85 tff(8034,plain,
% 1.64/1.85 (r(s(s(s(z))), s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[910, 51, 30, 8033])).
% 1.64/1.85 tff(8035,plain,
% 1.64/1.85 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[6884, 297, 2169, 8034])).
% 1.64/1.85 tff(8036,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(8037,plain,
% 1.64/1.85 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(8038,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(z)))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[8037])).
% 1.64/1.85 tff(8039,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[8038, 8036])).
% 1.64/1.85 tff(8040,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(8041,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(z)))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[8040, 8039])).
% 1.64/1.85 tff(8042,plain,
% 1.64/1.85 (~b(s(s(z)), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[8041, 319, 3390, 7967, 4787])).
% 1.64/1.85 tff(8043,plain,
% 1.64/1.85 (r(s(s(z)), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[663, 51, 28, 8042])).
% 1.64/1.85 tff(8044,plain,
% 1.64/1.85 (~r(s(s(elem!1)), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[3526, 8043, 2578])).
% 1.64/1.85 tff(8045,plain,
% 1.64/1.85 (b(s(s(elem!1)), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[75, 8044])).
% 1.64/1.85 tff(8046,plain,
% 1.64/1.85 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5548, 319, 7967, 8045, 7971])).
% 1.64/1.85 tff(8047,plain,
% 1.64/1.85 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2827, 7999])).
% 1.64/1.85 tff(8048,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4066, 51, 8047, 8046, 8035])).
% 1.64/1.85 tff(8049,plain,((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | b(s(z), s(elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(8050,plain,
% 1.64/1.85 (~r(s(s(elem!1)), s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[8049, 7940, 7949, 7947, 7965, 7944, 7942, 7958, 114, 4282, 7957])).
% 1.64/1.85 tff(8051,plain,
% 1.64/1.85 (b(s(s(elem!1)), s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[871, 8050])).
% 1.64/1.85 tff(8052,plain,
% 1.64/1.85 (~b(s(s(s(elem!1))), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1073, 319, 8051, 7944, 7942])).
% 1.64/1.85 tff(8053,plain,
% 1.64/1.85 (r(s(s(s(elem!1))), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1077, 51, 160, 8052])).
% 1.64/1.85 tff(8054,plain,
% 1.64/1.85 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4448, 319, 8051, 7958, 7942])).
% 1.64/1.85 tff(8055,plain,
% 1.64/1.85 (~(s(s(elem!1)) = s(s(z)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2521, 7939])).
% 1.64/1.85 tff(8056,plain,
% 1.64/1.85 (~b(s(s(elem!1)), s(s(z)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[7369, 319, 8051, 7949, 7947])).
% 1.64/1.85 tff(8057,plain,
% 1.64/1.85 (r(s(s(elem!1)), s(s(z)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2555, 51, 8056, 8055])).
% 1.64/1.85 tff(8058,plain,
% 1.64/1.85 (~b(s(elem!1), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[794, 8051, 7958, 7944])).
% 1.64/1.85 tff(8059,plain,
% 1.64/1.85 (r(s(elem!1), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2602, 8058])).
% 1.64/1.85 tff(8060,plain,
% 1.64/1.85 (~r(z, s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[3982, 8059, 7957])).
% 1.64/1.85 tff(8061,plain,
% 1.64/1.85 (b(z, s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1099, 8060])).
% 1.64/1.85 tff(8062,plain,
% 1.64/1.85 (~b(z, s(s(z)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4795, 8061, 7949, 7947])).
% 1.64/1.85 tff(8063,plain,
% 1.64/1.85 (r(z, s(s(z)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[729, 8062])).
% 1.64/1.85 tff(8064,plain,
% 1.64/1.85 (~r(s(s(elem!1)), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4014, 8057, 8063])).
% 1.64/1.85 tff(8065,plain,
% 1.64/1.85 (b(s(s(elem!1)), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[75, 8064])).
% 1.64/1.85 tff(8066,plain,
% 1.64/1.85 (s(s(s(z))) = s(s(elem!1))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4087, 8065, 2915, 8063, 8057, 7944])).
% 1.64/1.85 tff(8067,plain,
% 1.64/1.85 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2827, 8066])).
% 1.64/1.85 tff(8068,plain,
% 1.64/1.85 (r(s(elem!1), s(s(s(elem!1))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[434, 8067, 8054])).
% 1.64/1.85 tff(8069,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[7997, 297, 8059, 8068, 8053])).
% 1.64/1.85 tff(8070,plain,((~r(s(z), s(s(elem!1)))) | b(s(s(s(z))), s(s(z))) | (~b(s(elem!1), s(s(z)))) | (s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(elem!1), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(8071,plain,
% 1.64/1.85 (b(s(s(s(z))), s(s(z)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[8070, 7938, 33, 444, 58, 7933])).
% 1.64/1.85 tff(8072,plain,
% 1.64/1.85 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(elem!1), s(s(z)))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[7935])).
% 1.64/1.85 tff(8073,plain,
% 1.64/1.85 (b(s(elem!1), s(s(z))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 1.64/1.85 inference(symmetry,[status(thm)],[8072])).
% 1.64/1.85 tff(8074,plain,
% 1.64/1.85 (b(s(s(s(elem!1))), s(s(z)))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[7933, 8073])).
% 1.64/1.85 tff(8075,assumption,(r(s(s(z)), s(s(s(elem!1))))), introduced(assumption)).
% 1.64/1.85 tff(8076,plain,
% 1.64/1.85 (r(s(s(z)), s(elem!1))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[8075, 4895])).
% 1.64/1.85 tff(8077,plain,
% 1.64/1.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(elem!1))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(8078,plain,
% 1.64/1.85 (((~r(s(s(z)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(z))))) <=> ((~r(z, s(elem!1))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(elem!1))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(8079,plain,
% 1.64/1.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(elem!1)))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[8078])).
% 1.64/1.85 tff(8080,plain,
% 1.64/1.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(elem!1))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[8079, 8077])).
% 1.64/1.85 tff(8081,plain,
% 1.64/1.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(z)))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(8082,plain,
% 1.64/1.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(elem!1)))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[8081, 8080])).
% 1.64/1.85 tff(8083,plain,
% 1.64/1.85 (~r(s(s(z)), s(elem!1))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[8082, 297, 732, 4112])).
% 1.64/1.85 tff(8084,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[8083, 8076])).
% 1.64/1.85 tff(8085,plain,((~r(s(s(z)), s(s(s(elem!1))))) | (~(s(s(s(s(elem!1)))) = s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(8086,plain,
% 1.64/1.85 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[8085, 7921, 732, 7929])).
% 1.64/1.85 tff(8087,plain,
% 1.64/1.85 (b(s(s(z)), s(s(s(elem!1))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1571, 8086])).
% 1.64/1.85 tff(8088,plain,
% 1.64/1.85 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4571, 8087, 8074, 8071])).
% 1.64/1.85 tff(8089,plain,
% 1.64/1.85 (r(s(s(s(z))), s(s(s(elem!1))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[3794, 8088, 3739])).
% 1.64/1.85 tff(8090,plain,
% 1.64/1.85 (r(s(s(s(z))), s(elem!1))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[4878, 4892])).
% 1.64/1.85 tff(8091,plain,
% 1.64/1.85 (~r(s(s(s(z))), s(elem!1))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2892, 297, 4112, 5978])).
% 1.64/1.85 tff(8092,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[8091, 8090])).
% 1.64/1.85 tff(8093,plain,((~r(s(s(s(z))), s(s(s(elem!1))))) | (~(s(s(s(s(elem!1)))) = s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(8094,plain,
% 1.64/1.85 (~r(s(s(s(z))), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[8093, 8089, 7929, 7921])).
% 1.64/1.85 tff(8095,plain,
% 1.64/1.85 (b(s(s(s(z))), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4584, 8094])).
% 1.64/1.85 tff(8096,plain,
% 1.64/1.85 (((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(8097,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[8096])).
% 1.64/1.85 tff(8098,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[8097, 4077])).
% 1.64/1.85 tff(8099,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(8100,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[8099, 8098])).
% 1.64/1.85 tff(8101,plain,
% 1.64/1.85 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[8100, 319, 7301, 7778, 8095])).
% 1.64/1.85 tff(8102,plain,
% 1.64/1.85 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2827, 7920])).
% 1.64/1.85 tff(8103,plain,
% 1.64/1.85 (r(s(s(s(z))), s(s(elem!1)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4066, 51, 8102, 8101])).
% 1.64/1.85 tff(8104,plain,
% 1.64/1.85 (~r(s(s(s(z))), s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[6886, 8103, 2169])).
% 1.64/1.85 tff(8105,plain,
% 1.64/1.85 (b(s(s(s(z))), s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4549, 8104])).
% 1.64/1.85 tff(8106,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4916, 319, 6544, 5692, 8071, 8105])).
% 1.64/1.85 tff(8107,plain,((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(z, s(s(z)))) | b(s(s(z)), s(s(elem!1))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(s(z)), s(s(elem!1)))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(8108,plain,
% 1.64/1.85 (~r(s(z), s(s(elem!1)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[8107, 58, 3739, 732, 33, 2169, 2578, 776])).
% 1.64/1.85 tff(8109,plain,
% 1.64/1.85 (b(s(z), s(s(elem!1)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1047, 8108])).
% 1.64/1.85 tff(8110,plain,
% 1.64/1.85 ((~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[3955, 7301])).
% 1.64/1.85 tff(8111,plain,
% 1.64/1.85 (~b(z, s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[8110, 8109, 6544, 2578])).
% 1.64/1.85 tff(8112,plain,
% 1.64/1.85 (r(z, s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1099, 8111])).
% 1.64/1.85 tff(8113,plain,
% 1.64/1.85 (~r(s(elem!1), s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[3992, 2169, 2142, 202, 917])).
% 1.64/1.85 tff(8114,plain,
% 1.64/1.85 ((s(elem!1) = s(z)) | b(s(elem!1), s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[781, 51, 8113])).
% 1.64/1.85 tff(8115,plain,
% 1.64/1.85 (b(s(elem!1), s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[8114, 2690])).
% 1.64/1.85 tff(8116,plain,
% 1.64/1.85 ((s(s(z)) = s(z)) | b(s(s(z)), s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[698, 51, 6543])).
% 1.64/1.85 tff(8117,plain,
% 1.64/1.85 (b(s(s(z)), s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[8116, 691])).
% 1.64/1.85 tff(8118,plain,
% 1.64/1.85 (~b(s(elem!1), s(s(z)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[3963, 319, 8117, 8115, 817])).
% 1.64/1.85 tff(8119,plain,
% 1.64/1.85 (r(s(elem!1), s(s(z)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2527, 51, 8118, 2523])).
% 1.64/1.85 tff(8120,plain,
% 1.64/1.85 (~r(s(elem!1), s(s(elem!1)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[3361, 8119, 2578])).
% 1.64/1.85 tff(8121,plain,
% 1.64/1.85 (b(s(elem!1), s(s(elem!1)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[807, 8120, 2142])).
% 1.64/1.85 tff(8122,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(8123,plain,
% 1.64/1.85 (((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(8124,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[8123])).
% 1.64/1.85 tff(8125,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[8124, 8122])).
% 1.64/1.85 tff(8126,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(8127,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[8126, 8125])).
% 1.64/1.85 tff(8128,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[8127, 319, 8115, 8121, 817, 3969])).
% 1.64/1.85 tff(8129,plain,((~r(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | (~r(s(s(z)), s(s(elem!1)))) | (s(elem!1) = s(s(z))) | (s(z) = s(elem!1)) | (~b(z, s(s(elem!1)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(8130,plain,
% 1.64/1.85 ((~r(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | (~r(s(s(z)), s(s(elem!1)))) | (s(elem!1) = s(s(z))) | (s(z) = s(elem!1)) | (~r(z, s(z)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[8129, 7301])).
% 1.64/1.85 tff(8131,plain,
% 1.64/1.85 (s(elem!1) = s(s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[8130, 8112, 2578, 7798, 2169, 114, 8109])).
% 1.64/1.85 tff(8132,plain,
% 1.64/1.85 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(z)), s(s(elem!1)))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[8131])).
% 1.64/1.85 tff(8133,plain,
% 1.64/1.85 (r(s(s(z)), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.64/1.85 inference(symmetry,[status(thm)],[8132])).
% 1.64/1.85 tff(8134,plain,
% 1.64/1.85 (r(s(elem!1), s(s(elem!1)))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[2578, 8133])).
% 1.64/1.85 tff(8135,plain,
% 1.64/1.85 (b(s(s(z)), elem!1)),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[3390, 3486])).
% 1.64/1.85 tff(8136,plain,
% 1.64/1.85 ((~b(s(elem!1), elem!1)) <=> (~b(s(s(z)), elem!1))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[3483])).
% 1.64/1.85 tff(8137,assumption,(~b(s(elem!1), elem!1)), introduced(assumption)).
% 1.64/1.85 tff(8138,plain,
% 1.64/1.85 (~b(s(s(z)), elem!1)),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[8137, 8136])).
% 1.64/1.85 tff(8139,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[8138, 8135])).
% 1.64/1.85 tff(8140,plain,((~(s(elem!1) = s(s(z)))) | (~b(s(s(z)), s(z))) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(8141,plain,
% 1.64/1.85 (b(s(elem!1), elem!1)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[8140, 8131, 6544])).
% 1.64/1.85 tff(8142,plain,
% 1.64/1.85 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[8131])).
% 1.64/1.85 tff(8143,plain,
% 1.64/1.85 (elem!1 = s(z)),
% 1.64/1.85 inference(transitivity,[status(thm)],[258, 8142, 126])).
% 1.64/1.85 tff(8144,plain,
% 1.64/1.85 (b(elem!1, s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[8143])).
% 1.64/1.85 tff(8145,plain,
% 1.64/1.85 (b(s(z), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 1.64/1.85 inference(symmetry,[status(thm)],[8144])).
% 1.64/1.85 tff(8146,plain,
% 1.64/1.85 (b(elem!1, s(s(elem!1)))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[8109, 8145])).
% 1.64/1.85 tff(8147,plain,
% 1.64/1.85 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[3623, 8146, 2169, 8131, 8141, 8134])).
% 1.64/1.85 tff(8148,plain,
% 1.64/1.85 (b(s(s(s(z))), z) | (~(s(elem!1) = s(s(z))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[7870, 7778])).
% 1.64/1.85 tff(8149,plain,
% 1.64/1.85 (b(s(s(s(z))), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[8148, 8131])).
% 1.64/1.85 tff(8150,plain,
% 1.64/1.85 (s(s(elem!1)) = s(s(s(z)))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[8131])).
% 1.64/1.85 tff(8151,plain,
% 1.64/1.85 (b(z, s(s(elem!1))) <=> b(z, s(s(s(z))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[8150])).
% 1.64/1.85 tff(8152,plain,
% 1.64/1.85 (b(z, s(s(s(z))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[7301, 8151])).
% 1.64/1.85 tff(8153,plain,
% 1.64/1.85 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[3595, 8152, 8109, 8112, 8149, 8131])).
% 1.64/1.85 tff(8154,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[3600, 8153, 8147, 7779])).
% 1.64/1.85 tff(8155,plain,((s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(z, s(s(z)))) | b(s(s(z)), s(s(elem!1))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(8156,plain,
% 1.64/1.85 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[8155, 2169, 2578, 3739, 732, 33, 776])).
% 1.64/1.85 tff(8157,plain,
% 1.64/1.85 (~r(s(s(s(z))), s(s(z)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[6527, 4878, 2578, 5177])).
% 1.64/1.86 tff(8158,plain,
% 1.64/1.86 (b(s(s(s(z))), s(s(z)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2920, 8157])).
% 1.64/1.86 tff(8159,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4916, 319, 3390, 4787, 8158, 6506])).
% 1.64/1.86 tff(8160,plain,((~r(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(8161,plain,
% 1.64/1.86 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[8160, 5692, 6544, 2578, 5177, 6492])).
% 1.64/1.86 tff(8162,plain,
% 1.64/1.86 (b(s(s(s(z))), s(s(s(elem!1))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[3794, 8161, 3739])).
% 1.64/1.86 tff(8163,plain,
% 1.64/1.86 (b(s(s(s(z))), s(s(elem!1)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[6520, 8162, 5177])).
% 1.64/1.86 tff(8164,plain,
% 1.64/1.86 (~b(s(s(s(z))), z)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4082, 319, 7301, 7778, 4230])).
% 1.64/1.86 tff(8165,plain,
% 1.64/1.86 (r(s(s(s(z))), z)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4584, 8164])).
% 1.64/1.86 tff(8166,plain,
% 1.64/1.86 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4314, 297, 2467, 8165])).
% 1.64/1.86 tff(8167,plain,
% 1.64/1.86 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2281, 8166])).
% 1.64/1.86 tff(8168,plain,
% 1.64/1.86 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[7508, 297, 2467, 8165])).
% 1.64/1.86 tff(8169,plain,
% 1.64/1.86 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2252, 8168])).
% 1.64/1.86 tff(8170,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[6586, 319, 4230, 8169, 8167, 6352])).
% 1.64/1.86 tff(8171,plain,((~r(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(8172,plain,
% 1.64/1.86 (~r(s(s(s(s(z)))), z)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[8171, 6352, 4230])).
% 1.64/1.86 tff(8173,plain,
% 1.64/1.86 (b(s(s(s(s(z)))), z)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2482, 8172])).
% 1.64/1.86 tff(8174,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(8175,plain,
% 1.64/1.86 (((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(8176,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[8175])).
% 1.64/1.86 tff(8177,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[8176, 8174])).
% 1.64/1.86 tff(8178,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(8179,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[8178, 8177])).
% 1.64/1.86 tff(8180,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[8179, 319, 7301, 7778, 8173, 6352])).
% 1.64/1.86 tff(8181,plain,((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(8182,plain,
% 1.64/1.86 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[8181, 8163])).
% 1.64/1.86 tff(8183,plain,
% 1.64/1.86 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[6350, 8182, 6474])).
% 1.64/1.86 tff(8184,plain,
% 1.64/1.86 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[6599, 8183, 2578])).
% 1.64/1.86 tff(8185,plain,
% 1.64/1.86 (b(s(s(z)), s(s(s(s(z)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[6249, 8184])).
% 1.64/1.86 tff(8186,plain,
% 1.64/1.86 (~r(s(s(s(s(z)))), s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2452, 8183, 2169])).
% 1.64/1.86 tff(8187,plain,
% 1.64/1.86 (b(s(s(s(s(z)))), s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2461, 8186])).
% 1.64/1.86 tff(8188,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(8189,plain,
% 1.64/1.86 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(8190,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[8189])).
% 1.64/1.86 tff(8191,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[8190, 8188])).
% 1.64/1.86 tff(8192,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(8193,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[8192, 8191])).
% 1.64/1.86 tff(8194,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[8193, 319, 6544, 5692, 8187, 8185])).
% 1.64/1.86 tff(8195,plain,((~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (s(s(s(z))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(8196,plain,
% 1.64/1.86 (~r(s(z), s(s(elem!1)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[8195, 2169, 2578, 8156, 3739])).
% 1.64/1.86 tff(8197,plain,
% 1.64/1.86 (b(s(z), s(s(elem!1)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1047, 8196])).
% 1.64/1.86 tff(8198,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(8199,plain,
% 1.64/1.86 (((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(8200,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[8199])).
% 1.64/1.86 tff(8201,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[8200, 8198])).
% 1.64/1.86 tff(8202,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(8203,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[8202, 8201])).
% 1.64/1.86 tff(8204,plain,
% 1.64/1.86 (~b(s(z), z)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[8203, 319, 8197, 7301, 7778])).
% 1.64/1.86 tff(8205,plain,
% 1.64/1.86 (r(s(z), z)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[67, 8204])).
% 1.64/1.86 tff(8206,plain,
% 1.64/1.86 (~b(z, s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[8110, 8197, 6544, 2578])).
% 1.64/1.86 tff(8207,plain,
% 1.64/1.86 (r(z, s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1099, 8206])).
% 1.64/1.86 tff(8208,plain,
% 1.64/1.86 (~r(s(z), s(s(z)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[922, 8207, 732])).
% 1.64/1.86 tff(8209,plain,
% 1.64/1.86 (b(s(z), s(s(z)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[685, 8208])).
% 1.64/1.86 tff(8210,plain,
% 1.64/1.86 (r(s(s(s(z))), s(s(elem!1)))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[4878, 6479])).
% 1.64/1.86 tff(8211,plain,
% 1.64/1.86 (~r(s(s(z)), s(s(s(z))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[7631, 297, 2578, 8210])).
% 1.64/1.86 tff(8212,plain,
% 1.64/1.86 ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[6671, 51, 8211])).
% 1.64/1.86 tff(8213,plain,
% 1.64/1.86 (b(s(s(z)), s(s(s(z))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[8212, 6656])).
% 1.64/1.86 tff(8214,plain,
% 1.64/1.86 (~r(s(s(s(z))), s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[6886, 8210, 2169])).
% 1.64/1.86 tff(8215,plain,
% 1.64/1.86 (b(s(s(s(z))), s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4549, 8214])).
% 1.64/1.86 tff(8216,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(8217,plain,
% 1.64/1.86 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(8218,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[8217])).
% 1.64/1.86 tff(8219,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[8218, 8216])).
% 1.64/1.86 tff(8220,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(8221,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[8220, 8219])).
% 1.64/1.86 tff(8222,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[8221, 319, 4787, 8158, 8215, 8213])).
% 1.64/1.86 tff(8223,plain,((~r(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~(s(s(s(elem!1))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(8224,plain,
% 1.64/1.86 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[8223, 8209, 2169, 2578, 8156])).
% 1.64/1.86 tff(8225,plain,
% 1.64/1.86 (b(s(s(s(z))), s(s(s(elem!1))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[3794, 8224, 3739])).
% 1.64/1.86 tff(8226,plain,
% 1.64/1.86 (b(s(s(s(z))), s(s(elem!1)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[6520, 8225, 8156])).
% 1.64/1.86 tff(8227,plain,
% 1.64/1.86 (~b(s(s(s(z))), z)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4082, 319, 7301, 7778, 8226])).
% 1.64/1.86 tff(8228,plain,
% 1.64/1.86 (r(s(s(s(z))), z)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4584, 8227])).
% 1.64/1.86 tff(8229,plain,
% 1.64/1.86 (~r(s(z), s(s(s(z))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5986, 8228, 8205])).
% 1.64/1.86 tff(8230,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(z), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(8231,plain,
% 1.64/1.86 (((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(8232,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[8231])).
% 1.64/1.86 tff(8233,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[8232, 8230])).
% 1.64/1.86 tff(8234,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(8235,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[8234, 8233])).
% 1.64/1.86 tff(8236,plain,
% 1.64/1.86 (~b(s(z), s(s(s(z))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[8235, 319, 8197, 7778, 8226])).
% 1.64/1.86 tff(8237,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[6558, 51, 8236, 8229, 32])).
% 1.64/1.86 tff(8238,plain,((~r(s(s(elem!1)), s(z))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))) | b(s(s(z)), s(s(elem!1))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(8239,plain,
% 1.64/1.86 (~r(s(s(elem!1)), s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[8238, 7310, 7309, 7308, 33, 7307])).
% 1.64/1.86 tff(8240,plain,
% 1.64/1.86 (b(s(s(elem!1)), s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[871, 8239])).
% 1.64/1.86 tff(8241,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(8242,plain,
% 1.64/1.86 (((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(8243,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[8242])).
% 1.64/1.87 tff(8244,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[8243, 8241])).
% 1.64/1.87 tff(8245,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(8246,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[8245, 8244])).
% 1.64/1.87 tff(8247,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[8246, 319, 1, 7301, 7778, 2493])).
% 1.64/1.87 tff(8248,plain,((~b(s(z), z)) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(8249,plain,
% 1.64/1.87 (~b(s(z), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[8248, 8240])).
% 1.64/1.87 tff(8250,plain,
% 1.64/1.87 (r(s(z), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[67, 8249])).
% 1.64/1.87 tff(8251,plain,
% 1.64/1.87 (~r(s(z), s(s(z)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[6004, 8250, 7308])).
% 1.64/1.87 tff(8252,plain,
% 1.64/1.87 (b(s(z), s(s(z)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[685, 8251])).
% 1.64/1.87 tff(8253,plain,
% 1.64/1.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(8254,plain,
% 1.64/1.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(8255,plain,
% 1.64/1.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z)))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[8254, 8253])).
% 1.64/1.87 tff(8256,plain,
% 1.64/1.87 (~r(s(s(s(elem!1))), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[8255, 297, 666, 1078])).
% 1.64/1.87 tff(8257,plain,
% 1.64/1.87 (b(s(s(s(elem!1))), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4750, 8256])).
% 1.64/1.87 tff(8258,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(8259,plain,
% 1.64/1.87 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(8260,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[8259])).
% 1.64/1.87 tff(8261,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[8260, 8258])).
% 1.64/1.87 tff(8262,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(8263,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[8262, 8261])).
% 1.64/1.87 tff(8264,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[8263, 319, 1, 4787, 116, 8257])).
% 1.64/1.87 tff(8265,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~r(s(z), z)) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(8266,plain,
% 1.64/1.87 ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~r(s(z), z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[8265, 7301])).
% 1.64/1.87 tff(8267,plain,
% 1.64/1.87 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[8266, 8252, 8240, 8250])).
% 1.64/1.87 tff(8268,plain,
% 1.64/1.87 (~r(s(z), s(s(elem!1)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2583, 2511, 2578])).
% 1.64/1.87 tff(8269,plain,
% 1.64/1.87 (b(s(z), s(s(elem!1)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1047, 8268])).
% 1.64/1.87 tff(8270,plain,
% 1.64/1.87 (~r(z, s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[7320, 2511, 732])).
% 1.64/1.87 tff(8271,plain,
% 1.64/1.87 (b(z, s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1099, 8270])).
% 1.64/1.87 tff(8272,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1095, 319, 1, 8271, 8269, 7301])).
% 1.64/1.87 tff(8273,plain,((~r(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(8274,plain,
% 1.64/1.87 (~r(s(s(z)), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[8273, 8240, 7309, 7308])).
% 1.64/1.87 tff(8275,plain,
% 1.64/1.87 (b(s(s(z)), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4102, 8274])).
% 1.64/1.87 tff(8276,plain,
% 1.64/1.87 (~(s(s(elem!1)) = s(s(z)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2521, 7306])).
% 1.64/1.87 tff(8277,plain,
% 1.64/1.87 (~r(s(s(z)), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[7320, 917, 732])).
% 1.64/1.87 tff(8278,plain,
% 1.64/1.87 (b(s(s(z)), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4102, 8277])).
% 1.64/1.87 tff(8279,plain,
% 1.64/1.87 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 1.64/1.87 inference(symmetry,[status(thm)],[220])).
% 1.64/1.87 tff(8280,plain,
% 1.64/1.87 ((~(s(s(s(elem!1))) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[8279])).
% 1.64/1.87 tff(8281,plain,
% 1.64/1.87 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[58, 8280])).
% 1.64/1.87 tff(8282,plain,
% 1.64/1.87 (b(s(s(elem!1)), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[7777, 202])).
% 1.64/1.87 tff(8283,plain,
% 1.64/1.87 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1105, 817, 202, 1])).
% 1.64/1.87 tff(8284,plain,
% 1.64/1.87 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[348, 58, 8283])).
% 1.64/1.87 tff(8285,plain,
% 1.64/1.87 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4139, 297, 2578, 8284])).
% 1.64/1.87 tff(8286,plain,
% 1.64/1.87 ((s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2728, 51, 8285])).
% 1.64/1.87 tff(8287,plain,
% 1.64/1.87 (b(s(s(s(elem!1))), s(s(z)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[8286, 2516])).
% 1.64/1.87 tff(8288,plain,
% 1.64/1.87 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[3890, 297, 2578, 8284])).
% 1.64/1.87 tff(8289,plain,
% 1.64/1.87 (b(s(s(z)), s(s(s(elem!1))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1571, 8288])).
% 1.64/1.87 tff(8290,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(8291,plain,
% 1.64/1.87 (((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(8292,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[8291])).
% 1.64/1.87 tff(8293,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[8292, 8290])).
% 1.64/1.87 tff(8294,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(8295,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[8294, 8293])).
% 1.64/1.87 tff(8296,plain,
% 1.64/1.87 (~b(s(s(s(elem!1))), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[8295, 319, 8289, 8287, 7359])).
% 1.64/1.87 tff(8297,plain,
% 1.64/1.87 (r(s(s(s(elem!1))), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4750, 8296])).
% 1.64/1.87 tff(8298,plain,
% 1.64/1.87 (~r(s(s(s(elem!1))), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1103, 297, 917, 8297])).
% 1.64/1.87 tff(8299,plain,
% 1.64/1.87 (b(s(s(s(elem!1))), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1077, 51, 160, 8298])).
% 1.64/1.87 tff(8300,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(8301,plain,
% 1.64/1.87 (((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(8302,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[8301])).
% 1.64/1.87 tff(8303,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[8302, 8300])).
% 1.64/1.87 tff(8304,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(8305,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[8304, 8303])).
% 1.64/1.87 tff(8306,plain,
% 1.64/1.87 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[8305, 319, 8299, 202, 8282])).
% 1.64/1.87 tff(8307,plain,
% 1.64/1.87 ((s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2222, 51, 8306])).
% 1.64/1.87 tff(8308,plain,
% 1.64/1.87 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[8307, 8281])).
% 1.64/1.87 tff(8309,plain,
% 1.64/1.87 (~r(z, s(s(s(elem!1))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5896, 297, 917, 8297])).
% 1.64/1.87 tff(8310,plain,
% 1.64/1.87 (b(z, s(s(s(elem!1))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[416, 8309])).
% 1.64/1.87 tff(8311,plain,
% 1.64/1.87 (~b(s(s(s(z))), s(s(z)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4571, 4561, 4562, 4563])).
% 1.64/1.87 tff(8312,plain,
% 1.64/1.87 (r(s(s(s(z))), s(s(z)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2920, 8311])).
% 1.64/1.87 tff(8313,plain,
% 1.64/1.87 (~r(s(s(s(z))), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[6685, 8312, 732])).
% 1.64/1.87 tff(8314,plain,
% 1.64/1.87 (b(s(s(s(z))), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4584, 8313])).
% 1.64/1.87 tff(8315,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(8316,plain,
% 1.64/1.87 (((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(8317,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1)))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[8316])).
% 1.64/1.87 tff(8318,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[8317, 8315])).
% 1.64/1.87 tff(8319,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(8320,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1)))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[8319, 8318])).
% 1.64/1.87 tff(8321,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[8320, 319, 4562, 4561, 3741, 8314])).
% 1.64/1.87 tff(8322,plain,((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(8323,plain,
% 1.64/1.87 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[8322, 8287, 8310, 732, 8289])).
% 1.64/1.87 tff(8324,plain,
% 1.64/1.87 (r(s(s(s(z))), s(s(s(elem!1))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[3794, 8323, 3739])).
% 1.64/1.87 tff(8325,plain,
% 1.64/1.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(8326,plain,
% 1.64/1.87 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(8327,plain,
% 1.64/1.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1)))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[8326])).
% 1.64/1.87 tff(8328,plain,
% 1.64/1.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[8327, 8325])).
% 1.64/1.87 tff(8329,plain,
% 1.64/1.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(8330,plain,
% 1.64/1.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[8329, 8328])).
% 1.64/1.87 tff(8331,plain,
% 1.64/1.87 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[8330, 297, 8324, 8308])).
% 1.64/1.87 tff(8332,plain,
% 1.64/1.87 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[7604, 817, 202, 1])).
% 1.64/1.87 tff(8333,plain,
% 1.64/1.87 (s(s(s(z))) = s(s(elem!1))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4066, 51, 8332, 8331])).
% 1.64/1.87 tff(8334,plain,
% 1.64/1.87 (b(s(s(s(z))), s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[8333])).
% 1.64/1.87 tff(8335,plain,
% 1.64/1.87 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(s(z))), s(s(z)))),
% 1.64/1.87 inference(symmetry,[status(thm)],[8334])).
% 1.64/1.87 tff(8336,plain,
% 1.64/1.87 ((~b(s(s(elem!1)), s(s(z)))) <=> (~b(s(s(s(z))), s(s(z))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[8335])).
% 1.64/1.87 tff(8337,plain,
% 1.64/1.87 (~b(s(s(elem!1)), s(s(z)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4000, 319, 1, 8278, 817])).
% 1.64/1.87 tff(8338,plain,
% 1.64/1.87 (~b(s(s(s(z))), s(s(z)))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[8337, 8336])).
% 1.64/1.87 tff(8339,plain,
% 1.64/1.87 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[8333])).
% 1.64/1.87 tff(8340,plain,
% 1.64/1.87 (inj_0(s(s(elem!1))) = inj_0(s(s(s(z))))),
% 1.64/1.87 inference(symmetry,[status(thm)],[8339])).
% 1.64/1.87 tff(8341,plain,
% 1.64/1.87 (s(elem!1) = s(s(z))),
% 1.64/1.87 inference(transitivity,[status(thm)],[206, 8340, 17])).
% 1.64/1.87 tff(8342,plain,
% 1.64/1.87 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(z)), s(s(elem!1)))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[8341])).
% 1.64/1.87 tff(8343,plain,
% 1.64/1.87 (r(s(s(z)), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.64/1.87 inference(symmetry,[status(thm)],[8342])).
% 1.64/1.87 tff(8344,plain,
% 1.64/1.87 (r(s(elem!1), s(s(elem!1)))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[2578, 8343])).
% 1.64/1.87 tff(8345,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[3921, 8344, 8341, 8338, 8278, 2578, 58, 817])).
% 1.64/1.87 tff(8346,plain,((s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(z, s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(8347,plain,
% 1.64/1.87 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[8346, 817, 2578, 3739, 732, 1, 202, 917])).
% 1.64/1.88 tff(8348,plain,
% 1.64/1.88 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[8347])).
% 1.64/1.88 tff(8349,plain,
% 1.64/1.88 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[6520, 8347, 8332])).
% 1.64/1.88 tff(8350,plain,
% 1.64/1.88 (r(s(s(s(z))), s(s(s(elem!1))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[3794, 8349, 3739])).
% 1.64/1.88 tff(8351,plain,
% 1.64/1.88 (r(s(s(s(z))), s(s(elem!1)))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[8350, 8348])).
% 1.64/1.88 tff(8352,plain,
% 1.64/1.88 (~r(s(s(z)), s(s(s(z))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[7631, 297, 2578, 8351])).
% 1.64/1.88 tff(8353,plain,
% 1.64/1.88 ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[6671, 51, 8352])).
% 1.64/1.88 tff(8354,plain,
% 1.64/1.88 (b(s(s(z)), s(s(s(z))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[8353, 6656])).
% 1.64/1.88 tff(8355,plain,
% 1.64/1.88 (~r(s(s(s(z))), s(s(z)))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[6527, 8350, 2578, 8347])).
% 1.64/1.88 tff(8356,plain,
% 1.64/1.88 (b(s(s(s(z))), s(s(z)))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[2920, 8355])).
% 1.64/1.88 tff(8357,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(8358,plain,
% 1.64/1.88 (((~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(z), s(s(z)))) | (~b(s(s(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(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(8359,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[8358])).
% 1.64/1.88 tff(8360,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[8359, 8357])).
% 1.64/1.88 tff(8361,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(8362,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[8361, 8360])).
% 1.64/1.88 tff(8363,plain,
% 1.64/1.88 (~b(s(z), s(s(s(z))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[8362, 319, 7359, 8356, 8354])).
% 1.64/1.88 tff(8364,plain,
% 1.64/1.88 (r(s(z), s(s(s(z))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[6558, 51, 8363, 32])).
% 1.64/1.88 tff(8365,plain,
% 1.64/1.88 (~r(s(s(s(z))), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5986, 8364, 666])).
% 1.64/1.88 tff(8366,plain,
% 1.64/1.88 (b(s(s(s(z))), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4584, 8365])).
% 1.64/1.88 tff(8367,plain,
% 1.64/1.88 (s(s(elem!1)) = s(s(s(elem!1)))),
% 1.64/1.88 inference(symmetry,[status(thm)],[8347])).
% 1.64/1.88 tff(8368,plain,
% 1.64/1.88 (r(s(s(elem!1)), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[8367])).
% 1.64/1.88 tff(8369,plain,
% 1.64/1.88 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 1.64/1.88 inference(symmetry,[status(thm)],[8368])).
% 1.64/1.88 tff(8370,plain,
% 1.64/1.88 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[8347])).
% 1.64/1.88 tff(8371,plain,
% 1.64/1.88 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 1.64/1.88 inference(symmetry,[status(thm)],[8370])).
% 1.64/1.88 tff(8372,plain,
% 1.64/1.88 ((~b(s(s(elem!1)), s(s(s(z))))) <=> (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[8371])).
% 1.64/1.88 tff(8373,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(8374,plain,
% 1.64/1.88 (((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(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))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(8375,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[8374])).
% 1.64/1.88 tff(8376,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[8375, 8373])).
% 1.64/1.88 tff(8377,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(8378,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[8377, 8376])).
% 1.64/1.88 tff(8379,plain,
% 1.64/1.88 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[8378, 319, 202, 8282, 8366])).
% 1.64/1.88 tff(8380,plain,
% 1.64/1.88 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[8379, 8372])).
% 1.64/1.88 tff(8381,plain,
% 1.64/1.88 (r(s(s(s(elem!1))), s(s(s(z))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[3600, 8380, 7779])).
% 1.64/1.88 tff(8382,plain,
% 1.64/1.88 (r(s(s(elem!1)), s(s(s(z))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[8381, 8369])).
% 1.64/1.88 tff(8383,assumption,(r(s(s(elem!1)), s(s(s(z))))), introduced(assumption)).
% 1.64/1.88 tff(8384,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(8385,plain,
% 1.64/1.88 (((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(8386,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[8385])).
% 1.64/1.88 tff(8387,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.64/1.88 inference(transitivity,[status(thm)],[8386, 8384])).
% 1.64/1.88 tff(8388,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(8389,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[8388, 8387])).
% 1.64/1.88 tff(8390,plain,
% 1.64/1.88 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[8389, 319, 202, 3756, 3585])).
% 1.64/1.88 tff(8391,plain,
% 1.64/1.88 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[2252, 8390])).
% 1.64/1.88 tff(8392,plain,
% 1.64/1.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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)))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(8393,plain,
% 1.64/1.88 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(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)))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(8394,plain,
% 1.64/1.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[8393])).
% 1.64/1.88 tff(8395,plain,
% 1.64/1.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[8394, 8392])).
% 1.64/1.88 tff(8396,plain,
% 1.64/1.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(8397,plain,
% 1.64/1.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[8396, 8395])).
% 1.64/1.88 tff(8398,plain,
% 1.64/1.88 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[8397, 297, 8391, 8383])).
% 1.64/1.88 tff(8399,plain,
% 1.64/1.88 ((~b(s(s(elem!1)), s(s(s(s(z)))))) <=> (~b(elem!1, s(s(s(s(z))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[6778])).
% 1.64/1.88 tff(8400,plain,
% 1.64/1.88 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[8179, 319, 202, 8282, 3756])).
% 1.64/1.88 tff(8401,plain,
% 1.64/1.88 (~b(elem!1, s(s(s(s(z)))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[8400, 8399])).
% 1.64/1.88 tff(8402,plain,
% 1.64/1.88 (r(elem!1, s(s(s(s(z)))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[3036, 8401, 6473])).
% 1.64/1.88 tff(8403,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[6775, 8402, 8398, 5177])).
% 1.64/1.88 tff(8404,plain,((~b(s(s(s(s(z)))), z)) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(8405,plain,
% 1.64/1.88 (~b(s(s(s(s(z)))), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[8404, 8347, 8382, 202, 8366])).
% 1.64/1.88 tff(8406,plain,
% 1.64/1.88 (r(s(s(s(s(z)))), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[2482, 8405])).
% 1.64/1.88 tff(8407,plain,
% 1.64/1.88 (~b(s(s(s(z))), s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[8221, 319, 7359, 8356, 8354])).
% 1.64/1.88 tff(8408,plain,
% 1.64/1.88 (r(s(s(s(z))), s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4549, 8407])).
% 1.64/1.88 tff(8409,plain,
% 1.64/1.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(8410,plain,
% 1.64/1.88 (((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(8411,plain,
% 1.64/1.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z)))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[8410])).
% 1.64/1.88 tff(8412,plain,
% 1.64/1.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[8411, 8409])).
% 1.64/1.88 tff(8413,plain,
% 1.64/1.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(8414,plain,
% 1.64/1.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z)))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[8413, 8412])).
% 1.64/1.88 tff(8415,plain,
% 1.64/1.88 (~r(z, s(s(s(z))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[8414, 297, 917, 8408])).
% 1.64/1.88 tff(8416,plain,
% 1.64/1.88 ((z = s(s(s(z)))) | b(z, s(s(s(z))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[6714, 51, 8415])).
% 1.64/1.88 tff(8417,plain,
% 1.64/1.88 (b(z, s(s(s(z))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[8416, 6704])).
% 1.64/1.88 tff(8418,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(8419,plain,
% 1.64/1.88 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(8420,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z)))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[8419])).
% 1.64/1.88 tff(8421,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[8420, 8418])).
% 1.64/1.88 tff(8422,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(8423,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z)))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[8422, 8421])).
% 1.64/1.88 tff(8424,plain,
% 1.64/1.88 (~b(s(s(z)), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[8423, 319, 8356, 8417, 8354])).
% 1.64/1.88 tff(8425,plain,
% 1.64/1.88 (r(s(s(z)), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[663, 51, 28, 8424])).
% 1.64/1.88 tff(8426,plain,
% 1.64/1.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(8427,plain,
% 1.64/1.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(8428,plain,
% 1.64/1.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[8427, 8426])).
% 1.64/1.88 tff(8429,plain,
% 1.64/1.88 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[8428, 297, 8425, 8406])).
% 1.64/1.88 tff(8430,plain,
% 1.64/1.88 (b(s(s(s(s(z)))), s(s(z)))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[6174, 8429])).
% 1.64/1.88 tff(8431,plain,
% 1.64/1.88 (~r(s(s(s(s(z)))), s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[6145, 297, 666, 8406])).
% 1.64/1.88 tff(8432,plain,
% 1.64/1.88 (b(s(s(s(s(z)))), s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[2461, 8431])).
% 1.64/1.88 tff(8433,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(8434,plain,
% 1.64/1.88 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(8435,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[8434])).
% 1.64/1.88 tff(8436,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[8435, 8433])).
% 1.64/1.88 tff(8437,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(8438,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[8437, 8436])).
% 1.64/1.88 tff(8439,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[8438, 319, 8278, 817, 8432, 8430])).
% 1.64/1.88 tff(8440,plain,((~b(s(z), s(s(elem!1)))) | (~r(s(z), z)) | (~b(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(z, s(s(z)))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(8441,plain,
% 1.64/1.88 (~b(s(z), s(s(elem!1)))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[8440, 917, 202, 666, 2578, 3739, 732, 1])).
% 1.64/1.89 tff(8442,plain,
% 1.64/1.89 (r(s(z), s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1047, 8441])).
% 1.64/1.89 tff(8443,plain,
% 1.64/1.89 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[7791, 8442, 2578])).
% 1.64/1.89 tff(8444,plain,
% 1.64/1.89 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[8265, 7359, 1, 666, 202])).
% 1.64/1.89 tff(8445,plain,
% 1.64/1.89 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[348, 8444, 8443])).
% 1.64/1.89 tff(8446,plain,
% 1.64/1.89 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(elem!1)))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[8445])).
% 1.64/1.89 tff(8447,plain,
% 1.64/1.89 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(elem!1))))),
% 1.64/1.89 inference(symmetry,[status(thm)],[8446])).
% 1.64/1.89 tff(8448,plain,
% 1.64/1.89 (r(s(z), s(s(s(elem!1))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[8442, 8447])).
% 1.64/1.89 tff(8449,plain,
% 1.64/1.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(8450,plain,
% 1.64/1.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(8451,plain,
% 1.64/1.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[8450, 8449])).
% 1.64/1.89 tff(8452,plain,
% 1.64/1.89 (~r(s(s(s(z))), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[8451, 297, 666, 7602])).
% 1.64/1.89 tff(8453,plain,
% 1.64/1.89 (b(s(s(s(z))), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4549, 8452])).
% 1.64/1.89 tff(8454,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(8455,plain,
% 1.64/1.89 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(8456,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z)))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[8455])).
% 1.64/1.89 tff(8457,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[8456, 8454])).
% 1.64/1.89 tff(8458,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(8459,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z)))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[8458, 8457])).
% 1.64/1.89 tff(8460,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[8459, 319, 1, 4787, 4230, 8453])).
% 1.64/1.89 tff(8461,plain,((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~r(s(z), z)) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(8462,plain,
% 1.64/1.89 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[8461, 7359, 1, 666, 202])).
% 1.64/1.89 tff(8463,plain,
% 1.64/1.89 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[6520, 8462, 8445])).
% 1.64/1.89 tff(8464,plain,
% 1.64/1.89 (r(s(s(s(z))), s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[3794, 8463, 3739])).
% 1.64/1.89 tff(8465,plain,
% 1.64/1.89 (~r(s(s(s(z))), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4886, 8464, 8448])).
% 1.64/1.89 tff(8466,plain,
% 1.64/1.89 (b(s(s(s(z))), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4549, 8465])).
% 1.64/1.89 tff(8467,plain,
% 1.64/1.89 (~b(s(s(elem!1)), s(s(z)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[7369, 319, 1, 8278, 7359])).
% 1.64/1.89 tff(8468,plain,
% 1.64/1.89 (r(s(s(elem!1)), s(s(z)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5327, 8467, 2542])).
% 1.64/1.89 tff(8469,plain,
% 1.64/1.89 (s(s(elem!1)) = s(s(s(elem!1)))),
% 1.64/1.89 inference(symmetry,[status(thm)],[8445])).
% 1.64/1.89 tff(8470,plain,
% 1.64/1.89 ((s(s(s(z))) = s(s(elem!1))) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[8469])).
% 1.64/1.89 tff(8471,plain,
% 1.64/1.89 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 1.64/1.89 inference(symmetry,[status(thm)],[8470])).
% 1.64/1.89 tff(8472,plain,
% 1.64/1.89 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(s(s(z))) = s(s(elem!1))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[8471])).
% 1.64/1.89 tff(8473,plain,
% 1.64/1.89 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[3739, 8472])).
% 1.64/1.89 tff(8474,plain,
% 1.64/1.89 (b(s(s(s(z))), s(s(z)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4087, 8473, 732, 8468, 8282, 202])).
% 1.64/1.89 tff(8475,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4916, 319, 8278, 7359, 8474, 8466])).
% 1.64/1.89 tff(8476,plain,((~r(z, s(z))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~b(z, s(s(elem!1)))) | (~r(z, s(s(z)))) | (s(s(elem!1)) = s(s(z))) | (~r(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(8477,plain,
% 1.64/1.89 ((~r(z, s(z))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (s(s(elem!1)) = s(s(z))) | (~r(s(s(z)), s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[8476, 7301])).
% 1.64/1.89 tff(8478,plain,
% 1.64/1.89 (~r(z, s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[8477, 8250, 8240, 7310, 7308, 8276, 7309])).
% 1.64/1.89 tff(8479,plain,
% 1.64/1.89 (b(z, s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1099, 8478])).
% 1.64/1.89 tff(8480,plain,
% 1.64/1.89 (~b(s(z), s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[8110, 8479, 8275, 7309])).
% 1.64/1.89 tff(8481,plain,
% 1.64/1.89 (r(s(z), s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1047, 8480])).
% 1.64/1.89 tff(8482,plain,
% 1.64/1.89 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[7791, 8481, 7309])).
% 1.64/1.89 tff(8483,plain,
% 1.64/1.89 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[348, 8482, 8267])).
% 1.64/1.89 tff(8484,plain,
% 1.64/1.89 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(elem!1)))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[8483])).
% 1.64/1.89 tff(8485,plain,
% 1.64/1.89 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(elem!1))))),
% 1.64/1.89 inference(symmetry,[status(thm)],[8484])).
% 1.64/1.89 tff(8486,plain,
% 1.64/1.89 (r(s(z), s(s(s(elem!1))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[8481, 8485])).
% 1.64/1.89 tff(8487,plain,
% 1.64/1.89 ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~r(s(z), z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[8461, 7301])).
% 1.64/1.89 tff(8488,plain,
% 1.64/1.89 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[8487, 8252, 8240, 8250])).
% 1.64/1.89 tff(8489,plain,
% 1.64/1.89 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[6520, 8483, 8488])).
% 1.64/1.89 tff(8490,plain,
% 1.64/1.89 (r(s(s(s(z))), s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[3794, 8489, 7310])).
% 1.64/1.89 tff(8491,plain,
% 1.64/1.89 (~r(s(z), s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[8160, 8490, 8275, 7309, 8483, 8252])).
% 1.64/1.89 tff(8492,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[8491, 8486])).
% 1.64/1.89 tff(8493,plain,(b(z, s(s(z))) | b(s(s(z)), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(8494,plain,
% 1.64/1.89 (b(z, s(s(z)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[8493, 33])).
% 1.64/1.89 tff(8495,plain,
% 1.64/1.89 (r(s(s(elem!1)), s(z)) | (~b(z, s(s(z)))) | r(s(s(z)), s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[7714, 7301])).
% 1.64/1.89 tff(8496,plain,
% 1.64/1.89 (r(s(s(z)), s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[8495, 180, 8494])).
% 1.64/1.89 tff(8497,plain,
% 1.64/1.89 (~b(s(z), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[8248, 1])).
% 1.64/1.89 tff(8498,plain,
% 1.64/1.89 (r(s(z), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[67, 8497])).
% 1.64/1.89 tff(8499,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[8266, 7793, 5692, 1, 8498])).
% 1.64/1.89 tff(8500,plain,((~r(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(8501,plain,
% 1.64/1.89 (~r(s(z), s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[8500, 872, 58, 8496])).
% 1.64/1.89 tff(8502,plain,
% 1.64/1.89 (b(s(z), s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1047, 8501])).
% 1.64/1.89 tff(8503,plain,
% 1.64/1.89 ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1105, 7301])).
% 1.64/1.89 tff(8504,plain,
% 1.64/1.89 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[8503, 8502, 872])).
% 1.64/1.89 tff(8505,plain,
% 1.64/1.89 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[348, 8504, 58])).
% 1.64/1.89 tff(8506,plain,
% 1.64/1.89 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4139, 297, 8496, 8505])).
% 1.64/1.89 tff(8507,plain,
% 1.64/1.89 (b(s(s(s(elem!1))), s(s(z)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5676, 8506])).
% 1.64/1.89 tff(8508,plain,
% 1.64/1.89 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[3890, 297, 8496, 8505])).
% 1.64/1.89 tff(8509,plain,
% 1.64/1.89 (b(s(s(z)), s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1571, 8508])).
% 1.64/1.89 tff(8510,plain,
% 1.64/1.89 (~b(s(s(s(elem!1))), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[7585, 319, 8509, 8507, 8494])).
% 1.64/1.89 tff(8511,plain,
% 1.64/1.89 (r(s(s(s(elem!1))), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1077, 51, 160, 8510])).
% 1.64/1.89 tff(8512,plain,
% 1.64/1.89 (~b(s(z), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[8248, 872])).
% 1.64/1.89 tff(8513,plain,
% 1.64/1.89 (r(s(z), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[67, 8512])).
% 1.64/1.89 tff(8514,plain,
% 1.64/1.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(8515,plain,
% 1.64/1.89 (((~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(8516,plain,
% 1.64/1.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[8515])).
% 1.64/1.89 tff(8517,plain,
% 1.64/1.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 1.64/1.89 inference(transitivity,[status(thm)],[8516, 8514])).
% 1.64/1.89 tff(8518,plain,
% 1.64/1.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(8519,plain,
% 1.64/1.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[8518, 8517])).
% 1.64/1.89 tff(8520,plain,
% 1.64/1.89 (~r(s(z), s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[8519, 297, 8513, 8511])).
% 1.64/1.89 tff(8521,plain,
% 1.64/1.89 (b(s(z), s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5817, 51, 8520, 5798])).
% 1.64/1.89 tff(8522,plain,
% 1.64/1.89 (~r(s(s(s(elem!1))), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[8255, 297, 8513, 8511])).
% 1.64/1.89 tff(8523,plain,
% 1.64/1.89 (b(s(s(s(elem!1))), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4750, 8522])).
% 1.64/1.89 tff(8524,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~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))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(8525,plain,
% 1.64/1.89 (((~b(s(s(s(elem!1))), s(z))) | (~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(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~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))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(8526,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~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(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~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)))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[8525])).
% 1.64/1.89 tff(8527,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~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(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~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))))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[8526, 8524])).
% 1.64/1.89 tff(8528,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~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(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(8529,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~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)))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[8528, 8527])).
% 1.64/1.89 tff(8530,plain,
% 1.64/1.89 (~b(s(z), s(s(z)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[8529, 319, 8509, 8523, 8521])).
% 1.64/1.89 tff(8531,plain,
% 1.64/1.89 (r(s(z), s(s(z)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[685, 8530])).
% 1.64/1.89 tff(8532,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~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))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(8533,plain,
% 1.64/1.89 (((~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(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(z)), s(z))) | (~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))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(8534,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)), s(s(s(elem!1))))) | (~b(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~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)))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[8533])).
% 1.64/1.89 tff(8535,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)), s(s(s(elem!1))))) | (~b(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~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))))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[8534, 8532])).
% 1.64/1.89 tff(8536,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(8537,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~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)))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[8536, 8535])).
% 1.64/1.89 tff(8538,plain,
% 1.64/1.89 (~b(s(s(z)), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[8537, 319, 8509, 8523, 8521])).
% 1.64/1.89 tff(8539,plain,
% 1.64/1.89 (r(s(s(z)), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4102, 8538])).
% 1.64/1.89 tff(8540,plain,
% 1.64/1.89 (~(s(s(z)) = s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5160, 8539, 180])).
% 1.64/1.89 tff(8541,plain,
% 1.64/1.89 (~(s(elem!1) = s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[774, 8540])).
% 1.64/1.89 tff(8542,plain,
% 1.64/1.89 (~(s(z) = s(elem!1))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[2503, 8541])).
% 1.64/1.89 tff(8543,plain,
% 1.64/1.89 (~r(s(elem!1), s(s(z)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[2703, 8542, 8496, 114, 872, 8531])).
% 1.64/1.89 tff(8544,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(8545,plain,
% 1.64/1.89 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(8546,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[8545])).
% 1.64/1.89 tff(8547,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[8546, 8544])).
% 1.64/1.89 tff(8548,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(8549,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[8548, 8547])).
% 1.64/1.89 tff(8550,plain,
% 1.64/1.89 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[8549, 319, 872, 8502, 8523])).
% 1.64/1.89 tff(8551,plain,
% 1.64/1.89 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[2222, 51, 8550, 81])).
% 1.64/1.89 tff(8552,plain,
% 1.64/1.89 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[2509, 8540])).
% 1.64/1.89 tff(8553,plain,
% 1.64/1.89 (~b(s(s(z)), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[8537, 319, 4563, 4727, 7184])).
% 1.64/1.89 tff(8554,plain,
% 1.64/1.89 (r(s(s(z)), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4102, 8553])).
% 1.64/1.89 tff(8555,plain,
% 1.64/1.89 (~b(s(s(s(z))), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[7197, 4561, 4727, 7184])).
% 1.64/1.89 tff(8556,plain,
% 1.64/1.89 (r(s(s(s(z))), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4549, 8555])).
% 1.64/1.89 tff(8557,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4544, 8556, 8312, 8554])).
% 1.64/1.89 tff(8558,plain,((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.90 tff(8559,plain,
% 1.64/1.90 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.64/1.90 inference(unit_resolution,[status(thm)],[8558, 8523, 8521, 8507, 8509])).
% 1.64/1.90 tff(8560,plain,
% 1.64/1.90 (r(s(s(s(z))), s(s(s(elem!1))))),
% 1.64/1.90 inference(unit_resolution,[status(thm)],[3794, 8559, 8552])).
% 1.64/1.90 tff(8561,plain,
% 1.64/1.90 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.64/1.90 inference(unit_resolution,[status(thm)],[8330, 297, 8560, 8551])).
% 1.64/1.90 tff(8562,plain,
% 1.64/1.90 ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1))))),
% 1.64/1.90 inference(unit_resolution,[status(thm)],[7604, 7301])).
% 1.64/1.90 tff(8563,plain,
% 1.64/1.90 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.64/1.90 inference(unit_resolution,[status(thm)],[8562, 8502, 872])).
% 1.64/1.90 tff(8564,plain,
% 1.64/1.90 (s(s(s(z))) = s(s(elem!1))),
% 1.64/1.90 inference(unit_resolution,[status(thm)],[4066, 51, 8563, 8561])).
% 1.64/1.90 tff(8565,plain,
% 1.64/1.90 (b(s(s(s(z))), s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 1.64/1.90 inference(monotonicity,[status(thm)],[8564])).
% 1.64/1.90 tff(8566,plain,
% 1.64/1.90 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(s(z))), s(s(z)))),
% 1.64/1.90 inference(symmetry,[status(thm)],[8565])).
% 1.64/1.90 tff(8567,plain,
% 1.64/1.90 ((~b(s(s(elem!1)), s(s(z)))) <=> (~b(s(s(s(z))), s(s(z))))),
% 1.64/1.90 inference(monotonicity,[status(thm)],[8566])).
% 1.64/1.90 tff(8568,plain,
% 1.64/1.90 (~b(z, s(z))),
% 1.64/1.90 inference(unit_resolution,[status(thm)],[1095, 319, 872, 8502, 7301])).
% 1.64/1.90 tff(8569,plain,
% 1.64/1.90 (r(z, s(z))),
% 1.64/1.90 inference(unit_resolution,[status(thm)],[1099, 8568])).
% 1.64/1.90 tff(8570,plain,
% 1.64/1.90 (~r(s(s(z)), z)),
% 1.64/1.90 inference(unit_resolution,[status(thm)],[4162, 297, 8569, 8539])).
% 1.64/1.90 tff(8571,plain,
% 1.64/1.90 (b(s(s(z)), z)),
% 1.64/1.90 inference(unit_resolution,[status(thm)],[663, 51, 28, 8570])).
% 1.64/1.90 tff(8572,plain,
% 1.64/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.64/1.90 inference(rewrite,[status(thm)],[])).
% 1.64/1.90 tff(8573,plain,
% 1.64/1.90 (((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.64/1.90 inference(rewrite,[status(thm)],[])).
% 1.64/1.90 tff(8574,plain,
% 1.64/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 1.64/1.90 inference(monotonicity,[status(thm)],[8573])).
% 1.64/1.90 tff(8575,plain,
% 1.64/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.64/1.90 inference(transitivity,[status(thm)],[8574, 8572])).
% 1.64/1.90 tff(8576,plain,
% 1.64/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(8577,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[8576, 8575])).
% 1.74/1.90 tff(8578,plain,
% 1.74/1.90 (~b(s(s(elem!1)), s(s(z)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[8577, 319, 8509, 8507, 8494, 7778, 8571])).
% 1.74/1.90 tff(8579,plain,
% 1.74/1.90 (~b(s(s(s(z))), s(s(z)))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[8578, 8567])).
% 1.74/1.90 tff(8580,plain,
% 1.74/1.90 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[8564])).
% 1.74/1.90 tff(8581,plain,
% 1.74/1.90 (inj_0(s(s(elem!1))) = inj_0(s(s(s(z))))),
% 1.74/1.90 inference(symmetry,[status(thm)],[8580])).
% 1.74/1.90 tff(8582,plain,
% 1.74/1.90 (s(elem!1) = s(s(z))),
% 1.74/1.90 inference(transitivity,[status(thm)],[206, 8581, 17])).
% 1.74/1.90 tff(8583,plain,
% 1.74/1.90 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(z)), s(s(elem!1)))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[8582])).
% 1.74/1.90 tff(8584,plain,
% 1.74/1.90 (r(s(s(z)), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.74/1.90 inference(symmetry,[status(thm)],[8583])).
% 1.74/1.90 tff(8585,plain,
% 1.74/1.90 (r(s(elem!1), s(s(elem!1)))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[8496, 8584])).
% 1.74/1.90 tff(8586,plain,
% 1.74/1.90 (r(s(s(z)), s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[122, 772, 33])).
% 1.74/1.90 tff(8587,plain,
% 1.74/1.90 (~b(s(z), s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4433, 8586, 58, 2524, 2915, 197, 2522, 2498])).
% 1.74/1.90 tff(8588,plain,
% 1.74/1.90 (r(s(z), s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1047, 8587])).
% 1.74/1.90 tff(8589,plain,
% 1.74/1.90 (~r(s(s(z)), s(z))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2583, 8588, 8586])).
% 1.74/1.90 tff(8590,plain,
% 1.74/1.90 (b(s(s(z)), s(z))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4102, 8589])).
% 1.74/1.90 tff(8591,plain,
% 1.74/1.90 ((~(s(elem!1) = s(z))) <=> (~(s(z) = s(elem!1)))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[2499])).
% 1.74/1.90 tff(8592,plain,
% 1.74/1.90 (~(s(z) = s(elem!1))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[2498, 8591])).
% 1.74/1.90 tff(8593,plain,
% 1.74/1.90 (~r(s(z), s(elem!1))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[3309, 297, 8588, 197])).
% 1.74/1.90 tff(8594,plain,
% 1.74/1.90 (b(s(z), s(elem!1))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2638, 51, 8593, 8592])).
% 1.74/1.90 tff(8595,plain,
% 1.74/1.90 (~r(s(elem!1), s(z))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[853, 297, 8588, 197])).
% 1.74/1.90 tff(8596,plain,
% 1.74/1.90 (b(s(elem!1), s(z))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[783, 8595, 2498])).
% 1.74/1.90 tff(8597,plain,
% 1.74/1.90 (~b(s(elem!1), s(s(z)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[6952, 319, 8590, 8596, 8594])).
% 1.74/1.90 tff(8598,plain,
% 1.74/1.90 (s(elem!1) = s(s(z))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2529, 8597, 2524])).
% 1.74/1.90 tff(8599,plain,
% 1.74/1.90 (s(s(elem!1)) = s(s(s(z)))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[8598])).
% 1.74/1.90 tff(8600,plain,
% 1.74/1.90 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[8599])).
% 1.74/1.90 tff(8601,plain,
% 1.74/1.90 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.74/1.90 inference(symmetry,[status(thm)],[8600])).
% 1.74/1.90 tff(8602,plain,
% 1.74/1.90 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[8601])).
% 1.74/1.90 tff(8603,plain,
% 1.74/1.90 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.90 inference(symmetry,[status(thm)],[8602])).
% 1.74/1.90 tff(8604,plain,
% 1.74/1.90 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[8599])).
% 1.74/1.90 tff(8605,plain,
% 1.74/1.90 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[7791, 8588, 8586])).
% 1.74/1.90 tff(8606,plain,
% 1.74/1.90 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[348, 8605, 58])).
% 1.74/1.90 tff(8607,plain,
% 1.74/1.90 (b(s(s(s(elem!1))), s(s(s(z))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[8606, 8604])).
% 1.74/1.90 tff(8608,plain,
% 1.74/1.90 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[8607, 8603])).
% 1.74/1.90 tff(8609,plain,
% 1.74/1.90 (b(z, s(s(elem!1))) <=> b(z, s(s(s(z))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[8599])).
% 1.74/1.90 tff(8610,plain,
% 1.74/1.90 (~r(z, s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[5702, 8588, 8586])).
% 1.74/1.90 tff(8611,plain,
% 1.74/1.90 (b(z, s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[56, 8610])).
% 1.74/1.90 tff(8612,plain,
% 1.74/1.90 (b(z, s(s(s(z))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[8611, 8609])).
% 1.74/1.90 tff(8613,plain,
% 1.74/1.90 (s(s(z)) = s(elem!1)),
% 1.74/1.90 inference(symmetry,[status(thm)],[8598])).
% 1.74/1.90 tff(8614,plain,
% 1.74/1.90 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[8613])).
% 1.74/1.90 tff(8615,plain,
% 1.74/1.90 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.74/1.90 inference(transitivity,[status(thm)],[8614, 276])).
% 1.74/1.90 tff(8616,plain,
% 1.74/1.90 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[8615])).
% 1.74/1.90 tff(8617,plain,
% 1.74/1.90 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[231, 8616])).
% 1.74/1.90 tff(8618,plain,
% 1.74/1.90 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[178, 8617])).
% 1.74/1.90 tff(8619,plain,
% 1.74/1.90 (r(s(s(s(s(elem!1)))), s(s(elem!1))) <=> r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[8599])).
% 1.74/1.90 tff(8620,plain,
% 1.74/1.90 (r(s(s(s(s(elem!1)))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/1.90 inference(symmetry,[status(thm)],[8619])).
% 1.74/1.90 tff(8621,plain,
% 1.74/1.90 ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) <=> (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[8620])).
% 1.74/1.90 tff(8622,plain,
% 1.74/1.90 (r(s(s(z)), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[3496, 8598, 8586])).
% 1.74/1.90 tff(8623,plain,
% 1.74/1.90 (~r(s(z), s(s(z)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[5690, 8588, 8586])).
% 1.74/1.90 tff(8624,plain,
% 1.74/1.90 (b(s(z), s(s(z)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[685, 8623])).
% 1.74/1.90 tff(8625,plain,
% 1.74/1.90 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[7835, 8598, 8590, 8624, 8588, 8622])).
% 1.74/1.90 tff(8626,plain,
% 1.74/1.90 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[8625, 8621])).
% 1.74/1.90 tff(8627,plain,
% 1.74/1.90 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[571, 8626, 8618])).
% 1.74/1.90 tff(8628,plain,
% 1.74/1.90 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[3246, 8627, 8598])).
% 1.74/1.90 tff(8629,plain,
% 1.74/1.90 (~b(s(s(s(z))), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[7865, 8628, 8598, 8612, 93, 8608])).
% 1.74/1.90 tff(8630,plain,
% 1.74/1.90 (~b(s(s(elem!1)), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[7870, 8629, 8598])).
% 1.74/1.90 tff(8631,plain,
% 1.74/1.90 (r(s(s(elem!1)), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[75, 8630])).
% 1.74/1.90 tff(8632,plain,
% 1.74/1.90 (~r(s(s(z)), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[3526, 8631, 8586])).
% 1.74/1.90 tff(8633,plain,
% 1.74/1.90 (~r(s(elem!1), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[3179, 8632, 8598])).
% 1.74/1.90 tff(8634,plain,
% 1.74/1.90 (b(s(elem!1), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2602, 8633])).
% 1.74/1.90 tff(8635,plain,
% 1.74/1.90 (b(s(s(z)), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[3187, 8634, 8598])).
% 1.74/1.90 tff(8636,plain,
% 1.74/1.90 (~b(s(z), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[7888, 8635, 8590, 8586])).
% 1.74/1.90 tff(8637,plain,
% 1.74/1.90 (~r(s(z), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[304, 8631, 8588])).
% 1.74/1.90 tff(8638,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[65, 51, 62, 8637, 8636])).
% 1.74/1.90 tff(8639,plain,((s(s(z)) = s(s(elem!1))) | r(s(elem!1), s(s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(z))), s(s(z))) | b(s(s(z)), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(8640,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[8639, 8585, 8579, 8540, 33, 58, 8543])).
% 1.74/1.90 tff(8641,plain,(r(s(s(elem!1)), s(z)) | b(s(s(z)), s(s(elem!1))) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(8642,plain,
% 1.74/1.90 (r(s(s(elem!1)), s(z))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[8641, 58, 33])).
% 1.74/1.90 tff(8643,plain,
% 1.74/1.90 (b(elem!1, s(s(elem!1)))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[7301, 1115])).
% 1.74/1.90 tff(8644,plain,
% 1.74/1.90 (b(s(s(s(z))), s(z)) <=> b(s(s(s(z))), s(elem!1))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[135])).
% 1.74/1.90 tff(8645,plain,
% 1.74/1.90 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(z))),
% 1.74/1.90 inference(symmetry,[status(thm)],[8644])).
% 1.74/1.90 tff(8646,plain,
% 1.74/1.90 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[937])).
% 1.74/1.90 tff(8647,plain,
% 1.74/1.90 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(z))), s(elem!1))),
% 1.74/1.90 inference(symmetry,[status(thm)],[8646])).
% 1.74/1.90 tff(8648,plain,
% 1.74/1.90 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(z))), s(z))),
% 1.74/1.90 inference(transitivity,[status(thm)],[8647, 8645])).
% 1.74/1.90 tff(8649,plain,
% 1.74/1.90 ((~b(s(s(s(elem!1))), s(elem!1))) <=> (~b(s(s(s(z))), s(z)))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[8648])).
% 1.74/1.90 tff(8650,plain,
% 1.74/1.90 (b(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[434, 6104, 1114])).
% 1.74/1.90 tff(8651,plain,
% 1.74/1.90 (~(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[107, 1138])).
% 1.74/1.90 tff(8652,plain,
% 1.74/1.90 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[960, 135])).
% 1.74/1.90 tff(8653,plain,
% 1.74/1.90 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[544, 297, 197, 335])).
% 1.74/1.90 tff(8654,plain,
% 1.74/1.90 (b(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[958, 8653, 183])).
% 1.74/1.90 tff(8655,plain,
% 1.74/1.90 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[343, 335, 197])).
% 1.74/1.90 tff(8656,plain,
% 1.74/1.90 (b(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[434, 8655, 1114])).
% 1.74/1.90 tff(8657,plain,
% 1.74/1.90 (b(s(s(elem!1)), s(s(s(s(elem!1))))) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[961])).
% 1.74/1.90 tff(8658,plain,
% 1.74/1.90 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/1.90 inference(symmetry,[status(thm)],[8657])).
% 1.74/1.90 tff(8659,plain,
% 1.74/1.90 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[133])).
% 1.74/1.90 tff(8660,plain,
% 1.74/1.90 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 1.74/1.90 inference(transitivity,[status(thm)],[8659, 6121])).
% 1.74/1.90 tff(8661,plain,
% 1.74/1.90 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[8660, 6451])).
% 1.74/1.90 tff(8662,plain,
% 1.74/1.90 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(elem!1)) = s(s(s(s(z))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[8661])).
% 1.74/1.90 tff(8663,plain,
% 1.74/1.90 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[6244, 8662])).
% 1.74/1.90 tff(8664,plain,
% 1.74/1.90 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[6350, 6348, 8663])).
% 1.74/1.90 tff(8665,plain,
% 1.74/1.90 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[8664, 8658])).
% 1.74/1.90 tff(8666,plain,
% 1.74/1.90 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[960])).
% 1.74/1.90 tff(8667,plain,
% 1.74/1.90 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(z)))), elem!1)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[187])).
% 1.74/1.90 tff(8668,plain,
% 1.74/1.90 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.90 inference(transitivity,[status(thm)],[8667, 8666])).
% 1.74/1.90 tff(8669,plain,
% 1.74/1.90 (b(s(s(z)), z)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[7778, 5780])).
% 1.74/1.90 tff(8670,plain,
% 1.74/1.90 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[133])).
% 1.74/1.90 tff(8671,plain,
% 1.74/1.90 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[6591, 8670])).
% 1.74/1.90 tff(8672,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[6348, 8671])).
% 1.74/1.90 tff(8673,plain,((~r(s(s(z)), s(s(s(s(z)))))) | r(s(s(elem!1)), s(s(s(s(z))))) | (~(s(s(z)) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(8674,plain,
% 1.74/1.90 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[8673, 6348, 133])).
% 1.74/1.90 tff(8675,plain,
% 1.74/1.90 (b(s(s(z)), s(s(s(s(z)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[6249, 8674])).
% 1.74/1.90 tff(8676,plain,
% 1.74/1.90 (~b(s(s(s(s(z)))), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[6604, 8675, 711, 8669])).
% 1.74/1.90 tff(8677,plain,
% 1.74/1.90 (r(s(s(s(s(z)))), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2482, 8676])).
% 1.74/1.90 tff(8678,plain,
% 1.74/1.90 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[8677, 8668])).
% 1.74/1.90 tff(8679,plain,
% 1.74/1.90 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1166, 297, 286, 8678])).
% 1.74/1.90 tff(8680,plain,
% 1.74/1.90 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[595, 8679, 2213])).
% 1.74/1.90 tff(8681,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(8682,plain,
% 1.74/1.90 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(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(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))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(8683,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[8682])).
% 1.74/1.90 tff(8684,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[8683, 8681])).
% 1.74/1.90 tff(8685,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(8686,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[8685, 8684])).
% 1.74/1.90 tff(8687,plain,
% 1.74/1.90 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[8686, 319, 309, 548, 8680])).
% 1.74/1.90 tff(8688,plain,
% 1.74/1.90 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[8687, 2218])).
% 1.74/1.90 tff(8689,plain,
% 1.74/1.90 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2252, 8688])).
% 1.74/1.90 tff(8690,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)],[8689, 1494])).
% 1.74/1.90 tff(8691,plain,
% 1.74/1.90 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1340, 8690, 335])).
% 1.74/1.90 tff(8692,plain,
% 1.74/1.90 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[571, 8691, 2202])).
% 1.74/1.90 tff(8693,plain,
% 1.74/1.90 (b(s(s(elem!1)), elem!1) | (~(z = elem!1))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[500, 7778])).
% 1.74/1.90 tff(8694,plain,
% 1.74/1.90 (b(s(s(elem!1)), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[8693, 187])).
% 1.74/1.90 tff(8695,plain,
% 1.74/1.90 (~r(s(s(s(elem!1))), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2259, 8690, 8678])).
% 1.74/1.90 tff(8696,plain,
% 1.74/1.90 (b(s(s(s(elem!1))), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[361, 8695, 249])).
% 1.74/1.90 tff(8697,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)],[1402, 319, 448, 397, 1523])).
% 1.74/1.90 tff(8698,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)],[1412, 51, 1539, 8697])).
% 1.74/1.90 tff(8699,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), 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(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), 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(s(elem!1))))), elem!1)))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(8700,plain,
% 1.74/1.90 (((~b(elem!1, s(s(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(s(elem!1))))), 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(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(8701,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(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(s(elem!1))))), 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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), 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(s(elem!1))))), elem!1))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[8700])).
% 1.74/1.90 tff(8702,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(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(s(elem!1))))), 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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), 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(s(elem!1))))), elem!1)))),
% 1.74/1.90 inference(transitivity,[status(thm)],[8701, 8699])).
% 1.74/1.90 tff(8703,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(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(s(elem!1))))), 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)))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(8704,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[8703, 8702])).
% 1.74/1.90 tff(8705,plain,
% 1.74/1.90 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[8704, 319, 308, 1021, 397, 1523, 2336])).
% 1.74/1.90 tff(8706,plain,
% 1.74/1.90 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1243, 51, 1785, 8705])).
% 1.74/1.90 tff(8707,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1431, 297, 335, 8706, 8698])).
% 1.74/1.90 tff(8708,plain,((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(8709,plain,
% 1.74/1.90 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[8708, 8696, 2267, 2270, 335, 8643, 8694, 8692, 8665])).
% 1.74/1.90 tff(8710,plain,
% 1.74/1.90 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1320, 8709, 1060])).
% 1.74/1.90 tff(8711,plain,
% 1.74/1.90 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1142, 297, 8678, 8710])).
% 1.74/1.90 tff(8712,plain,
% 1.74/1.90 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1146, 51, 1522, 8711])).
% 1.74/1.90 tff(8713,plain,
% 1.74/1.90 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1298, 8710, 286])).
% 1.74/1.90 tff(8714,plain,
% 1.74/1.90 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1291, 51, 1418, 8713])).
% 1.74/1.90 tff(8715,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(8716,plain,
% 1.74/1.90 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(8717,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[8716])).
% 1.74/1.91 tff(8718,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[8717, 8715])).
% 1.74/1.91 tff(8719,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(8720,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[8719, 8718])).
% 1.74/1.91 tff(8721,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[8720, 319, 309, 8680, 8714, 8712])).
% 1.74/1.91 tff(8722,plain,(r(s(s(elem!1)), s(s(s(s(z))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~(s(s(z)) = s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(8723,plain,
% 1.74/1.91 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[8722, 8656, 1522, 286, 335, 133, 8654, 711])).
% 1.74/1.91 tff(8724,plain,
% 1.74/1.91 (~r(s(s(s(s(z)))), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2452, 8723, 2169])).
% 1.74/1.91 tff(8725,plain,
% 1.74/1.91 (b(s(s(s(s(z)))), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2461, 8724])).
% 1.74/1.91 tff(8726,plain,
% 1.74/1.91 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[8725, 8652])).
% 1.74/1.91 tff(8727,plain,
% 1.74/1.91 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[554, 319, 8656, 8654, 8726])).
% 1.74/1.91 tff(8728,plain,
% 1.74/1.91 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2027, 8727, 133])).
% 1.74/1.91 tff(8729,plain,
% 1.74/1.91 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2281, 8728])).
% 1.74/1.91 tff(8730,plain,
% 1.74/1.91 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[8729, 2272])).
% 1.74/1.91 tff(8731,plain,
% 1.74/1.91 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[8723, 7723])).
% 1.74/1.91 tff(8732,plain,
% 1.74/1.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(8733,plain,
% 1.74/1.91 (((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(8734,plain,
% 1.74/1.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[8733])).
% 1.74/1.91 tff(8735,plain,
% 1.74/1.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[8734, 8732])).
% 1.74/1.91 tff(8736,plain,
% 1.74/1.91 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(8737,plain,
% 1.74/1.91 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[8736, 8735])).
% 1.74/1.91 tff(8738,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[8737, 297, 335, 8731, 8730])).
% 1.74/1.91 tff(8739,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~(s(s(z)) = s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~b(z, s(s(z)))) | (~r(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(8740,plain,
% 1.74/1.91 (~r(s(elem!1), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[8739, 197, 2169, 8651, 133, 711, 335])).
% 1.74/1.91 tff(8741,plain,
% 1.74/1.91 (b(s(elem!1), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[375, 8740, 2165])).
% 1.74/1.91 tff(8742,plain,
% 1.74/1.91 (~b(s(s(s(elem!1))), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[457, 8741, 8650, 8643])).
% 1.74/1.91 tff(8743,plain,
% 1.74/1.91 (r(s(s(s(elem!1))), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[361, 8742, 249])).
% 1.74/1.91 tff(8744,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(8745,plain,
% 1.74/1.91 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(8746,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[8745])).
% 1.74/1.91 tff(8747,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[8746, 8744])).
% 1.74/1.91 tff(8748,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(8749,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[8748, 8747])).
% 1.74/1.91 tff(8750,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[8749, 319, 449, 548, 986, 1187])).
% 1.74/1.91 tff(8751,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(8752,plain,
% 1.74/1.91 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[8751, 8654, 335, 99, 2213, 8741, 197])).
% 1.74/1.91 tff(8753,plain,
% 1.74/1.91 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[571, 8752, 2202])).
% 1.74/1.91 tff(8754,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(8755,plain,
% 1.74/1.91 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(8756,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[8755])).
% 1.74/1.91 tff(8757,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.74/1.91 inference(transitivity,[status(thm)],[8756, 8754])).
% 1.74/1.91 tff(8758,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(8759,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[8758, 8757])).
% 1.74/1.91 tff(8760,plain,
% 1.74/1.91 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[8759, 319, 8694, 8753, 8643])).
% 1.74/1.91 tff(8761,plain,
% 1.74/1.91 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[616, 8760, 605])).
% 1.74/1.91 tff(8762,plain,
% 1.74/1.91 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.91 inference(symmetry,[status(thm)],[1494])).
% 1.74/1.91 tff(8763,plain,
% 1.74/1.91 ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[8762])).
% 1.74/1.91 tff(8764,plain,
% 1.74/1.91 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2259, 8761, 8743])).
% 1.74/1.91 tff(8765,plain,
% 1.74/1.91 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[8764, 8763])).
% 1.74/1.91 tff(8766,plain,
% 1.74/1.91 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2252, 8765])).
% 1.74/1.91 tff(8767,plain,
% 1.74/1.91 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[8766, 2216])).
% 1.74/1.91 tff(8768,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)],[1724, 297, 461, 1134])).
% 1.74/1.91 tff(8769,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)],[1412, 51, 1539, 8768])).
% 1.74/1.91 tff(8770,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(8771,plain,
% 1.74/1.91 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), 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(s(elem!1))))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(8772,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), 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(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[8771])).
% 1.74/1.91 tff(8773,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), 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(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[8772, 8770])).
% 1.74/1.91 tff(8774,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), 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(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(8775,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[8774, 8773])).
% 1.74/1.91 tff(8776,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[8775, 319, 548, 2335, 1504, 8769])).
% 1.74/1.91 tff(8777,plain,((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(8778,plain,
% 1.74/1.91 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[8777, 8654, 8767, 8651, 2267, 8761, 8743])).
% 1.74/1.91 tff(8779,plain,
% 1.74/1.91 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1320, 8778, 1060])).
% 1.74/1.91 tff(8780,plain,
% 1.74/1.91 (~(elem!1 = s(elem!1))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2167, 2165])).
% 1.74/1.91 tff(8781,plain,
% 1.74/1.91 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[8749, 319, 449, 548, 547])).
% 1.74/1.91 tff(8782,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[558, 51, 99, 8781, 1893])).
% 1.74/1.91 tff(8783,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(8784,plain,
% 1.74/1.91 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[8783, 8761, 8741, 8743, 8654, 99])).
% 1.74/1.91 tff(8785,plain,
% 1.74/1.91 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[595, 8784, 2213])).
% 1.74/1.91 tff(8786,plain,
% 1.74/1.91 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2393, 297, 2390, 620])).
% 1.74/1.91 tff(8787,plain,
% 1.74/1.91 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[571, 8786, 560])).
% 1.74/1.91 tff(8788,plain,
% 1.74/1.91 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[611, 297, 419, 620])).
% 1.74/1.91 tff(8789,plain,
% 1.74/1.91 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[616, 8788, 987])).
% 1.74/1.91 tff(8790,plain,
% 1.74/1.91 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[629, 620, 419])).
% 1.74/1.91 tff(8791,plain,
% 1.74/1.91 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[634, 8790, 1185])).
% 1.74/1.91 tff(8792,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[641, 319, 8791, 308, 8789, 8787])).
% 1.74/1.91 tff(8793,plain,((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (s(s(s(s(elem!1)))) = elem!1) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (elem!1 = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(8794,plain,
% 1.74/1.91 (~r(elem!1, s(elem!1))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[8793, 8785, 2202, 5102, 8694, 605, 619])).
% 1.74/1.91 tff(8795,plain,
% 1.74/1.91 (b(elem!1, s(elem!1))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[389, 8794, 8780])).
% 1.74/1.91 tff(8796,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(8797,plain,
% 1.74/1.91 (((~b(elem!1, s(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(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~b(elem!1, 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)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(8798,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(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(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[8797])).
% 1.74/1.91 tff(8799,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(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(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.74/1.91 inference(transitivity,[status(thm)],[8798, 8796])).
% 1.74/1.91 tff(8800,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(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(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(8801,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[8800, 8799])).
% 1.74/1.91 tff(8802,plain,
% 1.74/1.91 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[8801, 319, 8795, 8694, 8779])).
% 1.74/1.91 tff(8803,plain,
% 1.74/1.91 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1243, 51, 2270, 8802])).
% 1.74/1.91 tff(8804,plain,
% 1.74/1.91 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1704, 319, 8795, 8741, 8779])).
% 1.74/1.91 tff(8805,plain,
% 1.74/1.91 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1291, 51, 1418, 8804])).
% 1.74/1.91 tff(8806,plain,
% 1.74/1.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(8807,plain,
% 1.74/1.91 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(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)))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(8808,plain,
% 1.74/1.91 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[8807, 8806])).
% 1.74/1.91 tff(8809,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[8808, 297, 5102, 8805, 8803])).
% 1.74/1.91 tff(8810,plain,((~r(s(elem!1), s(s(elem!1)))) | (~(s(s(z)) = s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (s(elem!1) = elem!1) | (~r(s(s(elem!1)), s(z))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(8811,plain,
% 1.74/1.91 (~r(s(elem!1), s(s(elem!1)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[8810, 335, 99, 133, 2160, 2169, 711])).
% 1.74/1.91 tff(8812,plain,
% 1.74/1.91 (~r(s(z), s(s(elem!1)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1045, 8811, 133])).
% 1.74/1.91 tff(8813,plain,
% 1.74/1.91 (b(s(z), s(s(elem!1)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1047, 8812])).
% 1.74/1.91 tff(8814,plain,
% 1.74/1.91 ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(elem!1))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5714, 7778])).
% 1.74/1.91 tff(8815,plain,
% 1.74/1.91 (~b(s(z), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[8814, 8813, 711])).
% 1.74/1.91 tff(8816,plain,
% 1.74/1.91 (b(s(z), elem!1) <=> b(s(z), z)),
% 1.74/1.91 inference(symmetry,[status(thm)],[7717])).
% 1.74/1.91 tff(8817,plain,
% 1.74/1.91 (b(s(elem!1), elem!1) <=> b(s(z), z)),
% 1.74/1.91 inference(transitivity,[status(thm)],[887, 8816])).
% 1.74/1.91 tff(8818,plain,
% 1.74/1.91 (b(s(z), z)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[449, 8817])).
% 1.74/1.91 tff(8819,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[60, 8818])).
% 1.74/1.91 tff(8820,plain,((~b(s(elem!1), elem!1)) | b(s(z), z) | (~(s(s(z)) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(8821,plain,
% 1.74/1.91 (~b(s(elem!1), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[8820, 8815, 133])).
% 1.74/1.91 tff(8822,plain,
% 1.74/1.91 (r(s(elem!1), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[375, 8821, 2160])).
% 1.74/1.91 tff(8823,plain,
% 1.74/1.91 (b(s(elem!1), s(s(elem!1)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[807, 8811, 2142])).
% 1.74/1.91 tff(8824,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(8825,plain,
% 1.74/1.92 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(8826,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[8825])).
% 1.74/1.92 tff(8827,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[8826, 8824])).
% 1.74/1.92 tff(8828,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(8829,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[8828, 8827])).
% 1.74/1.92 tff(8830,plain,
% 1.74/1.92 (~b(elem!1, s(elem!1))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8829, 319, 8823, 8694, 8643])).
% 1.74/1.92 tff(8831,plain,
% 1.74/1.92 (r(elem!1, s(elem!1))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[389, 8830, 2168])).
% 1.74/1.92 tff(8832,plain,
% 1.74/1.92 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8793, 8831, 2202, 5102, 8694, 605, 619])).
% 1.74/1.92 tff(8833,plain,
% 1.74/1.92 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[595, 8832, 2213])).
% 1.74/1.92 tff(8834,plain,
% 1.74/1.92 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1365, 297, 286, 8678])).
% 1.74/1.92 tff(8835,plain,
% 1.74/1.92 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(symmetry,[status(thm)],[2203])).
% 1.74/1.92 tff(8836,plain,
% 1.74/1.92 ((s(z) = s(s(s(s(elem!1))))) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[2205, 8835])).
% 1.74/1.92 tff(8837,plain,
% 1.74/1.92 ((~(s(z) = s(s(s(s(elem!1)))))) <=> (~(s(elem!1) = s(s(s(s(elem!1))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[8836])).
% 1.74/1.92 tff(8838,plain,
% 1.74/1.92 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[2212, 8837])).
% 1.74/1.92 tff(8839,plain,
% 1.74/1.92 (((~![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))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(8840,plain,
% 1.74/1.92 ((~![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))))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(8841,plain,
% 1.74/1.92 ((~![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)))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[8840, 8839])).
% 1.74/1.92 tff(8842,plain,
% 1.74/1.92 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8841, 51, 8838, 8834])).
% 1.74/1.92 tff(8843,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(8844,plain,
% 1.74/1.92 (((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(8845,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[8844])).
% 1.74/1.92 tff(8846,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[8845, 8843])).
% 1.74/1.92 tff(8847,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(8848,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[8847, 8846])).
% 1.74/1.92 tff(8849,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8848, 319, 785, 547, 8665, 8842])).
% 1.74/1.92 tff(8850,plain,(r(s(s(elem!1)), s(s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~(s(s(z)) = s(s(elem!1)))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(8851,plain,
% 1.74/1.92 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8850, 8823, 8833, 8822, 133, 711])).
% 1.74/1.92 tff(8852,plain,
% 1.74/1.92 (r(s(z), s(s(s(s(elem!1))))) <=> r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[135])).
% 1.74/1.92 tff(8853,plain,
% 1.74/1.92 (r(s(elem!1), s(s(s(s(elem!1))))) <=> r(s(z), s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(symmetry,[status(thm)],[8852])).
% 1.74/1.92 tff(8854,plain,
% 1.74/1.92 (r(s(z), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[135, 960])).
% 1.74/1.92 tff(8855,plain,
% 1.74/1.92 (r(s(z), s(s(s(s(z))))) <=> r(s(z), s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[8854, 8853])).
% 1.74/1.92 tff(8856,plain,
% 1.74/1.92 (((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(8857,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[8856])).
% 1.74/1.92 tff(8858,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.74/1.92 inference(transitivity,[status(thm)],[8857, 8754])).
% 1.74/1.92 tff(8859,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(8860,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[8859, 8858])).
% 1.74/1.92 tff(8861,plain,
% 1.74/1.92 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8860, 319, 8694, 1445, 8643])).
% 1.74/1.92 tff(8862,plain,
% 1.74/1.92 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[571, 8861, 2202])).
% 1.74/1.92 tff(8863,plain,
% 1.74/1.92 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[578, 297, 335, 8862])).
% 1.74/1.92 tff(8864,plain,
% 1.74/1.92 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[558, 51, 99, 8863])).
% 1.74/1.92 tff(8865,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1462, 319, 785, 448, 1445, 397, 547, 1444])).
% 1.74/1.92 tff(8866,plain,((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(8867,plain,
% 1.74/1.92 (~b(s(s(s(elem!1))), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8866, 1445, 785, 8643, 547, 8864])).
% 1.74/1.92 tff(8868,plain,
% 1.74/1.92 (r(s(s(s(elem!1))), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[361, 8867, 249])).
% 1.74/1.92 tff(8869,plain,
% 1.74/1.92 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1394, 8868, 286])).
% 1.74/1.92 tff(8870,plain,
% 1.74/1.92 (b(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[434, 8869, 1114])).
% 1.74/1.92 tff(8871,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(8872,plain,
% 1.74/1.92 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(8873,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[8872])).
% 1.74/1.92 tff(8874,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[8873, 8871])).
% 1.74/1.92 tff(8875,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(8876,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[8875, 8874])).
% 1.74/1.92 tff(8877,plain,
% 1.74/1.92 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8876, 319, 309, 1445, 1444])).
% 1.74/1.92 tff(8878,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8877, 1376])).
% 1.74/1.92 tff(8879,plain,((~b(s(z), s(s(s(s(z)))))) | (~(s(s(z)) = s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(8880,plain,
% 1.74/1.92 (~b(s(z), s(s(s(s(z)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8879, 8870, 1445, 8864, 133])).
% 1.74/1.92 tff(8881,plain,
% 1.74/1.92 (r(s(z), s(s(s(s(z)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2301, 8880])).
% 1.74/1.92 tff(8882,plain,
% 1.74/1.92 (r(s(z), s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[8881, 8855])).
% 1.74/1.92 tff(8883,plain,
% 1.74/1.92 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[2443, 7723])).
% 1.74/1.92 tff(8884,assumption,(r(s(z), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.74/1.92 tff(8885,plain,
% 1.74/1.92 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(8886,plain,
% 1.74/1.92 (((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(8887,plain,
% 1.74/1.92 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1))))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[8886])).
% 1.74/1.92 tff(8888,plain,
% 1.74/1.92 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[8887, 8885])).
% 1.74/1.92 tff(8889,plain,
% 1.74/1.92 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(z))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(8890,plain,
% 1.74/1.92 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1))))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[8889, 8888])).
% 1.74/1.92 tff(8891,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8890, 297, 2169, 1560, 8884])).
% 1.74/1.92 tff(8892,plain,((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(8893,plain,
% 1.74/1.92 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8892, 8883, 2169])).
% 1.74/1.92 tff(8894,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8893, 8882])).
% 1.74/1.92 tff(8895,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~(s(s(z)) = s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(8896,plain,
% 1.74/1.92 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8895, 8822, 133, 8823, 8833, 99, 335, 2169, 8851])).
% 1.74/1.92 tff(8897,plain,
% 1.74/1.92 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[616, 8896, 605])).
% 1.74/1.92 tff(8898,plain,
% 1.74/1.92 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1365, 297, 8822, 8897])).
% 1.74/1.92 tff(8899,plain,
% 1.74/1.92 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8841, 51, 8838, 8898])).
% 1.74/1.92 tff(8900,plain,
% 1.74/1.92 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[8851, 7723])).
% 1.74/1.92 tff(8901,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8737, 297, 335, 1560, 2032])).
% 1.74/1.92 tff(8902,plain,((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(8903,plain,
% 1.74/1.92 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8902, 335, 8900])).
% 1.74/1.92 tff(8904,plain,
% 1.74/1.92 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[558, 51, 99, 8903])).
% 1.74/1.92 tff(8905,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(8906,plain,
% 1.74/1.92 (((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(8907,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[8906])).
% 1.74/1.92 tff(8908,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[8907, 8905])).
% 1.74/1.92 tff(8909,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(8910,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[8909, 8908])).
% 1.74/1.93 tff(8911,plain,
% 1.74/1.93 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[8910, 319, 8833, 8904, 8899])).
% 1.74/1.93 tff(8912,plain,
% 1.74/1.93 (~b(s(s(s(z))), s(z))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[8911, 8649])).
% 1.74/1.93 tff(8913,plain,
% 1.74/1.93 (r(s(s(elem!1)), s(z)) <=> r(s(s(z)), s(z))),
% 1.74/1.93 inference(symmetry,[status(thm)],[5157])).
% 1.74/1.93 tff(8914,plain,
% 1.74/1.93 (r(s(s(z)), s(z))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[2169, 8913])).
% 1.74/1.93 tff(8915,plain,
% 1.74/1.93 (r(s(s(s(z))), s(s(z)))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[943, 335, 133])).
% 1.74/1.93 tff(8916,plain,
% 1.74/1.93 (~r(s(s(s(z))), s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[4544, 8915, 8914])).
% 1.74/1.93 tff(8917,plain,
% 1.74/1.93 (b(s(s(s(z))), s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[4549, 8916])).
% 1.74/1.93 tff(8918,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[8917, 8912])).
% 1.74/1.93 tff(8919,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~(s(s(z)) = s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~b(z, s(s(z)))) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(8920,plain,
% 1.74/1.93 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[8919, 133, 93, 2169, 711, 114])).
% 1.74/1.93 tff(8921,plain,
% 1.74/1.93 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[348, 8920, 58])).
% 1.74/1.93 tff(8922,plain,
% 1.74/1.93 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[937])).
% 1.74/1.93 tff(8923,plain,
% 1.74/1.93 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.93 inference(symmetry,[status(thm)],[8922])).
% 1.74/1.93 tff(8924,plain,
% 1.74/1.93 (b(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[116, 8923])).
% 1.74/1.93 tff(8925,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[4063, 8924])).
% 1.74/1.93 tff(8926,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | b(s(s(s(z))), s(s(elem!1))) | (~(s(s(z)) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(8927,plain,
% 1.74/1.93 (b(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[8926, 8921, 133])).
% 1.74/1.93 tff(8928,plain,
% 1.74/1.93 ((~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6618, 7778])).
% 1.74/1.93 tff(8929,plain,
% 1.74/1.93 (~b(s(s(s(z))), z)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[8928, 8927, 711])).
% 1.74/1.93 tff(8930,plain,
% 1.74/1.93 (~b(s(s(s(elem!1))), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5559, 8929, 133])).
% 1.74/1.93 tff(8931,plain,
% 1.74/1.93 (r(s(s(s(elem!1))), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[361, 8930, 249])).
% 1.74/1.93 tff(8932,plain,
% 1.74/1.93 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[8181, 8927])).
% 1.74/1.93 tff(8933,plain,
% 1.74/1.93 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6350, 8932, 8663])).
% 1.74/1.93 tff(8934,plain,
% 1.74/1.93 (~r(s(s(s(s(z)))), s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[2452, 8933, 2169])).
% 1.74/1.93 tff(8935,plain,
% 1.74/1.93 (b(s(s(s(s(z)))), s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[2461, 8934])).
% 1.74/1.93 tff(8936,plain,
% 1.74/1.93 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[8935, 8652])).
% 1.74/1.93 tff(8937,plain,
% 1.74/1.93 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[187])).
% 1.74/1.93 tff(8938,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(8939,plain,
% 1.74/1.93 (((~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(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), 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(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(8940,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[8939])).
% 1.74/1.93 tff(8941,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[8940, 8938])).
% 1.74/1.93 tff(8942,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(8943,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[8942, 8941])).
% 1.74/1.93 tff(8944,plain,
% 1.74/1.93 (~b(elem!1, s(s(s(elem!1))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[8943, 319, 8694, 116, 8643])).
% 1.74/1.93 tff(8945,plain,
% 1.74/1.93 (~b(z, s(s(s(elem!1))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[8944, 1066])).
% 1.74/1.93 tff(8946,plain,
% 1.74/1.93 (r(z, s(s(s(elem!1))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[416, 8945])).
% 1.74/1.93 tff(8947,plain,
% 1.74/1.93 (r(elem!1, s(s(s(elem!1))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[8946, 8937])).
% 1.74/1.93 tff(8948,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(8949,plain,
% 1.74/1.93 (((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(8950,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[8949])).
% 1.74/1.93 tff(8951,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.74/1.93 inference(transitivity,[status(thm)],[8950, 8948])).
% 1.74/1.93 tff(8952,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(8953,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[8952, 8951])).
% 1.74/1.93 tff(8954,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[8953, 319, 449, 1445, 397, 547])).
% 1.74/1.93 tff(8955,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(8956,plain,
% 1.74/1.93 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[8955, 449, 8643, 547])).
% 1.74/1.93 tff(8957,plain,
% 1.74/1.93 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[616, 8956, 605])).
% 1.74/1.93 tff(8958,plain,
% 1.74/1.93 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[8783, 8957, 547, 461, 449, 99])).
% 1.74/1.93 tff(8959,plain,
% 1.74/1.93 (r(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[958, 8958, 183])).
% 1.74/1.93 tff(8960,plain,
% 1.74/1.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(8961,plain,
% 1.74/1.93 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(8962,plain,
% 1.74/1.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1)))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[8961])).
% 1.74/1.93 tff(8963,plain,
% 1.74/1.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[8962, 8960])).
% 1.74/1.93 tff(8964,plain,
% 1.74/1.93 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(8965,plain,
% 1.74/1.93 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[8964, 8963])).
% 1.74/1.93 tff(8966,plain,
% 1.74/1.93 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[8965, 297, 2390, 8959])).
% 1.74/1.93 tff(8967,plain,
% 1.74/1.93 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[2222, 51, 8966, 2146])).
% 1.74/1.93 tff(8968,plain,
% 1.74/1.93 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[2259, 8957, 461])).
% 1.74/1.93 tff(8969,plain,
% 1.74/1.93 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[8968, 8763])).
% 1.74/1.93 tff(8970,plain,
% 1.74/1.93 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[2252, 8969])).
% 1.74/1.93 tff(8971,plain,
% 1.74/1.93 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[8970, 2216])).
% 1.74/1.93 tff(8972,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(8973,plain,
% 1.74/1.93 (((~b(s(s(s(elem!1))), 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(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~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(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(8974,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1)))), s(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(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[8973])).
% 1.74/1.93 tff(8975,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1)))), s(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(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[8974, 8972])).
% 1.74/1.93 tff(8976,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1)))), s(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(elem!1)), s(s(s(s(elem!1)))))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(8977,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[8976, 8975])).
% 1.74/1.93 tff(8978,plain,
% 1.74/1.93 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[8977, 319, 116, 8971, 8967])).
% 1.74/1.93 tff(8979,assumption,(~(s(s(elem!1)) = s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.74/1.93 tff(8980,assumption,(~r(s(s(elem!1)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.74/1.93 tff(8981,assumption,(~b(s(s(elem!1)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.74/1.93 tff(8982,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1259, 51, 8981, 8980, 8979])).
% 1.74/1.93 tff(8983,plain,(r(s(s(elem!1)), s(s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(8984,plain,
% 1.74/1.93 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[8983, 8978, 2330])).
% 1.74/1.93 tff(8985,assumption,(r(s(elem!1), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.74/1.93 tff(8986,plain,
% 1.74/1.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(8987,plain,
% 1.74/1.93 (((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(8988,plain,
% 1.74/1.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[8987])).
% 1.74/1.93 tff(8989,plain,
% 1.74/1.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[8988, 8986])).
% 1.74/1.93 tff(8990,plain,
% 1.74/1.93 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(8991,plain,
% 1.74/1.93 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[8990, 8989])).
% 1.74/1.93 tff(8992,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[8991, 297, 2390, 1560, 8985])).
% 1.74/1.93 tff(8993,plain,((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(8994,plain,
% 1.74/1.93 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[8993, 8984, 2390])).
% 1.74/1.93 tff(8995,plain,
% 1.74/1.93 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[8841, 51, 8838, 8994])).
% 1.74/1.93 tff(8996,plain,
% 1.74/1.93 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1892, 297, 461, 8957])).
% 1.74/1.93 tff(8997,plain,
% 1.74/1.93 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[558, 51, 99, 8996])).
% 1.74/1.93 tff(8998,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(8999,plain,
% 1.74/1.93 (((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(9000,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[8999])).
% 1.74/1.93 tff(9001,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[9000, 8998])).
% 1.74/1.93 tff(9002,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(9003,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[9002, 9001])).
% 1.74/1.93 tff(9004,plain,
% 1.74/1.93 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[9003, 319, 547, 8997, 8995])).
% 1.74/1.93 tff(9005,plain,
% 1.74/1.93 (r(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[434, 9004, 1114])).
% 1.74/1.93 tff(9006,plain,
% 1.74/1.93 (~r(elem!1, s(elem!1))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[425, 297, 9005, 8947])).
% 1.74/1.93 tff(9007,plain,
% 1.74/1.93 (b(elem!1, s(elem!1))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[389, 9006, 1209])).
% 1.74/1.93 tff(9008,plain,
% 1.74/1.93 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[8801, 319, 275, 308, 1523])).
% 1.74/1.93 tff(9009,plain,
% 1.74/1.93 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1243, 51, 1785, 9008])).
% 1.74/1.93 tff(9010,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[8808, 297, 2390, 1707, 9009])).
% 1.74/1.93 tff(9011,plain,((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | (s(s(s(s(s(elem!1))))) = s(elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(9012,plain,
% 1.74/1.93 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[9011, 9007, 2270, 1418, 2390, 8694, 449])).
% 1.74/1.93 tff(9013,plain,
% 1.74/1.93 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1320, 9012, 1060])).
% 1.74/1.93 tff(9014,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)],[1724, 297, 461, 9013])).
% 1.74/1.93 tff(9015,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)],[1412, 51, 2267, 9014])).
% 1.74/1.93 tff(9016,plain,
% 1.74/1.93 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1142, 297, 8957, 9013])).
% 1.74/1.93 tff(9017,plain,
% 1.74/1.93 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1146, 51, 8651, 9016])).
% 1.74/1.93 tff(9018,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(9019,plain,
% 1.74/1.93 (((~b(s(s(s(elem!1))), 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(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(s(elem!1))))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(9020,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[9019])).
% 1.74/1.94 tff(9021,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[9020, 9018])).
% 1.74/1.94 tff(9022,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(9023,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[9022, 9021])).
% 1.74/1.94 tff(9024,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[9023, 319, 116, 9017, 8971, 9015])).
% 1.74/1.94 tff(9025,plain,((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (elem!1 = s(elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~(s(s(z)) = s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(9026,plain,
% 1.74/1.94 (~b(s(elem!1), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[9025, 8921, 8931, 5102, 5580, 8936, 81, 133, 93])).
% 1.74/1.94 tff(9027,plain,
% 1.74/1.94 (r(s(elem!1), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[375, 9026, 5579])).
% 1.74/1.94 tff(9028,plain,
% 1.74/1.94 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1394, 461, 286])).
% 1.74/1.94 tff(9029,plain,
% 1.74/1.94 (b(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[434, 9028, 1114])).
% 1.74/1.94 tff(9030,plain,
% 1.74/1.94 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[1372, 1374])).
% 1.74/1.94 tff(9031,plain,
% 1.74/1.94 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1168, 1117, 286])).
% 1.74/1.94 tff(9032,plain,
% 1.74/1.94 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[595, 9031, 587])).
% 1.74/1.94 tff(9033,plain,
% 1.74/1.94 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[9003, 319, 309, 9032, 1444])).
% 1.74/1.94 tff(9034,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[9033, 9030])).
% 1.74/1.94 tff(9035,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (~(s(s(z)) = s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(9036,plain,
% 1.74/1.94 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[9035, 9029, 133, 286, 1117])).
% 1.74/1.94 tff(9037,plain,
% 1.74/1.94 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2027, 9036, 133])).
% 1.74/1.94 tff(9038,plain,
% 1.74/1.94 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2281, 9037])).
% 1.74/1.94 tff(9039,plain,
% 1.74/1.94 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[9038, 2272])).
% 1.74/1.94 tff(9040,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1892, 297, 461, 1117, 9039])).
% 1.74/1.94 tff(9041,plain,((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~(s(s(z)) = s(s(elem!1)))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(9042,plain,
% 1.74/1.94 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[9041, 9027, 133, 8931])).
% 1.74/1.94 tff(9043,plain,
% 1.74/1.94 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[616, 9042, 605])).
% 1.74/1.94 tff(9044,plain,
% 1.74/1.94 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[8860, 319, 8694, 9043, 8643])).
% 1.74/1.94 tff(9045,plain,
% 1.74/1.94 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[571, 9044, 2202])).
% 1.74/1.94 tff(9046,plain,
% 1.74/1.94 (~b(elem!1, s(s(s(elem!1))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[8943, 319, 8694, 8921, 8643])).
% 1.74/1.94 tff(9047,plain,
% 1.74/1.94 (~b(z, s(s(s(elem!1))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[9046, 1066])).
% 1.74/1.94 tff(9048,plain,
% 1.74/1.94 (r(z, s(s(s(elem!1))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[416, 9047])).
% 1.74/1.94 tff(9049,plain,
% 1.74/1.94 (r(elem!1, s(s(s(elem!1))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[9048, 8937])).
% 1.74/1.94 tff(9050,plain,
% 1.74/1.94 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[517, 297, 9027, 8931])).
% 1.74/1.94 tff(9051,plain,
% 1.74/1.94 (b(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[958, 9050, 183])).
% 1.74/1.94 tff(9052,plain,
% 1.74/1.94 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1394, 9027, 8931])).
% 1.74/1.94 tff(9053,plain,
% 1.74/1.94 (b(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[434, 9052, 1114])).
% 1.74/1.94 tff(9054,plain,
% 1.74/1.94 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[8686, 319, 9053, 9051, 8936])).
% 1.74/1.94 tff(9055,plain,
% 1.74/1.94 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[9054, 2218])).
% 1.74/1.94 tff(9056,plain,
% 1.74/1.94 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2252, 9055])).
% 1.74/1.94 tff(9057,plain,
% 1.74/1.94 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[9056, 1494])).
% 1.74/1.94 tff(9058,plain,
% 1.74/1.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(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))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(9059,plain,
% 1.74/1.94 (((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1))))))) <=> ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(9060,plain,
% 1.74/1.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[9059])).
% 1.74/1.94 tff(9061,plain,
% 1.74/1.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[9060, 9058])).
% 1.74/1.94 tff(9062,plain,
% 1.74/1.94 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(9063,plain,
% 1.74/1.94 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[9062, 9061])).
% 1.74/1.94 tff(9064,plain,
% 1.74/1.94 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[9063, 297, 9057, 9049])).
% 1.74/1.94 tff(9065,plain,
% 1.74/1.94 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[634, 9064, 619])).
% 1.74/1.94 tff(9066,plain,
% 1.74/1.94 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1791, 9065, 108, 8694, 2270, 9043, 9045])).
% 1.74/1.94 tff(9067,plain,
% 1.74/1.94 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1320, 9066, 1060])).
% 1.74/1.94 tff(9068,plain,
% 1.74/1.94 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1724, 297, 8931, 9067])).
% 1.74/1.94 tff(9069,plain,
% 1.74/1.94 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1412, 51, 2267, 9068])).
% 1.74/1.94 tff(9070,plain,
% 1.74/1.94 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1298, 9067, 9027])).
% 1.74/1.94 tff(9071,plain,
% 1.74/1.94 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1291, 51, 1418, 9070])).
% 1.74/1.94 tff(9072,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1803, 319, 9053, 9051, 9071, 9069])).
% 1.74/1.94 tff(9073,plain,((~(s(s(z)) = s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~b(z, s(s(z)))) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(9074,plain,
% 1.74/1.94 (~(s(s(z)) = s(s(elem!1)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[9073, 8642, 8494, 58])).
% 1.74/1.94 tff(9075,plain,
% 1.74/1.94 (~(s(elem!1) = s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[774, 9074])).
% 1.74/1.94 tff(9076,plain,
% 1.74/1.94 (r(s(s(z)), s(s(elem!1)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[122, 9074, 33])).
% 1.74/1.94 tff(9077,plain,
% 1.74/1.94 (~(s(z) = s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2503, 9075])).
% 1.74/1.94 tff(9078,plain,
% 1.74/1.94 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2509, 9074])).
% 1.74/1.94 tff(9079,plain,
% 1.74/1.94 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[7059, 9078])).
% 1.74/1.94 tff(9080,plain,
% 1.74/1.94 (~r(s(s(z)), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4108, 2578, 2169])).
% 1.74/1.94 tff(9081,plain,
% 1.74/1.94 (b(s(s(z)), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4102, 9080])).
% 1.74/1.94 tff(9082,plain,
% 1.74/1.94 (~b(z, s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[8110, 817, 9081, 2578])).
% 1.74/1.94 tff(9083,plain,
% 1.74/1.94 (~r(z, s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[8130, 817, 2169, 136, 2142, 2578, 2523])).
% 1.74/1.94 tff(9084,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1099, 9083, 9082])).
% 1.74/1.94 tff(9085,plain,((~b(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (s(z) = s(elem!1)) | (s(elem!1) = s(s(elem!1))) | (~r(s(s(z)), s(s(elem!1)))) | (s(elem!1) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(9086,plain,
% 1.74/1.94 (s(elem!1) = s(s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[9085, 817, 136, 2142, 2578, 2169])).
% 1.74/1.94 tff(9087,plain,
% 1.74/1.94 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(z)), s(s(elem!1)))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[9086])).
% 1.74/1.94 tff(9088,plain,
% 1.74/1.94 (r(s(s(z)), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.74/1.94 inference(symmetry,[status(thm)],[9087])).
% 1.74/1.94 tff(9089,plain,
% 1.74/1.94 (r(s(elem!1), s(s(elem!1)))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[2578, 9088])).
% 1.74/1.94 tff(9090,plain,
% 1.74/1.94 (b(s(elem!1), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[8140, 9086, 9081])).
% 1.74/1.94 tff(9091,plain,
% 1.74/1.94 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[9086])).
% 1.74/1.94 tff(9092,plain,
% 1.74/1.94 (elem!1 = s(z)),
% 1.74/1.94 inference(transitivity,[status(thm)],[258, 9091, 126])).
% 1.74/1.94 tff(9093,plain,
% 1.74/1.94 (b(elem!1, s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[9092])).
% 1.74/1.94 tff(9094,plain,
% 1.74/1.94 (b(s(z), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 1.74/1.94 inference(symmetry,[status(thm)],[9093])).
% 1.74/1.94 tff(9095,plain,
% 1.74/1.94 (b(elem!1, s(s(elem!1)))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[817, 9094])).
% 1.74/1.94 tff(9096,plain,
% 1.74/1.94 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[3623, 9095, 2169, 9086, 9090, 9089])).
% 1.74/1.94 tff(9097,plain,
% 1.74/1.94 (b(s(s(s(z))), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[8148, 9086])).
% 1.74/1.94 tff(9098,plain,
% 1.74/1.94 (r(z, s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1099, 9082])).
% 1.74/1.94 tff(9099,plain,
% 1.74/1.94 (s(s(elem!1)) = s(s(s(z)))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[9086])).
% 1.74/1.94 tff(9100,plain,
% 1.74/1.94 (b(z, s(s(elem!1))) <=> b(z, s(s(s(z))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[9099])).
% 1.74/1.94 tff(9101,plain,
% 1.74/1.94 (b(z, s(s(s(z))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[7301, 9100])).
% 1.74/1.94 tff(9102,plain,
% 1.74/1.94 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[3595, 9101, 817, 9098, 9097, 9086])).
% 1.74/1.94 tff(9103,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[3600, 9102, 9096, 3521])).
% 1.74/1.94 tff(9104,plain,((~b(s(z), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (s(z) = s(elem!1)) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(9105,plain,
% 1.74/1.94 (~b(s(z), s(s(elem!1)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[9104, 9079, 8642, 9076, 9077, 114])).
% 1.74/1.94 tff(9106,plain,
% 1.74/1.94 (r(s(z), s(s(elem!1)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1047, 9105])).
% 1.74/1.94 tff(9107,plain,
% 1.74/1.94 (b(s(elem!1), s(s(elem!1)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[7892, 7793, 2169, 2578, 93, 444, 9081, 776, 114])).
% 1.74/1.94 tff(9108,plain,
% 1.74/1.94 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[7899, 319, 9107, 7778, 7793])).
% 1.74/1.94 tff(9109,plain,
% 1.74/1.94 (r(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[434, 9108, 430])).
% 1.74/1.94 tff(9110,plain,
% 1.74/1.94 (~b(s(elem!1), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[3990, 319, 9107, 7301, 7778])).
% 1.74/1.94 tff(9111,plain,
% 1.74/1.94 (r(s(elem!1), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2602, 9110])).
% 1.74/1.94 tff(9112,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[7918, 9111, 9109, 7910])).
% 1.74/1.94 tff(9113,plain,((~r(s(z), s(s(elem!1)))) | (s(elem!1) = s(s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (s(elem!1) = s(z)) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(9114,plain,
% 1.74/1.94 (s(elem!1) = s(s(s(elem!1)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[9113, 9106, 8642, 9076, 9075, 58])).
% 1.74/1.94 tff(9115,plain,
% 1.74/1.94 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6109, 9114])).
% 1.74/1.94 tff(9116,plain,
% 1.74/1.94 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(elem!1)))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[9115])).
% 1.74/1.94 tff(9117,plain,
% 1.74/1.94 (s(s(s(elem!1))) = s(elem!1)),
% 1.74/1.94 inference(transitivity,[status(thm)],[89, 9116, 118])).
% 1.74/1.94 tff(9118,plain,
% 1.74/1.94 (r(z, s(s(s(elem!1)))) <=> r(z, s(elem!1))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[9117])).
% 1.74/1.94 tff(9119,plain,
% 1.74/1.94 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[7791, 9106, 9076])).
% 1.74/1.94 tff(9120,plain,
% 1.74/1.94 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[348, 9119, 58])).
% 1.74/1.94 tff(9121,plain,
% 1.74/1.94 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6109, 266])).
% 1.74/1.94 tff(9122,plain,
% 1.74/1.94 (elem!1 = s(s(s(s(elem!1))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4681, 9121])).
% 1.74/1.94 tff(9123,plain,
% 1.74/1.94 (elem!1 = s(s(elem!1))),
% 1.74/1.94 inference(transitivity,[status(thm)],[9122, 9121])).
% 1.74/1.94 tff(9124,plain,
% 1.74/1.94 (r(elem!1, s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[9123])).
% 1.74/1.94 tff(9125,plain,
% 1.74/1.94 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(elem!1))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[266])).
% 1.74/1.94 tff(9126,plain,
% 1.74/1.94 (r(elem!1, s(elem!1)) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[9125, 9124])).
% 1.74/1.94 tff(9127,plain,
% 1.74/1.94 (b(elem!1, s(elem!1)) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[9123, 266])).
% 1.74/1.94 tff(9128,plain,
% 1.74/1.94 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(elem!1, s(elem!1))),
% 1.74/1.94 inference(symmetry,[status(thm)],[9127])).
% 1.74/1.94 tff(9129,plain,
% 1.74/1.94 ((~b(s(s(elem!1)), s(s(s(elem!1))))) <=> (~b(elem!1, s(elem!1)))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[9128])).
% 1.74/1.94 tff(9130,plain,
% 1.74/1.94 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[9121])).
% 1.74/1.94 tff(9131,plain,
% 1.74/1.94 ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) <=> (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[9130])).
% 1.74/1.94 tff(9132,plain,
% 1.74/1.94 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[266])).
% 1.74/1.94 tff(9133,plain,
% 1.74/1.94 ((~b(s(s(s(s(elem!1)))), s(elem!1))) <=> (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[9132])).
% 1.74/1.94 tff(9134,plain,
% 1.74/1.94 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[589, 9133])).
% 1.74/1.94 tff(9135,plain,
% 1.74/1.94 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[9134, 9131])).
% 1.74/1.94 tff(9136,plain,
% 1.74/1.94 (~b(elem!1, s(elem!1))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[9135, 9129])).
% 1.74/1.94 tff(9137,plain,
% 1.74/1.94 (r(elem!1, s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[389, 9136, 2168])).
% 1.74/1.94 tff(9138,plain,
% 1.74/1.94 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[9137, 9126])).
% 1.74/1.94 tff(9139,plain,
% 1.74/1.94 (b(s(elem!1), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[266])).
% 1.74/1.94 tff(9140,plain,
% 1.74/1.94 (~(s(elem!1) = s(s(z)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[3120, 9122])).
% 1.74/1.94 tff(9141,plain,
% 1.74/1.94 (~b(s(z), s(s(elem!1)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[9085, 9140, 7798, 2142, 2578, 2169])).
% 1.74/1.94 tff(9142,plain,
% 1.74/1.94 (r(s(z), s(s(elem!1)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1047, 9141])).
% 1.74/1.94 tff(9143,plain,
% 1.74/1.94 (~r(s(z), s(s(z)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5690, 9142, 2578])).
% 1.74/1.94 tff(9144,plain,
% 1.74/1.94 (b(s(z), s(s(z)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[685, 9143])).
% 1.74/1.94 tff(9145,plain,
% 1.74/1.94 (~b(z, s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4795, 9144, 711, 9081])).
% 1.74/1.94 tff(9146,plain,
% 1.74/1.94 (r(z, s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1099, 9145])).
% 1.74/1.94 tff(9147,plain,
% 1.74/1.94 ((~r(s(elem!1), s(z))) | (s(elem!1) = s(s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[3992, 7301])).
% 1.74/1.94 tff(9148,plain,
% 1.74/1.94 (~r(s(elem!1), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[9147, 9146, 2142, 2169])).
% 1.74/1.94 tff(9149,plain,
% 1.74/1.94 (b(s(elem!1), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[783, 9148, 776])).
% 1.74/1.94 tff(9150,plain,
% 1.74/1.94 (b(s(s(s(elem!1))), s(z))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[9149, 9139])).
% 1.74/1.94 tff(9151,plain,
% 1.74/1.94 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[7789, 319, 9081, 9144, 9150])).
% 1.74/1.94 tff(9152,plain,
% 1.74/1.94 (r(s(s(z)), s(s(s(elem!1))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1571, 9151])).
% 1.74/1.94 tff(9153,plain,
% 1.74/1.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(9154,plain,
% 1.74/1.94 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1))))) <=> ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(9155,plain,
% 1.74/1.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1))))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[9154])).
% 1.74/1.94 tff(9156,plain,
% 1.74/1.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[9155, 9153])).
% 1.74/1.94 tff(9157,plain,
% 1.74/1.94 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(9158,plain,
% 1.74/1.94 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[9157, 9156])).
% 1.74/1.94 tff(9159,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[9158, 297, 9152, 2578, 9138])).
% 1.74/1.94 tff(9160,plain,((~(s(elem!1) = s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(elem!1)) | (s(elem!1) = s(z)) | (s(elem!1) = s(s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(9161,plain,
% 1.74/1.94 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[9160, 9114, 9076, 9075, 114, 8642, 8494])).
% 1.74/1.94 tff(9162,plain,
% 1.74/1.94 (b(s(s(elem!1)), s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4762, 9161, 9115])).
% 1.74/1.94 tff(9163,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[8015, 319, 274, 202, 3741, 116])).
% 1.74/1.94 tff(9164,plain,((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(9165,plain,
% 1.74/1.94 ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[9164, 7301])).
% 1.74/1.94 tff(9166,plain,
% 1.74/1.94 (~b(z, s(s(s(elem!1))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[9165, 9162, 9120])).
% 1.74/1.94 tff(9167,plain,
% 1.74/1.94 (r(z, s(s(s(elem!1))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[416, 9166])).
% 1.74/1.94 tff(9168,plain,
% 1.74/1.94 (r(z, s(elem!1))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[9167, 9118])).
% 1.74/1.94 tff(9169,plain,
% 1.74/1.94 (s(s(s(elem!1))) = s(elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[269, 9114])).
% 1.74/1.94 tff(9170,plain,
% 1.74/1.94 (r(elem!1, s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2834, 9169, 8642])).
% 1.74/1.94 tff(9171,plain,
% 1.74/1.94 (elem!1 = s(s(s(s(elem!1))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4681, 9115])).
% 1.74/1.94 tff(9172,plain,
% 1.74/1.94 (elem!1 = s(s(elem!1))),
% 1.74/1.94 inference(transitivity,[status(thm)],[9171, 9115])).
% 1.74/1.94 tff(9173,plain,
% 1.74/1.94 (b(elem!1, s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[9172])).
% 1.74/1.94 tff(9174,plain,
% 1.74/1.94 (b(s(s(elem!1)), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 1.74/1.94 inference(symmetry,[status(thm)],[9173])).
% 1.74/1.94 tff(9175,plain,
% 1.74/1.94 (b(elem!1, s(elem!1))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[9162, 9174])).
% 1.74/1.94 tff(9176,plain,
% 1.74/1.94 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2827, 9114])).
% 1.74/1.94 tff(9177,plain,
% 1.74/1.94 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(elem!1)))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[9172])).
% 1.74/1.94 tff(9178,plain,
% 1.74/1.94 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), elem!1)),
% 1.74/1.94 inference(symmetry,[status(thm)],[9177])).
% 1.74/1.94 tff(9179,plain,
% 1.74/1.94 (~r(s(s(z)), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4108, 9076, 8642])).
% 1.74/1.94 tff(9180,plain,
% 1.74/1.94 (b(s(s(z)), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4102, 9179])).
% 1.74/1.94 tff(9181,plain,
% 1.74/1.94 (b(s(elem!1), s(s(elem!1)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[7892, 9120, 8642, 9076, 93, 9106, 9180, 9075, 114])).
% 1.74/1.94 tff(9182,plain,
% 1.74/1.94 (b(s(elem!1), elem!1)),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[9181, 9178])).
% 1.74/1.94 tff(9183,plain,
% 1.74/1.94 (~b(s(elem!1), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[3990, 319, 9181, 7301, 7778])).
% 1.74/1.94 tff(9184,plain,
% 1.74/1.94 (r(s(elem!1), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2602, 9183])).
% 1.74/1.94 tff(9185,plain,
% 1.74/1.94 (~b(s(z), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[7710, 9106, 8494, 9076])).
% 1.74/1.94 tff(9186,plain,
% 1.74/1.94 (r(s(z), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[67, 9185])).
% 1.74/1.94 tff(9187,plain,
% 1.74/1.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(9188,plain,
% 1.74/1.94 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(9189,plain,
% 1.74/1.94 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1)))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[9188, 9187])).
% 1.74/1.94 tff(9190,plain,
% 1.74/1.94 (~r(s(z), s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[9189, 297, 9186, 9184])).
% 1.74/1.94 tff(9191,plain,
% 1.74/1.94 (b(s(z), s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4816, 9190, 9077])).
% 1.74/1.94 tff(9192,plain,
% 1.74/1.94 (~b(s(s(s(z))), s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2868, 9191, 9182, 9176, 9169, 9175, 9170])).
% 1.74/1.94 tff(9193,plain,
% 1.74/1.94 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4874, 9192, 9114])).
% 1.74/1.94 tff(9194,plain,
% 1.74/1.94 (r(s(s(s(z))), s(s(s(elem!1))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[3794, 9193, 9078])).
% 1.74/1.94 tff(9195,plain,
% 1.74/1.94 (~r(s(s(s(z))), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[8093, 9194, 9168, 9115])).
% 1.74/1.94 tff(9196,plain,
% 1.74/1.94 (b(s(s(s(z))), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4584, 9195])).
% 1.74/1.94 tff(9197,plain,
% 1.74/1.94 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[8928, 9196, 8494])).
% 1.74/1.94 tff(9198,plain,
% 1.74/1.94 (r(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4066, 51, 9176, 9197])).
% 1.74/1.94 tff(9199,plain,
% 1.74/1.94 (~r(s(s(s(z))), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6886, 9198, 8642])).
% 1.74/1.94 tff(9200,plain,
% 1.74/1.94 (b(s(s(s(z))), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4549, 9199])).
% 1.74/1.94 tff(9201,plain,
% 1.74/1.94 (~r(s(z), s(s(z)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5690, 9106, 9076])).
% 1.74/1.94 tff(9202,plain,
% 1.74/1.94 (b(s(z), s(s(z)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[685, 9201])).
% 1.74/1.94 tff(9203,plain,
% 1.74/1.94 (~b(z, s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4795, 9202, 8494, 9180])).
% 1.74/1.94 tff(9204,plain,
% 1.74/1.94 (r(z, s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1099, 9203])).
% 1.74/1.94 tff(9205,plain,
% 1.74/1.94 (~r(s(elem!1), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[9147, 9204, 114, 8642])).
% 1.74/1.94 tff(9206,plain,
% 1.74/1.94 (b(s(elem!1), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[783, 9205, 9075])).
% 1.74/1.94 tff(9207,plain,
% 1.74/1.94 (~b(s(elem!1), s(s(z)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[7802, 9191, 9180, 9206])).
% 1.74/1.94 tff(9208,plain,
% 1.74/1.94 (~(s(elem!1) = s(s(z)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[3120, 9171])).
% 1.74/1.94 tff(9209,plain,
% 1.74/1.94 (r(s(elem!1), s(s(z)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2529, 9207, 9208])).
% 1.74/1.94 tff(9210,plain,
% 1.74/1.94 (~b(s(z), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5730, 3390, 711, 2614])).
% 1.74/1.94 tff(9211,plain,
% 1.74/1.94 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[7791, 8586, 444])).
% 1.74/1.94 tff(9212,plain,
% 1.74/1.94 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[348, 9211, 58])).
% 1.74/1.94 tff(9213,plain,
% 1.74/1.94 (r(s(z), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[65, 51, 62, 60])).
% 1.74/1.94 tff(9214,plain,
% 1.74/1.94 (~r(s(s(elem!1)), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[304, 9213, 444])).
% 1.74/1.94 tff(9215,plain,
% 1.74/1.94 (b(s(s(elem!1)), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[75, 9214])).
% 1.74/1.94 tff(9216,plain,
% 1.74/1.94 (~r(z, s(s(elem!1)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[865, 9213, 444])).
% 1.74/1.94 tff(9217,plain,
% 1.74/1.94 (b(z, s(s(elem!1)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[56, 9216])).
% 1.74/1.94 tff(9218,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, 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)))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(9219,plain,
% 1.74/1.94 (((~b(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(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(z, 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)))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(9220,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, 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))))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[9219])).
% 1.74/1.94 tff(9221,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, 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)))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[9220, 9218])).
% 1.74/1.94 tff(9222,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(9223,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, 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))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[9222, 9221])).
% 1.74/1.94 tff(9224,plain,
% 1.74/1.94 (~b(s(s(s(elem!1))), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[9223, 319, 9217, 9215, 9212])).
% 1.74/1.94 tff(9225,plain,
% 1.74/1.94 (r(s(s(s(elem!1))), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1077, 51, 160, 9224])).
% 1.74/1.94 tff(9226,plain,
% 1.74/1.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(9227,plain,
% 1.74/1.94 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(9228,plain,
% 1.74/1.94 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[9227, 9226])).
% 1.74/1.94 tff(9229,plain,
% 1.74/1.94 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[9228, 297, 731, 9225])).
% 1.74/1.94 tff(9230,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(9231,plain,
% 1.74/1.95 (((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(9232,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[9231])).
% 1.74/1.95 tff(9233,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[9232, 9230])).
% 1.74/1.95 tff(9234,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(9235,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[9234, 9233])).
% 1.74/1.95 tff(9236,plain,
% 1.74/1.95 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[9235, 319, 785, 9215, 9212])).
% 1.74/1.95 tff(9237,plain,
% 1.74/1.95 ((s(s(s(elem!1))) = s(elem!1)) | r(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[521, 51, 9236])).
% 1.74/1.95 tff(9238,plain,
% 1.74/1.95 (s(s(s(elem!1))) = s(elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[9237, 9229])).
% 1.74/1.95 tff(9239,plain,
% 1.74/1.95 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[7899, 319, 785, 9215, 9212])).
% 1.74/1.95 tff(9240,plain,
% 1.74/1.95 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[7997, 297, 731, 9225])).
% 1.74/1.95 tff(9241,plain,
% 1.74/1.95 (s(elem!1) = s(s(s(elem!1)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[434, 9240, 9239])).
% 1.74/1.95 tff(9242,plain,
% 1.74/1.95 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2827, 9241])).
% 1.74/1.95 tff(9243,plain,
% 1.74/1.95 (inj_0(s(s(s(elem!1)))) = inj_0(s(elem!1))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[9238])).
% 1.74/1.95 tff(9244,plain,
% 1.74/1.95 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.74/1.95 inference(symmetry,[status(thm)],[9243])).
% 1.74/1.95 tff(9245,plain,
% 1.74/1.95 (elem!1 = s(s(elem!1))),
% 1.74/1.95 inference(transitivity,[status(thm)],[258, 9244, 83])).
% 1.74/1.95 tff(9246,plain,
% 1.74/1.95 (r(elem!1, s(s(z))) <=> r(s(s(elem!1)), s(s(z)))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[9245])).
% 1.74/1.95 tff(9247,plain,
% 1.74/1.95 ((elem!1 = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.74/1.95 inference(commutativity,[status(thm)],[])).
% 1.74/1.95 tff(9248,plain,
% 1.74/1.95 ((s(s(z)) = elem!1) <=> (elem!1 = s(s(z)))),
% 1.74/1.95 inference(symmetry,[status(thm)],[9247])).
% 1.74/1.95 tff(9249,plain,
% 1.74/1.95 ((~(s(s(z)) = elem!1)) <=> (~(elem!1 = s(s(z))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[9248])).
% 1.74/1.95 tff(9250,plain,
% 1.74/1.95 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(elem!1)))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[9245])).
% 1.74/1.95 tff(9251,plain,
% 1.74/1.95 ((s(s(z)) = s(s(elem!1))) <=> (s(s(z)) = elem!1)),
% 1.74/1.95 inference(symmetry,[status(thm)],[9250])).
% 1.74/1.95 tff(9252,plain,
% 1.74/1.95 ((~(s(s(z)) = s(s(elem!1)))) <=> (~(s(s(z)) = elem!1))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[9251])).
% 1.74/1.95 tff(9253,plain,
% 1.74/1.95 (~(s(s(z)) = elem!1)),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[772, 9252])).
% 1.74/1.95 tff(9254,plain,
% 1.74/1.95 (~(elem!1 = s(s(z)))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[9253, 9249])).
% 1.74/1.95 tff(9255,plain,
% 1.74/1.95 (s(s(elem!1)) = elem!1),
% 1.74/1.95 inference(transitivity,[status(thm)],[168, 9243, 141])).
% 1.74/1.95 tff(9256,plain,
% 1.74/1.95 (b(s(s(elem!1)), z) <=> b(elem!1, z)),
% 1.74/1.95 inference(monotonicity,[status(thm)],[9255])).
% 1.74/1.95 tff(9257,plain,
% 1.74/1.95 (b(elem!1, z)),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[9215, 9256])).
% 1.74/1.95 tff(9258,plain,
% 1.74/1.95 (b(z, s(s(elem!1))) <=> b(z, elem!1)),
% 1.74/1.95 inference(monotonicity,[status(thm)],[9255])).
% 1.74/1.95 tff(9259,plain,
% 1.74/1.95 (b(z, elem!1)),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[9217, 9258])).
% 1.74/1.95 tff(9260,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, z)))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(9261,plain,
% 1.74/1.95 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z))))) <=> ((~b(elem!1, s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, z)))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(9262,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, z))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[9261])).
% 1.74/1.95 tff(9263,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, z)))),
% 1.74/1.95 inference(transitivity,[status(thm)],[9262, 9260])).
% 1.74/1.95 tff(9264,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(9265,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, z))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[9264, 9263])).
% 1.74/1.95 tff(9266,plain,
% 1.74/1.95 (~b(elem!1, s(s(z)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[9265, 319, 9259, 9257, 2614])).
% 1.74/1.95 tff(9267,plain,
% 1.74/1.95 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(9268,plain,
% 1.74/1.95 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(9269,plain,
% 1.74/1.95 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z)))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[9268, 9267])).
% 1.74/1.95 tff(9270,plain,
% 1.74/1.95 ((elem!1 = s(s(z))) | r(elem!1, s(s(z)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[9269, 51, 9266])).
% 1.74/1.95 tff(9271,plain,
% 1.74/1.95 (r(elem!1, s(s(z)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[9270, 9254])).
% 1.74/1.95 tff(9272,plain,
% 1.74/1.95 (r(s(s(elem!1)), s(s(z)))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[9271, 9246])).
% 1.74/1.95 tff(9273,plain,
% 1.74/1.95 (b(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[4226, 9272, 2915, 9242])).
% 1.74/1.95 tff(9274,plain,
% 1.74/1.95 (b(s(s(s(z))), elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[4234, 9273, 9238])).
% 1.74/1.95 tff(9275,plain,
% 1.74/1.95 ((s(elem!1) = s(s(elem!1))) <=> (s(elem!1) = elem!1)),
% 1.74/1.95 inference(monotonicity,[status(thm)],[9255])).
% 1.74/1.95 tff(9276,plain,
% 1.74/1.95 ((s(elem!1) = s(s(elem!1))) <=> (elem!1 = s(elem!1))),
% 1.74/1.95 inference(transitivity,[status(thm)],[9275, 184])).
% 1.74/1.95 tff(9277,plain,
% 1.74/1.95 ((~(s(elem!1) = s(s(elem!1)))) <=> (~(elem!1 = s(elem!1)))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[9276])).
% 1.74/1.95 tff(9278,plain,
% 1.74/1.95 (~(elem!1 = s(elem!1))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[114, 9277])).
% 1.74/1.95 tff(9279,plain,
% 1.74/1.95 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(z)))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(9280,plain,
% 1.74/1.95 (((~r(s(elem!1), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(elem!1)))) <=> ((~r(s(elem!1), s(s(z)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(z)))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(9281,plain,
% 1.74/1.95 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(z))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[9280])).
% 1.74/1.95 tff(9282,plain,
% 1.74/1.95 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(z)))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[9281, 9279])).
% 1.74/1.95 tff(9283,plain,
% 1.74/1.95 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(elem!1))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(9284,plain,
% 1.74/1.95 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(z))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[9283, 9282])).
% 1.74/1.95 tff(9285,plain,
% 1.74/1.95 (~r(elem!1, s(elem!1))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[9284, 297, 203, 9271])).
% 1.74/1.95 tff(9286,plain,
% 1.74/1.95 (b(elem!1, s(elem!1))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[389, 9285, 9278])).
% 1.74/1.95 tff(9287,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(9288,plain,
% 1.74/1.95 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z))) <=> ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(9289,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[9288])).
% 1.74/1.95 tff(9290,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)))),
% 1.74/1.95 inference(transitivity,[status(thm)],[9289, 9287])).
% 1.74/1.95 tff(9291,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(9292,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[9291, 9290])).
% 1.74/1.95 tff(9293,plain,
% 1.74/1.95 (~b(s(s(s(z))), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[9292, 319, 9286, 9259, 9274])).
% 1.74/1.95 tff(9294,plain,
% 1.74/1.95 (r(s(s(s(z))), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[901, 51, 898, 9293])).
% 1.74/1.95 tff(9295,plain,
% 1.74/1.95 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(9296,plain,
% 1.74/1.95 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(9297,plain,
% 1.74/1.95 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1)))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[9296, 9295])).
% 1.74/1.95 tff(9298,plain,
% 1.74/1.95 (~r(s(s(s(z))), s(elem!1))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[9297, 297, 731, 9294])).
% 1.74/1.95 tff(9299,plain,
% 1.74/1.95 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), elem!1)),
% 1.74/1.95 inference(monotonicity,[status(thm)],[9255])).
% 1.74/1.95 tff(9300,plain,
% 1.74/1.95 (b(s(elem!1), elem!1)),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[785, 9299])).
% 1.74/1.95 tff(9301,plain,
% 1.74/1.95 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(9302,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1)))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[9301])).
% 1.74/1.95 tff(9303,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[9302, 2856])).
% 1.74/1.95 tff(9304,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(9305,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1)))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[9304, 9303])).
% 1.74/1.95 tff(9306,plain,
% 1.74/1.95 (~b(s(s(s(z))), s(elem!1))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[9305, 319, 9286, 9300, 9274])).
% 1.74/1.95 tff(9307,plain,
% 1.74/1.95 ((s(s(s(z))) = s(elem!1)) | r(s(s(s(z))), s(elem!1))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2872, 51, 9306])).
% 1.74/1.95 tff(9308,plain,
% 1.74/1.95 (s(s(s(z))) = s(elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[9307, 9298])).
% 1.74/1.95 tff(9309,plain,
% 1.74/1.95 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[9308])).
% 1.74/1.95 tff(9310,plain,
% 1.74/1.95 (s(s(z)) = elem!1),
% 1.74/1.95 inference(transitivity,[status(thm)],[18, 9309, 141])).
% 1.74/1.95 tff(9311,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[9253, 9310])).
% 1.74/1.95 tff(9312,plain,((s(s(z)) = s(s(elem!1))) | (~r(s(elem!1), z)) | b(s(s(s(z))), s(s(z))) | (~r(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | b(s(z), z) | (s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(9313,plain,
% 1.74/1.95 (s(s(z)) = s(s(elem!1))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[9312, 9210, 2915, 203, 785, 444, 731, 58, 33])).
% 1.74/1.95 tff(9314,plain,
% 1.74/1.95 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[9313])).
% 1.74/1.95 tff(9315,plain,
% 1.74/1.95 (b(s(s(elem!1)), s(z)) <=> b(s(s(z)), s(z))),
% 1.74/1.95 inference(symmetry,[status(thm)],[9314])).
% 1.74/1.95 tff(9316,plain,
% 1.74/1.95 ((~b(s(s(elem!1)), s(z))) <=> (~b(s(s(z)), s(z)))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[9315])).
% 1.74/1.95 tff(9317,plain,
% 1.74/1.95 (b(z, s(s(elem!1)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[879, 9313, 711])).
% 1.74/1.95 tff(9318,plain,
% 1.74/1.95 (~b(s(s(elem!1)), s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[651, 9313, 9317, 203])).
% 1.74/1.95 tff(9319,plain,
% 1.74/1.95 (~b(s(s(z)), s(z))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[9318, 9316])).
% 1.74/1.95 tff(9320,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[3390, 9319])).
% 1.74/1.95 tff(9321,plain,((~b(s(s(z)), s(z))) | (~r(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | b(s(s(s(z))), s(s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), z)) | (s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(9322,plain,
% 1.74/1.95 (~b(s(s(z)), s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[9321, 785, 711, 2915, 203, 444, 731, 58, 33])).
% 1.74/1.95 tff(9323,plain,
% 1.74/1.95 (r(s(s(z)), s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[4102, 9322])).
% 1.74/1.95 tff(9324,plain,
% 1.74/1.95 (~r(s(s(z)), s(s(elem!1)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2583, 9323, 444])).
% 1.74/1.95 tff(9325,plain,
% 1.74/1.95 (s(s(z)) = s(s(elem!1))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[122, 9324, 33])).
% 1.74/1.95 tff(9326,plain,
% 1.74/1.95 (b(s(elem!1), s(s(z))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[9325])).
% 1.74/1.95 tff(9327,plain,
% 1.74/1.95 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(z)))),
% 1.74/1.95 inference(symmetry,[status(thm)],[9326])).
% 1.74/1.95 tff(9328,plain,
% 1.74/1.95 (b(s(elem!1), s(s(z)))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[785, 9327])).
% 1.74/1.95 tff(9329,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2512, 9328])).
% 1.74/1.95 tff(9330,plain,((~b(s(elem!1), s(s(elem!1)))) | b(s(elem!1), s(s(z))) | b(s(s(z)), s(s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~b(z, s(s(z)))) | b(s(s(s(z))), s(s(z))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), z)) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(9331,plain,
% 1.74/1.95 (b(s(s(s(z))), s(s(z)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[9330, 9209, 33, 9181, 9106, 8494, 9184, 9207, 58])).
% 1.74/1.95 tff(9332,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(9333,plain,
% 1.74/1.95 (((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(9334,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z)))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[9333])).
% 1.74/1.95 tff(9335,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[9334, 9332])).
% 1.74/1.95 tff(9336,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(9337,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z)))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[9336, 9335])).
% 1.74/1.96 tff(9338,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[9337, 319, 9180, 9191, 9331, 9200])).
% 1.74/1.96 tff(9339,plain,((s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(9340,plain,
% 1.74/1.96 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[9339, 33])).
% 1.74/1.96 tff(9341,plain,
% 1.74/1.96 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = s(s(elem!1)))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[9340])).
% 1.74/1.96 tff(9342,plain,
% 1.74/1.96 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(z)) = s(s(elem!1))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[9341])).
% 1.74/1.96 tff(9343,plain,
% 1.74/1.96 (~(s(s(z)) = s(s(elem!1)))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[231, 9342])).
% 1.74/1.96 tff(9344,plain,
% 1.74/1.96 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2509, 9343])).
% 1.74/1.96 tff(9345,plain,
% 1.74/1.96 (r(s(s(z)), s(s(elem!1)))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[122, 9343, 33])).
% 1.74/1.96 tff(9346,plain,
% 1.74/1.96 (b(s(elem!1), s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6459])).
% 1.74/1.96 tff(9347,plain,
% 1.74/1.96 ((~b(s(elem!1), s(s(z)))) <=> (~b(s(s(elem!1)), s(s(z))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[9346])).
% 1.74/1.96 tff(9348,plain,
% 1.74/1.96 ((~(s(s(s(elem!1))) = s(s(elem!1)))) | b(s(elem!1), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6765, 7778])).
% 1.74/1.96 tff(9349,plain,
% 1.74/1.96 (b(s(elem!1), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[9348, 5177])).
% 1.74/1.96 tff(9350,plain,
% 1.74/1.96 (~r(s(elem!1), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[802, 180, 6459])).
% 1.74/1.96 tff(9351,plain,
% 1.74/1.96 (b(s(elem!1), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[783, 9350, 6921])).
% 1.74/1.96 tff(9352,plain,
% 1.74/1.96 (b(z, s(elem!1)) <=> b(z, s(s(elem!1)))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6459])).
% 1.74/1.96 tff(9353,plain,
% 1.74/1.96 (b(z, s(s(elem!1))) <=> b(z, s(elem!1))),
% 1.74/1.96 inference(symmetry,[status(thm)],[9352])).
% 1.74/1.96 tff(9354,plain,
% 1.74/1.96 (b(z, s(elem!1))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[7301, 9353])).
% 1.74/1.96 tff(9355,plain,
% 1.74/1.96 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[8562, 8269, 1])).
% 1.74/1.96 tff(9356,plain,
% 1.74/1.96 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6520, 9355, 5177])).
% 1.74/1.96 tff(9357,plain,
% 1.74/1.96 (r(s(s(s(z))), s(s(s(elem!1))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[3794, 9356, 6482])).
% 1.74/1.96 tff(9358,plain,
% 1.74/1.96 (r(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[9357, 6479])).
% 1.74/1.96 tff(9359,plain,
% 1.74/1.96 (~r(s(s(z)), s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[7631, 297, 2578, 9358])).
% 1.74/1.96 tff(9360,plain,
% 1.74/1.96 ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6671, 51, 9359])).
% 1.74/1.96 tff(9361,plain,
% 1.74/1.96 (b(s(s(z)), s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[9360, 6656])).
% 1.74/1.96 tff(9362,plain,
% 1.74/1.96 (~r(s(s(s(z))), s(s(z)))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6527, 9357, 5177, 2578])).
% 1.74/1.96 tff(9363,plain,
% 1.74/1.96 (b(s(s(s(z))), s(s(z)))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2920, 9362])).
% 1.74/1.96 tff(9364,plain,
% 1.74/1.96 (~b(s(s(s(z))), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[7643, 319, 711, 9363, 9361])).
% 1.74/1.96 tff(9365,plain,
% 1.74/1.96 (r(s(s(s(z))), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4584, 9364])).
% 1.74/1.96 tff(9366,plain,
% 1.74/1.96 (~b(z, s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1095, 319, 1, 8269, 7301])).
% 1.74/1.96 tff(9367,plain,
% 1.74/1.96 (r(z, s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1099, 9366])).
% 1.74/1.96 tff(9368,plain,
% 1.74/1.96 (~r(s(s(z)), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4162, 297, 9367, 2511])).
% 1.74/1.96 tff(9369,plain,
% 1.74/1.96 (b(s(s(z)), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[663, 51, 28, 9368])).
% 1.74/1.96 tff(9370,plain,
% 1.74/1.96 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[3009, 2444, 2511])).
% 1.74/1.96 tff(9371,plain,
% 1.74/1.96 (b(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6174, 9370])).
% 1.74/1.96 tff(9372,plain,
% 1.74/1.96 (~r(s(s(z)), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4162, 297, 917, 2511])).
% 1.74/1.96 tff(9373,plain,
% 1.74/1.96 (b(s(s(z)), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[663, 51, 28, 9372])).
% 1.74/1.96 tff(9374,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(9375,plain,
% 1.74/1.96 (((~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(9376,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[9375])).
% 1.74/1.96 tff(9377,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 1.74/1.96 inference(transitivity,[status(thm)],[9376, 9374])).
% 1.74/1.96 tff(9378,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(9379,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[9378, 9377])).
% 1.74/1.96 tff(9380,plain,
% 1.74/1.96 (~b(s(s(s(s(z)))), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[9379, 319, 711, 7301, 7778, 9373, 9371])).
% 1.74/1.96 tff(9381,plain,
% 1.74/1.96 (~r(s(s(s(s(z)))), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[3580, 297, 917, 2444])).
% 1.74/1.96 tff(9382,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2482, 9381, 9380])).
% 1.74/1.96 tff(9383,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~b(z, s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(9384,plain,
% 1.74/1.96 (~r(s(s(s(s(z)))), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[9383, 9367, 711, 2511])).
% 1.74/1.96 tff(9385,plain,
% 1.74/1.96 (b(s(s(s(s(z)))), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2461, 9384])).
% 1.74/1.96 tff(9386,plain,
% 1.74/1.96 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6568, 9385, 1, 8269])).
% 1.74/1.96 tff(9387,plain,
% 1.74/1.96 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6350, 9386, 6474])).
% 1.74/1.96 tff(9388,plain,
% 1.74/1.96 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6599, 9387, 2578])).
% 1.74/1.96 tff(9389,plain,
% 1.74/1.96 (b(s(s(z)), s(s(s(s(z)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6249, 9388])).
% 1.74/1.96 tff(9390,plain,
% 1.74/1.96 (~b(s(s(s(s(z)))), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6604, 9389, 711, 9369])).
% 1.74/1.96 tff(9391,plain,
% 1.74/1.96 (r(s(s(s(s(z)))), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2482, 9390])).
% 1.74/1.96 tff(9392,plain,
% 1.74/1.96 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[7508, 297, 9391, 9365])).
% 1.74/1.96 tff(9393,plain,
% 1.74/1.96 (~r(s(s(s(z))), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[8451, 297, 8498, 9365])).
% 1.74/1.96 tff(9394,plain,
% 1.74/1.96 (b(s(s(s(z))), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4549, 9393])).
% 1.74/1.96 tff(9395,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(9396,plain,
% 1.74/1.96 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(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(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(9397,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[9396])).
% 1.74/1.96 tff(9398,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[9397, 9395])).
% 1.74/1.96 tff(9399,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(9400,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[9399, 9398])).
% 1.74/1.96 tff(9401,plain,
% 1.74/1.96 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[9400, 319, 8269, 9385, 9394])).
% 1.74/1.96 tff(9402,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2252, 9401, 9392])).
% 1.74/1.96 tff(9403,plain,((~r(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~(s(s(s(elem!1))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(9404,plain,
% 1.74/1.96 (~r(s(s(z)), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[9403, 872, 2578, 711, 5177])).
% 1.74/1.96 tff(9405,plain,
% 1.74/1.96 (b(s(s(z)), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4102, 9404])).
% 1.74/1.96 tff(9406,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(9407,plain,
% 1.74/1.96 (((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z))) <=> ((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(9408,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[9407])).
% 1.74/1.96 tff(9409,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)))),
% 1.74/1.96 inference(transitivity,[status(thm)],[9408, 9406])).
% 1.74/1.96 tff(9410,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(9411,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[9410, 9409])).
% 1.74/1.96 tff(9412,plain,
% 1.74/1.96 ((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[9411, 319])).
% 1.74/1.96 tff(9413,plain,
% 1.74/1.96 (~b(s(elem!1), s(s(z)))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[9412, 9405, 711, 9354, 9351, 9349])).
% 1.74/1.96 tff(9414,plain,
% 1.74/1.96 (~b(s(s(elem!1)), s(s(z)))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[9413, 9347])).
% 1.74/1.96 tff(9415,plain,
% 1.74/1.96 (r(s(s(elem!1)), s(s(z)))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2555, 51, 9414, 6478])).
% 1.74/1.96 tff(9416,plain,
% 1.74/1.96 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[8487, 5692, 1, 8498])).
% 1.74/1.96 tff(9417,plain,
% 1.74/1.96 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6520, 9416, 5177])).
% 1.74/1.96 tff(9418,plain,
% 1.74/1.96 (r(s(s(s(z))), s(s(s(elem!1))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[3794, 9417, 6482])).
% 1.74/1.96 tff(9419,plain,
% 1.74/1.96 (~r(s(z), s(s(s(elem!1))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[8160, 9418, 5177, 2578, 3390, 5692])).
% 1.74/1.96 tff(9420,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[9419, 6492])).
% 1.74/1.96 tff(9421,plain,((~r(s(z), s(s(elem!1)))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(9422,plain,
% 1.74/1.96 (~r(s(z), s(s(elem!1)))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[9421, 9405, 2578, 5177, 872])).
% 1.74/1.96 tff(9423,plain,
% 1.74/1.96 (b(s(z), s(s(elem!1)))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1047, 9422])).
% 1.74/1.96 tff(9424,plain,
% 1.74/1.96 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[8562, 9423, 872])).
% 1.74/1.96 tff(9425,plain,
% 1.74/1.96 (b(s(s(s(z))), s(s(z)))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4226, 9424, 7182, 9415])).
% 1.74/1.96 tff(9426,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(z))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(9427,plain,
% 1.74/1.96 (((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(z))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(9428,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(z)))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[9427])).
% 1.74/1.96 tff(9429,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(z))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[9428, 9426])).
% 1.74/1.96 tff(9430,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(9431,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(z)))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[9430, 9429])).
% 1.74/1.96 tff(9432,plain,
% 1.74/1.96 (~b(s(s(s(z))), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[9431, 319, 872, 9405, 711, 7301, 9425])).
% 1.74/1.96 tff(9433,plain,
% 1.74/1.96 (r(s(s(s(z))), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4584, 9432])).
% 1.74/1.96 tff(9434,plain,
% 1.74/1.96 (~r(s(s(s(z))), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[8451, 297, 8513, 9433])).
% 1.74/1.96 tff(9435,plain,
% 1.74/1.96 (b(s(s(s(z))), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4549, 9434])).
% 1.74/1.96 tff(9436,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(9437,plain,
% 1.74/1.96 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(9438,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z)))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[9437])).
% 1.74/1.96 tff(9439,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[9438, 9436])).
% 1.74/1.96 tff(9440,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(9441,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z)))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[9440, 9439])).
% 1.74/1.96 tff(9442,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[9441, 319, 9405, 9423, 9425, 9435])).
% 1.74/1.96 tff(9443,plain,(r(s(s(elem!1)), s(z)) | (~b(z, s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~(s(s(s(elem!1))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(9444,plain,
% 1.74/1.96 (r(s(s(elem!1)), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[9443, 8494, 9345, 9340])).
% 1.74/1.96 tff(9445,plain,
% 1.74/1.96 (~r(s(z), s(s(elem!1)))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[8195, 9444, 9340, 9345, 9344])).
% 1.74/1.96 tff(9446,plain,
% 1.74/1.96 (b(s(z), s(s(elem!1)))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1047, 9445])).
% 1.74/1.96 tff(9447,plain,
% 1.74/1.96 (~b(s(z), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[8814, 9446, 8494])).
% 1.74/1.96 tff(9448,plain,
% 1.74/1.96 (r(s(z), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[67, 9447])).
% 1.74/1.96 tff(9449,plain,
% 1.74/1.96 (r(s(s(elem!1)), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[9443, 711, 2578, 5177])).
% 1.74/1.96 tff(9450,plain,
% 1.74/1.96 (~r(s(s(s(z))), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6886, 8210, 9449])).
% 1.74/1.96 tff(9451,plain,
% 1.74/1.96 (b(s(s(s(z))), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4549, 9450])).
% 1.74/1.96 tff(9452,plain,
% 1.74/1.96 (~r(s(z), s(s(elem!1)))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[8195, 9449, 5177, 2578, 6482])).
% 1.74/1.97 tff(9453,plain,
% 1.74/1.97 (b(s(z), s(s(elem!1)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1047, 9452])).
% 1.74/1.97 tff(9454,plain,
% 1.74/1.97 (~b(s(z), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[8814, 9453, 711])).
% 1.74/1.97 tff(9455,plain,
% 1.74/1.97 (r(s(z), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[67, 9454])).
% 1.74/1.97 tff(9456,plain,
% 1.74/1.97 (~r(s(s(s(z))), s(s(z)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6527, 4878, 5177, 2578])).
% 1.74/1.97 tff(9457,plain,
% 1.74/1.97 (b(s(s(s(z))), s(s(z)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2920, 9456])).
% 1.74/1.97 tff(9458,plain,
% 1.74/1.97 (~b(s(s(s(z))), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[7643, 319, 711, 9457, 8213])).
% 1.74/1.97 tff(9459,plain,
% 1.74/1.97 (r(s(s(s(z))), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[4584, 9458])).
% 1.74/1.97 tff(9460,plain,
% 1.74/1.97 (~r(s(z), s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5986, 9459, 9455])).
% 1.74/1.97 tff(9461,plain,
% 1.74/1.97 (b(s(z), s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6558, 51, 9460, 32])).
% 1.74/1.97 tff(9462,plain,
% 1.74/1.97 (~r(s(s(z)), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[4108, 9449, 2578])).
% 1.74/1.97 tff(9463,plain,
% 1.74/1.97 (b(s(s(z)), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[4102, 9462])).
% 1.74/1.97 tff(9464,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(9465,plain,
% 1.74/1.97 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(9466,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z)))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[9465])).
% 1.74/1.97 tff(9467,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[9466, 9464])).
% 1.74/1.97 tff(9468,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(9469,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[9468, 9467])).
% 1.74/1.97 tff(9470,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[9469, 319, 9463, 9461, 9451, 8213])).
% 1.74/1.97 tff(9471,plain,((~r(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~(s(s(s(elem!1))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(9472,plain,
% 1.74/1.97 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[9471, 8494, 9345, 9340])).
% 1.74/1.97 tff(9473,plain,
% 1.74/1.97 (b(s(s(s(z))), s(s(s(elem!1))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[3794, 9472, 9344])).
% 1.74/1.97 tff(9474,plain,
% 1.74/1.97 (b(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6520, 9473, 9340])).
% 1.74/1.97 tff(9475,plain,
% 1.74/1.97 (~b(s(s(s(z))), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[8928, 9474, 8494])).
% 1.74/1.97 tff(9476,plain,
% 1.74/1.97 (r(s(s(s(z))), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[4584, 9475])).
% 1.74/1.97 tff(9477,plain,
% 1.74/1.97 (~r(s(z), s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5986, 9476, 9448])).
% 1.74/1.97 tff(9478,plain,
% 1.74/1.97 (~b(s(z), s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[8235, 319, 9446, 7778, 9474])).
% 1.74/1.97 tff(9479,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6558, 51, 9478, 9477, 32])).
% 1.74/1.97 tff(9480,plain,(b(s(s(z)), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(9481,plain,
% 1.74/1.97 (~r(s(s(z)), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[708, 687, 666, 1])).
% 1.74/1.97 tff(9482,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[663, 51, 28, 4616, 9481])).
% 1.74/1.97 tff(9483,plain,((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(9484,plain,
% 1.74/1.97 ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~r(s(z), z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[9483, 7301])).
% 1.74/1.97 tff(9485,plain,
% 1.74/1.97 ((~b(s(s(elem!1)), s(z))) | (~r(s(z), z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[9484, 9480])).
% 1.74/1.97 tff(9486,plain,
% 1.74/1.97 (~r(s(z), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[9485, 1])).
% 1.74/1.97 tff(9487,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[67, 8497, 9486])).
% 1.74/1.97 tff(9488,plain,(~b(s(s(elem!1)), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(9489,plain,
% 1.74/1.97 (r(s(s(elem!1)), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[871, 9488])).
% 1.74/1.97 tff(9490,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(9491,plain,
% 1.74/1.97 (((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(9492,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[9491])).
% 1.74/1.97 tff(9493,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)))),
% 1.74/1.97 inference(transitivity,[status(thm)],[9492, 9490])).
% 1.74/1.97 tff(9494,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(9495,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[9494, 9493])).
% 1.74/1.97 tff(9496,plain,
% 1.74/1.97 (~b(z, s(s(z)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[9495, 319, 9480, 7301, 7778])).
% 1.74/1.97 tff(9497,plain,
% 1.74/1.97 (~(s(s(z)) = s(s(elem!1)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[7305, 9496])).
% 1.74/1.97 tff(9498,plain,
% 1.74/1.97 ((~r(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[4668, 9497])).
% 1.74/1.97 tff(9499,plain,
% 1.74/1.97 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[9498, 2511, 58])).
% 1.74/1.97 tff(9500,plain,
% 1.74/1.97 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[348, 9499, 58])).
% 1.74/1.97 tff(9501,plain,
% 1.74/1.97 (r(z, s(s(z)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[729, 9496])).
% 1.74/1.97 tff(9502,plain,
% 1.74/1.97 ((~r(s(s(z)), s(z))) | (~r(z, s(z)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[7320, 9501])).
% 1.74/1.97 tff(9503,plain,
% 1.74/1.97 (~r(z, s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[9502, 2511])).
% 1.74/1.97 tff(9504,plain,
% 1.74/1.97 (b(z, s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1099, 9503])).
% 1.74/1.97 tff(9505,plain,
% 1.74/1.97 (~r(s(s(elem!1)), s(s(z)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2565, 2511, 9489])).
% 1.74/1.97 tff(9506,plain,
% 1.74/1.97 (~(s(s(elem!1)) = s(s(z)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2521, 9497])).
% 1.74/1.97 tff(9507,plain,
% 1.74/1.97 (b(s(s(elem!1)), s(s(z))) | r(s(s(elem!1)), s(s(z)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5327, 9506])).
% 1.74/1.97 tff(9508,plain,
% 1.74/1.97 (b(s(s(elem!1)), s(s(z)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[9507, 9505])).
% 1.74/1.97 tff(9509,plain,
% 1.74/1.97 ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5526, 7778])).
% 1.74/1.97 tff(9510,plain,
% 1.74/1.97 (~b(s(z), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[9509, 817, 2706])).
% 1.74/1.97 tff(9511,plain,
% 1.74/1.97 (r(s(z), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[67, 9510])).
% 1.74/1.97 tff(9512,plain,
% 1.74/1.97 ((~r(s(z), s(s(z)))) | (~r(s(z), z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6004, 9501])).
% 1.74/1.97 tff(9513,plain,
% 1.74/1.97 (~r(s(z), s(s(z)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[9512, 9511])).
% 1.74/1.97 tff(9514,plain,
% 1.74/1.97 (b(s(z), s(s(z)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[685, 9513])).
% 1.74/1.97 tff(9515,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5199, 319, 2543, 9480, 817, 9514])).
% 1.74/1.97 tff(9516,plain,((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(9517,plain,
% 1.74/1.97 (~b(s(z), s(s(elem!1)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[9516, 9508, 9504])).
% 1.74/1.97 tff(9518,plain,
% 1.74/1.97 (r(s(z), s(s(elem!1)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1047, 9517])).
% 1.74/1.97 tff(9519,plain,
% 1.74/1.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(9520,plain,
% 1.74/1.97 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(9521,plain,
% 1.74/1.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1)))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[9520])).
% 1.74/1.97 tff(9522,plain,
% 1.74/1.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[9521, 9519])).
% 1.74/1.97 tff(9523,plain,
% 1.74/1.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(9524,plain,
% 1.74/1.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1)))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[9523, 9522])).
% 1.74/1.97 tff(9525,plain,
% 1.74/1.97 (~r(s(z), s(s(s(elem!1))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[9524, 297, 9518, 9500])).
% 1.74/1.97 tff(9526,plain,
% 1.74/1.97 (b(s(z), s(s(s(elem!1))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5817, 51, 9525, 5798])).
% 1.74/1.97 tff(9527,plain,
% 1.74/1.97 (~r(s(s(s(elem!1))), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5135, 9518, 9500])).
% 1.74/1.97 tff(9528,plain,
% 1.74/1.97 (b(s(s(s(elem!1))), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[4750, 9527])).
% 1.74/1.97 tff(9529,plain,
% 1.74/1.97 (~r(s(s(s(z))), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6886, 6881, 9489])).
% 1.74/1.97 tff(9530,plain,
% 1.74/1.97 (b(s(s(s(z))), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[4549, 9529])).
% 1.74/1.97 tff(9531,plain,
% 1.74/1.97 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[7197, 9530, 4727, 7184])).
% 1.74/1.97 tff(9532,plain,
% 1.74/1.97 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2509, 9497])).
% 1.74/1.97 tff(9533,plain,
% 1.74/1.97 (b(s(s(s(z))), s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[3794, 9532])).
% 1.74/1.97 tff(9534,plain,
% 1.74/1.97 (r(s(s(s(z))), s(s(s(elem!1))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[9533, 9531])).
% 1.74/1.97 tff(9535,plain,
% 1.74/1.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(9536,plain,
% 1.74/1.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(9537,plain,
% 1.74/1.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[9536, 9535])).
% 1.74/1.97 tff(9538,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[9537, 297, 9534, 335, 6881])).
% 1.74/1.97 tff(9539,plain,((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(9540,plain,
% 1.74/1.97 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[9539, 9500, 9528, 9526])).
% 1.74/1.97 tff(9541,plain,
% 1.74/1.97 (inj_0(s(s(elem!1))) = inj_0(s(s(s(z))))),
% 1.74/1.97 inference(symmetry,[status(thm)],[2824])).
% 1.74/1.97 tff(9542,plain,
% 1.74/1.97 (s(elem!1) = s(s(z))),
% 1.74/1.97 inference(transitivity,[status(thm)],[206, 9541, 17])).
% 1.74/1.97 tff(9543,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2523, 9542])).
% 1.74/1.97 tff(9544,plain,((~(s(s(s(z))) = s(s(elem!1)))) | (s(elem!1) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(9545,plain,
% 1.74/1.97 (s(elem!1) = s(s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[9544, 2823])).
% 1.74/1.97 tff(9546,plain,
% 1.74/1.97 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[3120, 9545])).
% 1.74/1.97 tff(9547,plain,
% 1.74/1.97 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[4681, 9546])).
% 1.74/1.97 tff(9548,plain,
% 1.74/1.97 (s(s(z)) = s(elem!1)),
% 1.74/1.97 inference(transitivity,[status(thm)],[18, 2824, 118])).
% 1.74/1.97 tff(9549,plain,
% 1.74/1.97 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[9548])).
% 1.74/1.97 tff(9550,plain,
% 1.74/1.97 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 1.74/1.97 inference(symmetry,[status(thm)],[9549])).
% 1.74/1.97 tff(9551,plain,
% 1.74/1.97 (elem!1 = s(z)),
% 1.74/1.97 inference(transitivity,[status(thm)],[258, 9550, 126])).
% 1.74/1.97 tff(9552,plain,
% 1.74/1.97 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(elem!1))) = s(z))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[9551])).
% 1.74/1.97 tff(9553,plain,
% 1.74/1.97 ((s(s(s(elem!1))) = s(z)) <=> (s(s(s(elem!1))) = elem!1)),
% 1.74/1.97 inference(symmetry,[status(thm)],[9552])).
% 1.74/1.97 tff(9554,plain,
% 1.74/1.97 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[9553])).
% 1.74/1.97 tff(9555,plain,
% 1.74/1.97 (~(s(s(s(elem!1))) = elem!1)),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[171, 9554])).
% 1.74/1.97 tff(9556,plain,
% 1.74/1.97 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[9551])).
% 1.74/1.97 tff(9557,plain,
% 1.74/1.97 (r(s(z), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 1.74/1.97 inference(symmetry,[status(thm)],[9556])).
% 1.74/1.97 tff(9558,plain,
% 1.74/1.97 (r(elem!1, s(s(elem!1)))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[444, 9557])).
% 1.74/1.97 tff(9559,plain,
% 1.74/1.97 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[9546, 6281])).
% 1.74/1.97 tff(9560,plain,
% 1.74/1.97 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1206, 9559, 99, 335, 9546, 9558, 9555])).
% 1.74/1.97 tff(9561,plain,
% 1.74/1.97 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[571, 9560, 9547])).
% 1.74/1.97 tff(9562,plain,
% 1.74/1.97 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(elem!1)), s(elem!1))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[9548])).
% 1.74/1.97 tff(9563,plain,
% 1.74/1.97 (b(s(s(elem!1)), s(elem!1))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[2543, 9562])).
% 1.74/1.97 tff(9564,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(9565,plain,
% 1.74/1.97 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(9566,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[9565])).
% 1.74/1.97 tff(9567,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.74/1.97 inference(transitivity,[status(thm)],[9566, 9564])).
% 1.74/1.97 tff(9568,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(9569,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[9568, 9567])).
% 1.74/1.97 tff(9570,plain,
% 1.74/1.97 (~b(s(s(s(s(elem!1)))), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[9569, 319, 9563, 7301, 9561])).
% 1.74/1.97 tff(9571,plain,
% 1.74/1.97 (r(s(s(s(s(elem!1)))), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[3268, 51, 604, 9570])).
% 1.74/1.97 tff(9572,plain,
% 1.74/1.97 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[9548])).
% 1.74/1.97 tff(9573,plain,
% 1.74/1.97 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[9572])).
% 1.74/1.97 tff(9574,plain,
% 1.74/1.97 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[2140, 9573])).
% 1.74/1.97 tff(9575,plain,
% 1.74/1.97 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(z)), s(s(elem!1)))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[9542])).
% 1.74/1.97 tff(9576,plain,
% 1.74/1.97 (b(s(s(z)), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.74/1.97 inference(symmetry,[status(thm)],[9575])).
% 1.74/1.97 tff(9577,plain,
% 1.74/1.97 (b(s(elem!1), s(s(elem!1)))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[9480, 9576])).
% 1.74/1.97 tff(9578,plain,
% 1.74/1.97 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1839, 9561, 9563, 9577])).
% 1.74/1.97 tff(9579,plain,
% 1.74/1.97 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[595, 9578, 9574])).
% 1.74/1.97 tff(9580,plain,
% 1.74/1.97 (r(z, s(s(z))) <=> r(z, s(elem!1))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[9548])).
% 1.74/1.97 tff(9581,plain,
% 1.74/1.97 (r(z, s(elem!1))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[9501, 9580])).
% 1.74/1.97 tff(9582,plain,
% 1.74/1.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(9583,plain,
% 1.74/1.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(9584,plain,
% 1.74/1.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), z))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[9583, 9582])).
% 1.74/1.97 tff(9585,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[9584, 297, 9581, 9579, 9571])).
% 1.74/1.97 tff(9586,plain,((~(s(s(s(z))) = s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(9587,plain,
% 1.74/1.97 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[9586, 9500, 93, 9518, 9508])).
% 1.74/1.97 tff(9588,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[4066, 51, 2839, 4063, 7177])).
% 1.74/1.97 tff(9589,plain,(r(s(s(s(z))), s(s(elem!1))) | (s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(9590,plain,
% 1.74/1.97 (b(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[9589, 9587, 9540])).
% 1.74/1.97 tff(9591,plain,
% 1.74/1.97 ((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5550, 7778])).
% 1.74/1.97 tff(9592,plain,
% 1.74/1.97 (~b(s(s(s(z))), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[9591, 9590, 9504])).
% 1.74/1.97 tff(9593,plain,
% 1.74/1.97 (r(s(s(s(z))), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[4584, 9592])).
% 1.74/1.97 tff(9594,plain,
% 1.74/1.97 ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6685, 9501])).
% 1.74/1.97 tff(9595,plain,
% 1.74/1.98 (~r(s(s(s(z))), s(s(z)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[9594, 9593])).
% 1.74/1.98 tff(9596,plain,
% 1.74/1.98 (b(s(s(s(z))), s(s(z)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2920, 9595])).
% 1.74/1.98 tff(9597,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(9598,plain,
% 1.74/1.98 (((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(9599,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[9598])).
% 1.74/1.98 tff(9600,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[9599, 9597])).
% 1.74/1.98 tff(9601,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(9602,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[9601, 9600])).
% 1.74/1.98 tff(9603,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[9602, 319, 9508, 9480, 9596, 9590])).
% 1.74/1.98 tff(9604,plain,((~r(s(s(z)), s(z))) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(9605,plain,
% 1.74/1.98 (~r(s(s(z)), s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[9604, 58])).
% 1.74/1.98 tff(9606,plain,
% 1.74/1.98 (b(s(s(z)), s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[4102, 9605])).
% 1.74/1.98 tff(9607,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6735, 319, 3390, 9480, 817, 7778])).
% 1.74/1.98 tff(9608,plain,((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(9609,plain,
% 1.74/1.98 (~b(s(z), s(s(elem!1)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[9608, 9606])).
% 1.74/1.98 tff(9610,plain,
% 1.74/1.98 (r(s(z), s(s(elem!1)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1047, 9609])).
% 1.74/1.98 tff(9611,plain,
% 1.74/1.98 (~b(s(s(s(elem!1))), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[9223, 319, 7301, 7778, 116])).
% 1.74/1.98 tff(9612,plain,
% 1.74/1.98 (r(s(s(s(elem!1))), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1077, 51, 160, 9611])).
% 1.74/1.98 tff(9613,plain,
% 1.74/1.98 ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5662, 7778])).
% 1.74/1.98 tff(9614,plain,
% 1.74/1.98 ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[9613, 9480, 9501])).
% 1.74/1.98 tff(9615,plain,
% 1.74/1.98 (~b(z, s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[9614, 116])).
% 1.74/1.98 tff(9616,plain,
% 1.74/1.98 (r(z, s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1099, 9615])).
% 1.74/1.98 tff(9617,plain,
% 1.74/1.98 ((~r(s(z), s(s(z)))) | (~r(z, s(z)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[922, 9501])).
% 1.74/1.98 tff(9618,plain,
% 1.74/1.98 (~r(s(z), s(s(z)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[9617, 9616])).
% 1.74/1.98 tff(9619,plain,
% 1.74/1.98 (b(s(z), s(s(z)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[685, 9618])).
% 1.74/1.98 tff(9620,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(9621,plain,
% 1.74/1.98 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(9622,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[9621])).
% 1.74/1.98 tff(9623,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[9622, 9620])).
% 1.74/1.98 tff(9624,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(9625,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[9624, 9623])).
% 1.74/1.98 tff(9626,plain,
% 1.74/1.98 (~b(s(s(s(elem!1))), s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[9625, 319, 3390, 4562, 4787])).
% 1.74/1.98 tff(9627,plain,
% 1.74/1.98 (r(s(s(s(elem!1))), s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[4750, 9626])).
% 1.74/1.98 tff(9628,plain,
% 1.74/1.98 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5135, 9627, 444])).
% 1.74/1.98 tff(9629,plain,
% 1.74/1.98 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[348, 9628, 58])).
% 1.74/1.98 tff(9630,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5646, 319, 4562, 687, 496, 9629])).
% 1.74/1.98 tff(9631,plain,((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(9632,plain,
% 1.74/1.98 ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[9631, 7778])).
% 1.74/1.98 tff(9633,plain,
% 1.74/1.98 ((~b(s(s(s(elem!1))), s(s(z)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[9632, 9480])).
% 1.74/1.98 tff(9634,plain,
% 1.74/1.98 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[9633, 9619, 58, 9606, 9610])).
% 1.74/1.98 tff(9635,plain,
% 1.74/1.98 (r(s(s(s(elem!1))), s(s(z)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5676, 9634])).
% 1.74/1.98 tff(9636,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5652, 297, 9501, 9635, 9612])).
% 1.74/1.98 tff(9637,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(9638,plain,
% 1.74/1.98 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[9637, 58])).
% 1.74/1.98 tff(9639,plain,
% 1.74/1.98 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[348, 9638, 58])).
% 1.74/1.98 tff(9640,plain,
% 1.74/1.98 (~r(s(s(s(elem!1))), s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5135, 9639, 9610])).
% 1.74/1.98 tff(9641,plain,
% 1.74/1.98 (b(s(s(s(elem!1))), s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[4750, 9640])).
% 1.74/1.98 tff(9642,plain,
% 1.74/1.98 (~r(s(z), s(s(s(elem!1))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[9524, 297, 9610, 9639])).
% 1.74/1.98 tff(9643,plain,
% 1.74/1.98 (b(s(z), s(s(s(elem!1))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5817, 51, 9642, 5798])).
% 1.74/1.98 tff(9644,plain,
% 1.74/1.98 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[9539, 9643, 9639, 9641])).
% 1.74/1.98 tff(9645,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(9646,plain,
% 1.74/1.98 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(9647,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[9646])).
% 1.74/1.98 tff(9648,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[9647, 9645])).
% 1.74/1.98 tff(9649,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(9650,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[9649, 9648])).
% 1.74/1.98 tff(9651,plain,
% 1.74/1.98 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[9650, 319, 9606, 9641, 9643])).
% 1.74/1.98 tff(9652,plain,
% 1.74/1.98 (r(s(s(s(elem!1))), s(s(z)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5676, 9651])).
% 1.74/1.98 tff(9653,plain,
% 1.74/1.98 (~r(s(s(s(elem!1))), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5652, 297, 9501, 9652])).
% 1.74/1.98 tff(9654,plain,
% 1.74/1.98 (b(s(s(s(elem!1))), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1077, 51, 160, 9653])).
% 1.74/1.98 tff(9655,plain,
% 1.74/1.98 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[8305, 319, 9654, 7301, 7778])).
% 1.74/1.98 tff(9656,plain,
% 1.74/1.98 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2222, 51, 9655, 81])).
% 1.74/1.98 tff(9657,plain,
% 1.74/1.98 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(s(z)), s(z))) | (~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))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(9658,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~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)))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[9657])).
% 1.74/1.98 tff(9659,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), 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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~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))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[9658, 8532])).
% 1.74/1.98 tff(9660,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(9661,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~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)))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[9660, 9659])).
% 1.74/1.98 tff(9662,plain,
% 1.74/1.98 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[9661, 319, 9606, 9641, 9643])).
% 1.74/1.98 tff(9663,plain,
% 1.74/1.98 (r(s(s(z)), s(s(s(elem!1))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1571, 9662])).
% 1.74/1.98 tff(9664,plain,
% 1.74/1.98 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(9665,plain,
% 1.74/1.98 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(9666,plain,
% 1.74/1.98 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[9665, 9664])).
% 1.74/1.98 tff(9667,plain,
% 1.74/1.98 (~r(s(s(elem!1)), s(s(z)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[9666, 297, 9663, 9656])).
% 1.74/1.98 tff(9668,plain,
% 1.74/1.98 (b(s(s(elem!1)), s(s(z)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[9507, 9667])).
% 1.74/1.98 tff(9669,plain,
% 1.74/1.98 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[9586, 9668, 93, 9610, 9639])).
% 1.74/1.98 tff(9670,plain,
% 1.74/1.98 (b(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[9589, 9669, 9644])).
% 1.74/1.98 tff(9671,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(9672,plain,
% 1.74/1.98 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(9673,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[9672])).
% 1.74/1.98 tff(9674,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[9673, 9671])).
% 1.74/1.98 tff(9675,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(9676,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[9675, 9674])).
% 1.74/1.98 tff(9677,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[9676, 319, 3390, 2543, 3138, 4230])).
% 1.74/1.98 tff(9678,plain,((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(9679,plain,
% 1.74/1.98 (~b(s(s(s(z))), s(s(z)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[9678, 9606, 9668, 9670])).
% 1.74/1.98 tff(9680,plain,
% 1.74/1.98 (r(s(s(s(z))), s(s(z)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2920, 9679])).
% 1.74/1.98 tff(9681,plain,
% 1.74/1.98 (~r(s(s(s(z))), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[9594, 9680])).
% 1.74/1.98 tff(9682,plain,
% 1.74/1.98 (b(s(s(s(z))), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[4584, 9681])).
% 1.74/1.98 tff(9683,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(9684,plain,
% 1.74/1.98 (((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(9685,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[9684])).
% 1.74/1.98 tff(9686,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[9685, 9683])).
% 1.74/1.98 tff(9687,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(9688,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[9687, 9686])).
% 1.74/1.98 tff(9689,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[9688, 319, 9668, 7301, 9670, 9682])).
% 1.74/1.98 tff(9690,plain,(s(s(s(elem!1))) = s(s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(9691,plain,
% 1.74/1.98 (s(s(s(elem!1))) = elem!1),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5346, 9690])).
% 1.74/1.98 tff(9692,plain,
% 1.74/1.98 (elem!1 = s(s(s(elem!1)))),
% 1.74/1.98 inference(symmetry,[status(thm)],[9691])).
% 1.74/1.98 tff(9693,plain,
% 1.74/1.98 (elem!1 = s(s(elem!1))),
% 1.74/1.98 inference(transitivity,[status(thm)],[9692, 9690])).
% 1.74/1.98 tff(9694,plain,
% 1.74/1.98 ((elem!1 = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[9693])).
% 1.74/1.98 tff(9695,plain,
% 1.74/1.98 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 1.74/1.98 inference(transitivity,[status(thm)],[9694, 6121])).
% 1.74/1.98 tff(9696,plain,
% 1.74/1.98 ((elem!1 = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[9695, 6451])).
% 1.74/1.98 tff(9697,plain,
% 1.74/1.98 ((~(elem!1 = s(s(s(s(z)))))) <=> (~(s(s(elem!1)) = s(s(s(s(z))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[9696])).
% 1.74/1.98 tff(9698,plain,
% 1.74/1.98 (~(elem!1 = s(s(s(s(z)))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6472, 9690])).
% 1.74/1.98 tff(9699,plain,
% 1.74/1.98 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[9698, 9697])).
% 1.74/1.98 tff(9700,plain,
% 1.74/1.98 (b(s(elem!1), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[9348, 9690])).
% 1.74/1.98 tff(9701,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(9702,plain,
% 1.74/1.99 (((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(9703,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[9702])).
% 1.74/1.99 tff(9704,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)))),
% 1.74/1.99 inference(transitivity,[status(thm)],[9703, 9701])).
% 1.74/1.99 tff(9705,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(9706,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[9705, 9704])).
% 1.74/1.99 tff(9707,plain,
% 1.74/1.99 (~b(s(s(z)), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[9706, 319, 9480, 7301, 7778])).
% 1.74/1.99 tff(9708,plain,
% 1.74/1.99 ((~(s(elem!1) = s(s(z)))) | (~b(s(elem!1), z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[3187, 9707])).
% 1.74/1.99 tff(9709,plain,
% 1.74/1.99 (~(s(elem!1) = s(s(z)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[9708, 9700])).
% 1.74/1.99 tff(9710,plain,
% 1.74/1.99 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[9544, 9709])).
% 1.74/1.99 tff(9711,plain,
% 1.74/1.99 (b(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[9589, 7177, 9710])).
% 1.74/1.99 tff(9712,plain,
% 1.74/1.99 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[8181, 9711])).
% 1.74/1.99 tff(9713,plain,
% 1.74/1.99 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[6350, 9712, 9699])).
% 1.74/1.99 tff(9714,plain,
% 1.74/1.99 (~r(s(s(s(s(z)))), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2452, 9713, 9489])).
% 1.74/1.99 tff(9715,plain,
% 1.74/1.99 (b(s(s(s(s(z)))), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2461, 9714])).
% 1.74/1.99 tff(9716,plain,
% 1.74/1.99 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(elem!1)), s(z))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[9690])).
% 1.74/1.99 tff(9717,plain,
% 1.74/1.99 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 1.74/1.99 inference(symmetry,[status(thm)],[9716])).
% 1.74/1.99 tff(9718,plain,
% 1.74/1.99 (r(s(s(s(elem!1))), s(z))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[9489, 9717])).
% 1.74/1.99 tff(9719,plain,
% 1.74/1.99 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(elem!1)))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[9690])).
% 1.74/1.99 tff(9720,plain,
% 1.74/1.99 (b(z, s(s(elem!1))) <=> b(z, s(s(s(elem!1))))),
% 1.74/1.99 inference(symmetry,[status(thm)],[9719])).
% 1.74/1.99 tff(9721,plain,
% 1.74/1.99 (b(z, s(s(s(elem!1))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[7301, 9720])).
% 1.74/1.99 tff(9722,plain,
% 1.74/1.99 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(elem!1)))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[9690])).
% 1.74/1.99 tff(9723,plain,
% 1.74/1.99 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 1.74/1.99 inference(symmetry,[status(thm)],[9722])).
% 1.74/1.99 tff(9724,plain,
% 1.74/1.99 (b(s(s(z)), s(s(s(elem!1))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[9480, 9723])).
% 1.74/1.99 tff(9725,plain,
% 1.74/1.99 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[9690])).
% 1.74/1.99 tff(9726,plain,
% 1.74/1.99 (r(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[4878, 9725])).
% 1.74/1.99 tff(9727,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[7177, 9726])).
% 1.74/1.99 tff(9728,plain,((~r(s(s(s(z))), s(s(s(elem!1))))) | r(s(s(s(z))), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(9729,plain,
% 1.74/1.99 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[9728, 7177])).
% 1.74/1.99 tff(9730,plain,
% 1.74/1.99 (b(s(s(s(z))), s(s(s(elem!1))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[9533, 9729])).
% 1.74/1.99 tff(9731,plain,
% 1.74/1.99 ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[8322, 9501])).
% 1.74/1.99 tff(9732,plain,
% 1.74/1.99 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[9731, 9730, 9724, 9721])).
% 1.74/1.99 tff(9733,plain,
% 1.74/1.99 (r(s(s(s(elem!1))), s(s(z)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5676, 9732])).
% 1.74/1.99 tff(9734,plain,
% 1.74/1.99 (~r(s(z), s(s(z)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[4784, 9733, 9718])).
% 1.74/1.99 tff(9735,plain,
% 1.74/1.99 (b(s(z), s(s(z)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[685, 9734])).
% 1.74/1.99 tff(9736,plain,
% 1.74/1.99 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(elem!1)), s(s(z)))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[9690])).
% 1.74/1.99 tff(9737,plain,
% 1.74/1.99 (r(s(s(elem!1)), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 1.74/1.99 inference(symmetry,[status(thm)],[9736])).
% 1.74/1.99 tff(9738,plain,
% 1.74/1.99 ((~r(s(s(elem!1)), s(s(z)))) <=> (~r(s(s(s(elem!1))), s(s(z))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[9737])).
% 1.74/1.99 tff(9739,plain,
% 1.74/1.99 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[9505, 9738])).
% 1.74/1.99 tff(9740,plain,
% 1.74/1.99 (b(s(s(s(elem!1))), s(s(z)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5676, 9739])).
% 1.74/1.99 tff(9741,plain,
% 1.74/1.99 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[9731, 9740, 9724, 9721])).
% 1.74/1.99 tff(9742,plain,
% 1.74/1.99 (r(s(s(s(z))), s(s(s(elem!1))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[9533, 9741])).
% 1.74/1.99 tff(9743,plain,
% 1.74/1.99 (r(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[9742, 9725])).
% 1.74/1.99 tff(9744,plain,
% 1.74/1.99 (r(s(s(z)), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[663, 51, 28, 9707])).
% 1.74/1.99 tff(9745,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[694, 297, 666, 2511, 9744])).
% 1.74/1.99 tff(9746,plain,((~r(s(z), z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(9747,plain,
% 1.74/1.99 (~r(s(z), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[9746, 2511])).
% 1.74/1.99 tff(9748,plain,
% 1.74/1.99 (b(s(z), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[67, 9747])).
% 1.74/1.99 tff(9749,plain,
% 1.74/1.99 (~r(s(s(s(s(z)))), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[3009, 3004, 2511])).
% 1.74/1.99 tff(9750,plain,
% 1.74/1.99 (b(s(s(s(s(z)))), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2461, 9749])).
% 1.74/1.99 tff(9751,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[6825, 297, 732, 2467, 3004])).
% 1.74/1.99 tff(9752,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(9753,plain,
% 1.74/1.99 ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[9752, 9501])).
% 1.74/1.99 tff(9754,plain,
% 1.74/1.99 (~r(s(s(s(s(z)))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[9753, 3004])).
% 1.74/1.99 tff(9755,plain,
% 1.74/1.99 (b(s(s(s(s(z)))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2482, 9754])).
% 1.74/1.99 tff(9756,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(9757,plain,
% 1.74/1.99 (((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(9758,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[9757])).
% 1.74/1.99 tff(9759,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(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(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.74/1.99 inference(transitivity,[status(thm)],[9758, 9756])).
% 1.74/1.99 tff(9760,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(9761,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[9760, 9759])).
% 1.74/1.99 tff(9762,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[9761, 319, 9504, 7301, 7778, 2493, 9755, 9750])).
% 1.74/1.99 tff(9763,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(9764,plain,
% 1.74/1.99 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[9763, 2493, 2511])).
% 1.74/1.99 tff(9765,plain,
% 1.74/1.99 (b(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[6174, 9764])).
% 1.74/1.99 tff(9766,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[6964, 319, 2543, 9480, 6158, 6352])).
% 1.74/1.99 tff(9767,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(9768,plain,
% 1.74/1.99 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[9767, 9765, 9508])).
% 1.74/1.99 tff(9769,plain,
% 1.74/1.99 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[6350, 9768, 9699])).
% 1.74/1.99 tff(9770,plain,
% 1.74/1.99 (~r(s(s(s(s(z)))), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2452, 9769, 9489])).
% 1.74/1.99 tff(9771,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(9772,plain,
% 1.74/1.99 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(9773,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[9772])).
% 1.74/1.99 tff(9774,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[9773, 9771])).
% 1.74/1.99 tff(9775,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(9776,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[9775, 9774])).
% 1.74/1.99 tff(9777,plain,
% 1.74/1.99 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[9776, 319, 2493, 3154, 2965])).
% 1.74/1.99 tff(9778,plain,
% 1.74/1.99 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2281, 9777])).
% 1.74/1.99 tff(9779,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[7223, 297, 9778, 2443, 6881])).
% 1.74/1.99 tff(9780,plain,((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(9781,plain,
% 1.74/1.99 (~b(s(s(s(s(z)))), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[9780, 9769, 6881, 2493, 9530])).
% 1.74/1.99 tff(9782,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2461, 9781, 9770])).
% 1.74/1.99 tff(9783,plain,((~b(s(z), z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(9784,plain,
% 1.74/1.99 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[9783, 9748, 2511])).
% 1.74/1.99 tff(9785,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[9784, 9743])).
% 1.74/1.99 tff(9786,plain,(~r(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(9787,plain,
% 1.74/1.99 (b(s(s(z)), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[4102, 9786])).
% 1.74/1.99 tff(9788,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(9789,plain,
% 1.74/1.99 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(9790,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[9789])).
% 1.74/1.99 tff(9791,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[9790, 9788])).
% 1.74/1.99 tff(9792,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(9793,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[9792, 9791])).
% 1.74/1.99 tff(9794,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[9793, 319, 9787, 4787, 3154, 6158])).
% 1.74/1.99 tff(9795,plain,((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(9796,plain,
% 1.74/1.99 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[9795, 9735, 9715])).
% 1.74/1.99 tff(9797,plain,
% 1.74/1.99 (r(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[6174, 9796])).
% 1.74/1.99 tff(9798,plain,
% 1.74/1.99 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[7059, 9532])).
% 1.74/1.99 tff(9799,plain,
% 1.74/1.99 (~r(s(s(s(z))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[6685, 889, 732])).
% 1.74/1.99 tff(9800,plain,
% 1.74/1.99 (b(s(s(s(z))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[4584, 9799])).
% 1.74/1.99 tff(9801,plain,
% 1.74/1.99 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(9802,plain,
% 1.74/1.99 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(9803,plain,
% 1.74/1.99 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[9802])).
% 1.74/1.99 tff(9804,plain,
% 1.74/1.99 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[9803, 9801])).
% 1.74/1.99 tff(9805,plain,
% 1.74/1.99 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(9806,plain,
% 1.74/1.99 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[9805, 9804])).
% 1.74/1.99 tff(9807,plain,
% 1.74/1.99 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[9806, 297, 889, 4775])).
% 1.74/1.99 tff(9808,plain,
% 1.74/1.99 (b(s(s(s(elem!1))), s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[3600, 9807, 3521])).
% 1.74/1.99 tff(9809,plain,
% 1.74/1.99 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(9810,plain,
% 1.74/1.99 (((~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(9811,plain,
% 1.74/1.99 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[9810])).
% 1.74/1.99 tff(9812,plain,
% 1.74/1.99 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[9811, 9809])).
% 1.74/1.99 tff(9813,plain,
% 1.74/1.99 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(9814,plain,
% 1.74/1.99 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[9813, 9812])).
% 1.74/1.99 tff(9815,plain,
% 1.74/1.99 (~r(z, s(s(s(elem!1))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[9814, 297, 732, 4775])).
% 1.74/1.99 tff(9816,plain,
% 1.74/1.99 (b(z, s(s(s(elem!1))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[416, 9815])).
% 1.74/1.99 tff(9817,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(elem!1))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(9818,plain,
% 1.74/1.99 (((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(elem!1))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(9819,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(elem!1)))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[9818])).
% 1.74/1.99 tff(9820,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(elem!1))))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[9819, 9817])).
% 1.74/2.00 tff(9821,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(9822,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(elem!1)))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[9821, 9820])).
% 1.74/2.00 tff(9823,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[9822, 319, 4561, 9816, 9808, 9800])).
% 1.74/2.00 tff(9824,plain,((~r(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(9825,plain,
% 1.74/2.00 ((~r(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[9824, 9501, 9798])).
% 1.74/2.00 tff(9826,plain,
% 1.74/2.00 (~r(s(s(s(z))), s(s(z)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[9825, 9733, 9730])).
% 1.74/2.00 tff(9827,plain,
% 1.74/2.00 (b(s(s(s(z))), s(s(z)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2920, 9826])).
% 1.74/2.00 tff(9828,plain,
% 1.74/2.00 (~b(s(s(elem!1)), s(s(z)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[9678, 9827, 9787, 9711])).
% 1.74/2.00 tff(9829,plain,
% 1.74/2.00 (r(s(s(elem!1)), s(s(z)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[9507, 9828])).
% 1.74/2.00 tff(9830,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[6318, 9829, 9797, 9713])).
% 1.74/2.00 tff(9831,plain,(r(s(s(s(z))), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(9832,plain,
% 1.74/2.00 (~r(s(s(s(z))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[6886, 9831, 9489])).
% 1.74/2.00 tff(9833,plain,
% 1.74/2.00 (b(s(s(s(z))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4549, 9832])).
% 1.74/2.00 tff(9834,plain,
% 1.74/2.00 (~b(s(z), s(s(elem!1)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[9608, 9787])).
% 1.74/2.00 tff(9835,plain,
% 1.74/2.00 (r(s(z), s(s(elem!1)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1047, 9834])).
% 1.74/2.00 tff(9836,plain,
% 1.74/2.00 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(9837,plain,
% 1.74/2.00 (((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(9838,plain,
% 1.74/2.00 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z)))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[9837])).
% 1.74/2.00 tff(9839,plain,
% 1.74/2.00 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[9838, 9836])).
% 1.74/2.00 tff(9840,plain,
% 1.74/2.00 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(9841,plain,
% 1.74/2.00 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z)))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[9840, 9839])).
% 1.74/2.00 tff(9842,plain,
% 1.74/2.00 (~r(s(z), s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[9841, 297, 9835, 9831])).
% 1.74/2.00 tff(9843,assumption,(~r(s(z), s(s(s(z))))), introduced(assumption)).
% 1.74/2.00 tff(9844,assumption,(~b(s(z), s(s(s(z))))), introduced(assumption)).
% 1.74/2.00 tff(9845,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[6558, 51, 9844, 9843, 32])).
% 1.74/2.00 tff(9846,plain,(b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(9847,plain,
% 1.74/2.00 (b(s(z), s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[9846, 9842])).
% 1.74/2.00 tff(9848,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(9849,plain,
% 1.74/2.00 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(9850,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z)))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[9849])).
% 1.74/2.00 tff(9851,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[9850, 9848])).
% 1.74/2.00 tff(9852,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(9853,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z)))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[9852, 9851])).
% 1.74/2.00 tff(9854,plain,
% 1.74/2.00 (~b(s(s(s(z))), s(s(z)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[9853, 319, 9787, 9847, 9833])).
% 1.74/2.00 tff(9855,plain,
% 1.74/2.00 ((~r(z, s(s(z)))) | b(s(s(s(z))), s(s(z))) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4087, 7778, 7301])).
% 1.74/2.00 tff(9856,plain,
% 1.74/2.00 (b(s(s(s(z))), s(s(z))) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[9855, 9501])).
% 1.74/2.00 tff(9857,plain,
% 1.74/2.00 (~r(s(s(elem!1)), s(s(z)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[9856, 9854, 9710])).
% 1.74/2.00 tff(9858,plain,
% 1.74/2.00 (b(s(s(elem!1)), s(s(z)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[9507, 9857])).
% 1.74/2.00 tff(9859,plain,
% 1.74/2.00 (r(s(s(s(z))), s(s(z)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2920, 9854])).
% 1.74/2.00 tff(9860,plain,
% 1.74/2.00 (~r(s(s(s(z))), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[9594, 9859])).
% 1.74/2.00 tff(9861,plain,
% 1.74/2.00 (b(s(s(s(z))), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4584, 9860])).
% 1.74/2.00 tff(9862,plain,
% 1.74/2.00 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[9690])).
% 1.74/2.00 tff(9863,plain,
% 1.74/2.00 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.74/2.00 inference(transitivity,[status(thm)],[9862, 9690])).
% 1.74/2.00 tff(9864,plain,
% 1.74/2.00 (r(s(s(s(s(elem!1)))), s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[9863])).
% 1.74/2.00 tff(9865,plain,
% 1.74/2.00 ((s(s(elem!1)) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 1.74/2.00 inference(commutativity,[status(thm)],[])).
% 1.74/2.00 tff(9866,plain,
% 1.74/2.00 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[9863])).
% 1.74/2.00 tff(9867,plain,
% 1.74/2.00 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 1.74/2.00 inference(transitivity,[status(thm)],[9866, 9865])).
% 1.74/2.00 tff(9868,plain,
% 1.74/2.00 ((s(s(s(z))) = s(s(elem!1))) <=> (s(s(s(s(elem!1)))) = s(s(s(z))))),
% 1.74/2.00 inference(symmetry,[status(thm)],[9867])).
% 1.74/2.00 tff(9869,plain,
% 1.74/2.00 ((~(s(s(s(z))) = s(s(elem!1)))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(z)))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[9868])).
% 1.74/2.00 tff(9870,plain,
% 1.74/2.00 (~(s(s(s(s(elem!1)))) = s(s(s(z))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[9710, 9869])).
% 1.74/2.00 tff(9871,plain,
% 1.74/2.00 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[9863])).
% 1.74/2.00 tff(9872,plain,
% 1.74/2.00 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.74/2.00 inference(symmetry,[status(thm)],[9871])).
% 1.74/2.00 tff(9873,plain,
% 1.74/2.00 ((~b(s(s(elem!1)), s(s(s(z))))) <=> (~b(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[9872])).
% 1.74/2.00 tff(9874,plain,
% 1.74/2.00 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[8378, 319, 7301, 7778, 9861])).
% 1.74/2.00 tff(9875,plain,
% 1.74/2.00 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[9874, 9873])).
% 1.74/2.00 tff(9876,plain,
% 1.74/2.00 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1346, 9875, 9870])).
% 1.74/2.00 tff(9877,plain,
% 1.74/2.00 (r(s(s(elem!1)), s(s(s(z))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[9876, 9864])).
% 1.74/2.00 tff(9878,plain,
% 1.74/2.00 ((~b(s(s(s(s(z)))), z)) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[8404, 7301])).
% 1.74/2.00 tff(9879,plain,
% 1.74/2.00 (~b(s(s(s(s(z)))), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[9878, 9877, 9690, 9861])).
% 1.74/2.00 tff(9880,plain,
% 1.74/2.00 (r(s(s(s(s(z)))), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2482, 9879])).
% 1.74/2.00 tff(9881,plain,
% 1.74/2.00 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[9753, 9880])).
% 1.74/2.00 tff(9882,plain,
% 1.74/2.00 (b(s(s(s(s(z)))), s(s(z)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[6174, 9881])).
% 1.74/2.00 tff(9883,plain,
% 1.74/2.00 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[6812, 9882, 9787, 9858])).
% 1.74/2.00 tff(9884,plain,
% 1.74/2.00 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[6350, 9883, 9699])).
% 1.74/2.00 tff(9885,plain,
% 1.74/2.00 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(9886,plain,
% 1.74/2.00 (((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(9887,plain,
% 1.74/2.00 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[9886])).
% 1.74/2.00 tff(9888,plain,
% 1.74/2.00 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[9887, 9885])).
% 1.74/2.00 tff(9889,plain,
% 1.74/2.00 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(9890,plain,
% 1.74/2.00 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[9889, 9888])).
% 1.74/2.00 tff(9891,plain,
% 1.74/2.00 (~r(z, s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[9890, 297, 9501, 9859])).
% 1.74/2.00 tff(9892,plain,
% 1.74/2.00 ((z = s(s(s(z)))) | b(z, s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[6714, 51, 9891])).
% 1.74/2.00 tff(9893,plain,
% 1.74/2.00 (b(z, s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[9892, 6704])).
% 1.74/2.00 tff(9894,plain,
% 1.74/2.00 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z)))) <=> ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(9895,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(z)))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[9894])).
% 1.74/2.00 tff(9896,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(z))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[9895, 7109])).
% 1.74/2.00 tff(9897,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(9898,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z)))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[9897, 9896])).
% 1.74/2.00 tff(9899,plain,
% 1.74/2.00 (~b(z, s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[9898, 319, 9847, 9893, 9833])).
% 1.74/2.01 tff(9900,plain,
% 1.74/2.01 (r(z, s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[1099, 9899])).
% 1.74/2.01 tff(9901,plain,
% 1.74/2.01 (~r(s(z), s(s(z)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[9617, 9900])).
% 1.74/2.01 tff(9902,plain,
% 1.74/2.01 (b(s(z), s(s(z)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[685, 9901])).
% 1.74/2.01 tff(9903,plain,
% 1.74/2.01 (~b(s(s(s(s(z)))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[9795, 9882, 9902])).
% 1.74/2.01 tff(9904,plain,
% 1.74/2.01 (r(s(s(s(s(z)))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2461, 9903])).
% 1.74/2.01 tff(9905,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2452, 9904, 9884, 9489])).
% 1.74/2.01 % SZS output end Proof
% 1.74/2.01 % E exiting
%------------------------------------------------------------------------------